Maths-
General
Easy

Question

𝑉𝑒𝑟𝑖𝑓𝑦 open parentheses fraction numerator negative 7 over denominator 11 end fraction plus fraction numerator 2 over denominator negative 5 end fraction close parentheses plus fraction numerator negative 13 over denominator 22 end fraction equals fraction numerator negative 7 over denominator 11 end fraction plus open parentheses fraction numerator 2 over denominator negative 5 end fraction plus fraction numerator negative 13 over denominator 22 end fraction close parentheses

Hint:

Solve the LHS part and RHS part separately and then compare.

The correct answer is: verified.


    To verify open parentheses fraction numerator negative 7 over denominator 11 end fraction plus fraction numerator 2 over denominator negative 5 end fraction close parentheses plus fraction numerator negative 13 over denominator 22 end fraction equals fraction numerator negative 7 over denominator 11 end fraction plus open parentheses fraction numerator 2 over denominator negative 5 end fraction plus fraction numerator negative 13 over denominator 22 end fraction close parentheses
    Express the rational numbers with positive denominator by multiplying with -1.

    Here, fraction numerator 2 over denominator negative 5 end fraction equals fraction numerator 2 cross times negative 1 over denominator negative 5 cross times negative 1 end fraction equals fraction numerator negative 2 over denominator 5 end fraction
    Consider the LHS part, we have open parentheses fraction numerator negative 7 over denominator 11 end fraction plus fraction numerator negative 2 over denominator 5 end fraction close parentheses plus fraction numerator negative 13 over denominator 22 end fraction…(i)
    Determine the LCM of the denominators of rational numbers inside the brackets.
    LCM of 11 and 5 = 55
    On multiplying fraction numerator negative 7 over denominator 11 end fraction with 5, we get fraction numerator negative 7 cross times 5 over denominator 11 cross times 5 end fraction equals fraction numerator negative 35 over denominator 55 end fraction
    On multiplying fraction numerator negative 2 over denominator 5 end fraction with 11, we get fraction numerator negative 2 cross times 11 over denominator 5 cross times 11 end fraction equals fraction numerator negative 22 over denominator 55 end fraction
    On adding, we get fraction numerator negative 35 over denominator 55 end fraction plus fraction numerator negative 22 over denominator 55 end fraction equals fraction numerator negative 57 over denominator 55 end fraction
    On substituting this in (i), we get fraction numerator negative 57 over denominator 55 end fraction plus fraction numerator negative 13 over denominator 22 end fraction
    Determine the LCM of the denominators of rational numbers.
    LCM of 55 and 22 = 110
    On multiplying fraction numerator negative 57 over denominator 55 end fraction with 2, we get fraction numerator negative 57 cross times 2 over denominator 55 cross times 2 end fraction equals fraction numerator negative 114 over denominator 110 end fraction
    On multiplying fraction numerator negative 13 over denominator 22 end fraction with 5, we get fraction numerator negative 13 cross times 5 over denominator 22 cross times 5 end fraction equals fraction numerator negative 65 over denominator 110 end fraction
    On adding, we get fraction numerator negative 114 over denominator 110 end fraction plus fraction numerator negative 65 over denominator 110 end fraction equals fraction numerator negative 179 over denominator 110 end fraction
    Thus we have LHS to be open parentheses fraction numerator negative 7 over denominator 11 end fraction plus fraction numerator negative 2 over denominator 5 end fraction close parentheses plus fraction numerator negative 13 over denominator 22 end fraction equals fraction numerator negative 179 over denominator 110 end fraction
    Consider the RHS part, we have fraction numerator negative 7 over denominator 11 end fraction plus open parentheses fraction numerator negative 2 over denominator 5 end fraction plus fraction numerator negative 13 over denominator 22 end fraction close parentheses…(ii)
    Determine the LCM of the denominators of rational numbers inside the brackets.
    LCM of 5 and 22 = 110
    On multiplying fraction numerator negative 2 over denominator 5 end fraction with 22, we get fraction numerator negative 2 cross times 22 over denominator 5 cross times 22 end fraction equals fraction numerator negative 44 over denominator 110 end fraction
    On multiplying fraction numerator negative 13 over denominator 22 end fraction with 5, we get fraction numerator negative 13 cross times 5 over denominator 22 cross times 5 end fraction equals fraction numerator negative 65 over denominator 110 end fraction
    On adding, we get fraction numerator negative 44 over denominator 110 end fraction plus fraction numerator negative 65 over denominator 110 end fraction equals fraction numerator negative 109 over denominator 110 end fraction
    On substituting this in (ii), we get fraction numerator negative 7 over denominator 11 end fraction plus fraction numerator negative 109 over denominator 110 end fraction
    Determine the LCM of the denominators of rational numbers.
    LCM of 11 and 110 = 110
    On multiplying fraction numerator negative 7 over denominator 11 end fraction with 10, we get fraction numerator negative 7 cross times 10 over denominator 11 cross times 10 end fraction equals fraction numerator negative 70 over denominator 110 end fraction
    On multiplying fraction numerator negative 109 over denominator 110 end fraction with 1, we get fraction numerator negative 109 cross times 1 over denominator 110 cross times 1 end fraction equals fraction numerator negative 109 over denominator 110 end fraction
    On adding, we get fraction numerator negative 70 over denominator 110 end fraction plus fraction numerator negative 109 over denominator 110 end fraction equals fraction numerator negative 179 over denominator 110 end fraction
    Thus we have RHS to be fraction numerator negative 7 over denominator 11 end fraction plus open parentheses fraction numerator negative 2 over denominator 5 end fraction plus fraction numerator negative 13 over denominator 22 end fraction close parentheses equals fraction numerator negative 179 over denominator 110 end fraction
    So we get LHS = RHS = fraction numerator negative 179 over denominator 110 end fraction
    Hence verified.

    Related Questions to study

    General
    Maths-

    Verify fraction numerator negative 12 over denominator 5 end fraction plus 2 over 7 equals 2 over 7 plus fraction numerator negative 12 over denominator 5 end fraction

    To verify fraction numerator negative 12 over denominator 5 end fraction plus 2 over 7 equals 2 over 7 plus fraction numerator negative 12 over denominator 5 end fraction
    On LHS part, we have fraction numerator negative 12 over denominator 5 end fraction plus 2 over 7
    Here by taking LCM of denominators 5 and 7, we get it as 35.
    On multiplying fraction numerator negative 12 over denominator 5 end fraction with 7, we get fraction numerator negative 12 cross times 7 over denominator 5 cross times 7 end fraction equals fraction numerator negative 84 over denominator 35 end fraction
    On multiplying 2 over 7 with 5, we get fraction numerator 2 cross times 5 over denominator 7 cross times 5 end fraction equals 10 over 35
    On adding, we get fraction numerator negative 12 over denominator 5 end fraction plus 2 over 7 equals fraction numerator negative 84 over denominator 35 end fraction plus 10 over 35 equals fraction numerator negative 74 over denominator 35 end fraction…(i)
    On RHS part, we have 2 over 7 plus fraction numerator negative 12 over denominator 5 end fraction
    Here by taking LCM of denominators 7 and 5, we get it as 35.
    On multiplying 2 over 7 with 5, we get fraction numerator 2 cross times 5 over denominator 7 cross times 5 end fraction equals 10 over 35
    On multiplying fraction numerator negative 12 over denominator 5 end fraction with 7, we get fraction numerator negative 12 cross times 7 over denominator 5 cross times 7 end fraction equals fraction numerator negative 84 over denominator 35 end fraction
    On adding, we get 2 over 7 plus fraction numerator negative 12 over denominator 5 end fraction equals 10 over 35 plus fraction numerator negative 84 over denominator 35 end fraction equals fraction numerator negative 74 over denominator 35 end fraction…(ii)
    We have LHS = RHS.
    Hence verified.

    Verify fraction numerator negative 12 over denominator 5 end fraction plus 2 over 7 equals 2 over 7 plus fraction numerator negative 12 over denominator 5 end fraction

    Maths-General
    To verify fraction numerator negative 12 over denominator 5 end fraction plus 2 over 7 equals 2 over 7 plus fraction numerator negative 12 over denominator 5 end fraction
    On LHS part, we have fraction numerator negative 12 over denominator 5 end fraction plus 2 over 7
    Here by taking LCM of denominators 5 and 7, we get it as 35.
    On multiplying fraction numerator negative 12 over denominator 5 end fraction with 7, we get fraction numerator negative 12 cross times 7 over denominator 5 cross times 7 end fraction equals fraction numerator negative 84 over denominator 35 end fraction
    On multiplying 2 over 7 with 5, we get fraction numerator 2 cross times 5 over denominator 7 cross times 5 end fraction equals 10 over 35
    On adding, we get fraction numerator negative 12 over denominator 5 end fraction plus 2 over 7 equals fraction numerator negative 84 over denominator 35 end fraction plus 10 over 35 equals fraction numerator negative 74 over denominator 35 end fraction…(i)
    On RHS part, we have 2 over 7 plus fraction numerator negative 12 over denominator 5 end fraction
    Here by taking LCM of denominators 7 and 5, we get it as 35.
    On multiplying 2 over 7 with 5, we get fraction numerator 2 cross times 5 over denominator 7 cross times 5 end fraction equals 10 over 35
    On multiplying fraction numerator negative 12 over denominator 5 end fraction with 7, we get fraction numerator negative 12 cross times 7 over denominator 5 cross times 7 end fraction equals fraction numerator negative 84 over denominator 35 end fraction
    On adding, we get 2 over 7 plus fraction numerator negative 12 over denominator 5 end fraction equals 10 over 35 plus fraction numerator negative 84 over denominator 35 end fraction equals fraction numerator negative 74 over denominator 35 end fraction…(ii)
    We have LHS = RHS.
    Hence verified.
    General
    Maths-

    Find the perimeter and area of a semicircle whose radius is 14 cm.

    It is given that radius = 14 cm
    Perimeter of semi – circle  = fraction numerator text  perimeter of circle  end text over denominator 2 end fraction equals fraction numerator 2 pi straight r over denominator 2 end fraction
    straight pi r  =  22 over 7 ×14
    = 44 cm
    Area of semi – circle =  fraction numerator text  area of circle  end text over denominator 2 end fraction  = fraction numerator pi r squared over denominator 2 end fraction
    =  1 half ×  22 over 7 × 142
    =  308 cm2

    Find the perimeter and area of a semicircle whose radius is 14 cm.

    Maths-General
    It is given that radius = 14 cm
    Perimeter of semi – circle  = fraction numerator text  perimeter of circle  end text over denominator 2 end fraction equals fraction numerator 2 pi straight r over denominator 2 end fraction
    straight pi r  =  22 over 7 ×14
    = 44 cm
    Area of semi – circle =  fraction numerator text  area of circle  end text over denominator 2 end fraction  = fraction numerator pi r squared over denominator 2 end fraction
    =  1 half ×  22 over 7 × 142
    =  308 cm2
    General
    Maths-

    The diameter of a circular park is 98 m. Find the cost of fencing it at  Rs 4 per metre.

    It is given that diameter of the circular park = 98 m
    rightwards double arrowRadius  = fraction numerator d i a m e t e r over denominator 2 end fraction
    98 over 2  =  49 m
    Perimeter of the park = 2 straight pi r
    = 2 × 22 over 7 × 49
    = 308 m
    Now, Cost of fencing per metre = Rs. 4
    Cost of fencing 308 metre = Rs. 4 × 308
    = Rs. 1232

    The diameter of a circular park is 98 m. Find the cost of fencing it at  Rs 4 per metre.

    Maths-General
    It is given that diameter of the circular park = 98 m
    rightwards double arrowRadius  = fraction numerator d i a m e t e r over denominator 2 end fraction
    98 over 2  =  49 m
    Perimeter of the park = 2 straight pi r
    = 2 × 22 over 7 × 49
    = 308 m
    Now, Cost of fencing per metre = Rs. 4
    Cost of fencing 308 metre = Rs. 4 × 308
    = Rs. 1232
    parallel
    General
    Maths-

    The circumference of a circular park is 176 m. Find the area of the park.

    It is given that Circumference of the circular park = 176 m
    rightwards double arrowstraight pi r  =  176
    rightwards double arrow2 (22 over 7) r = 176
    rightwards double arrowr = fraction numerator 176 cross times 7 over denominator 2 cross times 22 end fraction
    rightwards double arrowr = 28 m
    Area of the park = straight pi r2
    22 over 7 × 282
    =  2464 cm2

    The circumference of a circular park is 176 m. Find the area of the park.

    Maths-General
    It is given that Circumference of the circular park = 176 m
    rightwards double arrowstraight pi r  =  176
    rightwards double arrow2 (22 over 7) r = 176
    rightwards double arrowr = fraction numerator 176 cross times 7 over denominator 2 cross times 22 end fraction
    rightwards double arrowr = 28 m
    Area of the park = straight pi r2
    22 over 7 × 282
    =  2464 cm2
    General
    Maths-

    A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent into the form of a circle, find the area of the circle.

    It is given that Area of  Square  =  121 cm2
    rightwards double arrow(side)= 121 cm
    rightwards double arrowside = square root of 121 = 11 cm
    Perimeter of square = 4 × side
    = 4 × 11 = 44 cm
    Now, since same wire is used to make circle it implies that perimeter of square which is the length of the wire will be equal to perimeter of the circle.
    Perimeter of circle  =  Perimeter of squar
    straight pi r =    44
    2 (22 over 7) r = 44
    r = 7  cm
    Now, Area of circle  = straight pi r2
    = 22 over 7 × 72  =  22 × 7 = 154 cm2

    A copper wire when bent in the form of a square encloses an area of 121 cm2. If the same wire is bent into the form of a circle, find the area of the circle.

    Maths-General
    It is given that Area of  Square  =  121 cm2
    rightwards double arrow(side)= 121 cm
    rightwards double arrowside = square root of 121 = 11 cm
    Perimeter of square = 4 × side
    = 4 × 11 = 44 cm
    Now, since same wire is used to make circle it implies that perimeter of square which is the length of the wire will be equal to perimeter of the circle.
    Perimeter of circle  =  Perimeter of squar
    straight pi r =    44
    2 (22 over 7) r = 44
    r = 7  cm
    Now, Area of circle  = straight pi r2
    = 22 over 7 × 72  =  22 × 7 = 154 cm2
    General
    Maths-

    Find the area of a circle whose radius is 14 cm.

    It is given that radius of the circle = 14 cm
    Area of circle =  straight pi r2
    straight pi (14)2
    22 over 7 × 14 × 14
    = 22 × 2 × 14
    = 616 cm2

    Find the area of a circle whose radius is 14 cm.

    Maths-General
    It is given that radius of the circle = 14 cm
    Area of circle =  straight pi r2
    straight pi (14)2
    22 over 7 × 14 × 14
    = 22 × 2 × 14
    = 616 cm2
    parallel
    General
    Maths-

    Find the circumference of the given circle.

    As we can see in the figure, Radius of the circle = 7
    Circumference of circle = 2 straight pi
    =  2 × 22 over 7 × 7
    = 44 units

    Find the circumference of the given circle.

    Maths-General
    As we can see in the figure, Radius of the circle = 7
    Circumference of circle = 2 straight pi
    =  2 × 22 over 7 × 7
    = 44 units
    General
    Maths-

    Evaluate 3 over 5 plus 7 over 3 plus fraction numerator negative 11 over denominator 5 end fraction plus fraction numerator negative 2 over denominator 3 end fraction

    To find: 3 over 5 plus 7 over 3 plus fraction numerator negative 11 over denominator 5 end fraction plus fraction numerator negative 2 over denominator 3 end fraction
    Here by taking the LCM of denominators 5 and 3, we have 15 as LCM.
    On multiplying 3 over 5 with 3, we get fraction numerator 3 cross times 3 over denominator 5 cross times 3 end fraction equals 9 over 15
    On multiplying 7 over 3 with 5, we get fraction numerator 7 cross times 5 over denominator 3 cross times 5 end fraction equals 35 over 15
    On multiplying fraction numerator negative 11 over denominator 5 end fraction with 3, we get fraction numerator negative 11 cross times 3 over denominator 5 cross times 3 end fraction equals fraction numerator negative 33 over denominator 15 end fraction
    On multiplying fraction numerator negative 2 over denominator 3 end fraction with 5, we get fraction numerator negative 2 cross times 5 over denominator 3 cross times 5 end fraction equals fraction numerator negative 10 over denominator 15 end fraction
    Now we have 4 fractions with the same denominators.
    On adding, we have 9 over 15 plus 35 over 15 plus fraction numerator negative 33 over denominator 15 end fraction plus fraction numerator negative 10 over denominator 15 end fraction equals 1 over 15
    Hence 3 over 5 plus 7 over 3 plus fraction numerator negative 11 over denominator 5 end fraction plus fraction numerator negative 2 over denominator 3 end fraction equals 1 over 15

    Evaluate 3 over 5 plus 7 over 3 plus fraction numerator negative 11 over denominator 5 end fraction plus fraction numerator negative 2 over denominator 3 end fraction

    Maths-General
    To find: 3 over 5 plus 7 over 3 plus fraction numerator negative 11 over denominator 5 end fraction plus fraction numerator negative 2 over denominator 3 end fraction
    Here by taking the LCM of denominators 5 and 3, we have 15 as LCM.
    On multiplying 3 over 5 with 3, we get fraction numerator 3 cross times 3 over denominator 5 cross times 3 end fraction equals 9 over 15
    On multiplying 7 over 3 with 5, we get fraction numerator 7 cross times 5 over denominator 3 cross times 5 end fraction equals 35 over 15
    On multiplying fraction numerator negative 11 over denominator 5 end fraction with 3, we get fraction numerator negative 11 cross times 3 over denominator 5 cross times 3 end fraction equals fraction numerator negative 33 over denominator 15 end fraction
    On multiplying fraction numerator negative 2 over denominator 3 end fraction with 5, we get fraction numerator negative 2 cross times 5 over denominator 3 cross times 5 end fraction equals fraction numerator negative 10 over denominator 15 end fraction
    Now we have 4 fractions with the same denominators.
    On adding, we have 9 over 15 plus 35 over 15 plus fraction numerator negative 33 over denominator 15 end fraction plus fraction numerator negative 10 over denominator 15 end fraction equals 1 over 15
    Hence 3 over 5 plus 7 over 3 plus fraction numerator negative 11 over denominator 5 end fraction plus fraction numerator negative 2 over denominator 3 end fraction equals 1 over 15
    General
    Maths-

    The sum of two rational numbers is -5. If one of them is,fraction numerator negative 13 over denominator negative 6 end fraction find the other.
     

    Given that one rational number is fraction numerator negative 13 over denominator negative 6 end fraction equals 13 over 6 and let the other one be x.
    Their sum = -5 , that is 13 over 6 plus x equals negative 5
    not stretchy rightwards double arrow x equals negative 5 minus 13 over 6
    not stretchy rightwards double arrow x equals fraction numerator negative 43 over denominator 6 end fraction
     

     

    The sum of two rational numbers is -5. If one of them is,fraction numerator negative 13 over denominator negative 6 end fraction find the other.
     

    Maths-General
    Given that one rational number is fraction numerator negative 13 over denominator negative 6 end fraction equals 13 over 6 and let the other one be x.
    Their sum = -5 , that is 13 over 6 plus x equals negative 5
    not stretchy rightwards double arrow x equals negative 5 minus 13 over 6
    not stretchy rightwards double arrow x equals fraction numerator negative 43 over denominator 6 end fraction
     

     
    parallel
    General
    Maths-

    Arrange the following rational numbers in descending order fraction numerator negative 5 over denominator 6 end fraction comma fraction numerator negative 7 over denominator 12 end fraction comma fraction numerator 13 over denominator negative 18 end fraction and fraction numerator 23 over denominator negative 24 end fraction.

    Given rational numbers are fraction numerator negative 5 over denominator 6 end fraction comma fraction numerator negative 7 over denominator 12 end fraction comma fraction numerator 13 over denominator negative 18 end fraction and fraction numerator 23 over denominator negative 24 end fraction.
    Express the rational numbers with positive denominator by multiplying with.
    Here, fraction numerator 13 over denominator negative 18 end fraction equals fraction numerator 13 x minus 1 over denominator negative 18 x minus 1 end fraction equals fraction numerator negative 13 over denominator 18 end fraction and fraction numerator 23 over denominator negative 24 end fraction equals fraction numerator 23 x minus 1 over denominator negative 24 x minus 1 end fraction equals fraction numerator negative 23 over denominator 24 end fraction
    So, Now we have fraction numerator negative 5 over denominator 6 end fraction comma fraction numerator negative 7 over denominator 12 end fraction comma fraction numerator negative 13 over denominator 18 end fraction and fraction numerator negative 23 over denominator 24 end fraction.
    By taking LCM of denominators 6,12,18 and 24, we get LCM as 72
    On multiplying fraction numerator negative 5 over denominator 6 end fraction with 12, we get fraction numerator negative 5 cross times 12 over denominator 6 cross times 12 end fraction equals fraction numerator negative 60 over denominator 72 end fraction
    On multiplying fraction numerator negative 7 over denominator 12 end fraction with 6, we get fraction numerator negative 7 cross times 6 over denominator 12 cross times 6 end fraction equals fraction numerator negative 42 over denominator 72 end fraction
    On multiplying fraction numerator negative 13 over denominator 18 end fraction with 4, we get fraction numerator negative 13 cross times 4 over denominator 18 cross times 4 end fraction equals fraction numerator negative 52 over denominator 72 end fraction
    On multiplying fraction numerator negative 23 over denominator 24 end fraction with 3, we get fraction numerator negative 23 cross times 3 over denominator 24 cross times 3 end fraction equals fraction numerator negative 69 over denominator 72 end fraction
    On comparing the above fractions with same denominator,
    we have  -42 > -52 > -60 > -69
    Hence fraction numerator negative 42 over denominator 72 end fraction greater than fraction numerator negative 52 over denominator 72 end fraction greater than fraction numerator negative 60 over denominator 72 end fraction greater than fraction numerator negative 69 over denominator 72 end fraction equals fraction numerator negative 7 over denominator 12 end fraction greater than fraction numerator 13 over denominator negative 18 end fraction greater than fraction numerator negative 5 over denominator 6 end fraction greater than fraction numerator 23 over denominator negative 24 end fraction
    So descending order is fraction numerator negative 7 over denominator 12 end fraction comma fraction numerator 13 over denominator negative 18 end fraction comma fraction numerator negative 5 over denominator 6 end fraction comma fraction numerator 23 over denominator negative 24 end fraction

    Arrange the following rational numbers in descending order fraction numerator negative 5 over denominator 6 end fraction comma fraction numerator negative 7 over denominator 12 end fraction comma fraction numerator 13 over denominator negative 18 end fraction and fraction numerator 23 over denominator negative 24 end fraction.

    Maths-General
    Given rational numbers are fraction numerator negative 5 over denominator 6 end fraction comma fraction numerator negative 7 over denominator 12 end fraction comma fraction numerator 13 over denominator negative 18 end fraction and fraction numerator 23 over denominator negative 24 end fraction.
    Express the rational numbers with positive denominator by multiplying with.
    Here, fraction numerator 13 over denominator negative 18 end fraction equals fraction numerator 13 x minus 1 over denominator negative 18 x minus 1 end fraction equals fraction numerator negative 13 over denominator 18 end fraction and fraction numerator 23 over denominator negative 24 end fraction equals fraction numerator 23 x minus 1 over denominator negative 24 x minus 1 end fraction equals fraction numerator negative 23 over denominator 24 end fraction
    So, Now we have fraction numerator negative 5 over denominator 6 end fraction comma fraction numerator negative 7 over denominator 12 end fraction comma fraction numerator negative 13 over denominator 18 end fraction and fraction numerator negative 23 over denominator 24 end fraction.
    By taking LCM of denominators 6,12,18 and 24, we get LCM as 72
    On multiplying fraction numerator negative 5 over denominator 6 end fraction with 12, we get fraction numerator negative 5 cross times 12 over denominator 6 cross times 12 end fraction equals fraction numerator negative 60 over denominator 72 end fraction
    On multiplying fraction numerator negative 7 over denominator 12 end fraction with 6, we get fraction numerator negative 7 cross times 6 over denominator 12 cross times 6 end fraction equals fraction numerator negative 42 over denominator 72 end fraction
    On multiplying fraction numerator negative 13 over denominator 18 end fraction with 4, we get fraction numerator negative 13 cross times 4 over denominator 18 cross times 4 end fraction equals fraction numerator negative 52 over denominator 72 end fraction
    On multiplying fraction numerator negative 23 over denominator 24 end fraction with 3, we get fraction numerator negative 23 cross times 3 over denominator 24 cross times 3 end fraction equals fraction numerator negative 69 over denominator 72 end fraction
    On comparing the above fractions with same denominator,
    we have  -42 > -52 > -60 > -69
    Hence fraction numerator negative 42 over denominator 72 end fraction greater than fraction numerator negative 52 over denominator 72 end fraction greater than fraction numerator negative 60 over denominator 72 end fraction greater than fraction numerator negative 69 over denominator 72 end fraction equals fraction numerator negative 7 over denominator 12 end fraction greater than fraction numerator 13 over denominator negative 18 end fraction greater than fraction numerator negative 5 over denominator 6 end fraction greater than fraction numerator 23 over denominator negative 24 end fraction
    So descending order is fraction numerator negative 7 over denominator 12 end fraction comma fraction numerator 13 over denominator negative 18 end fraction comma fraction numerator negative 5 over denominator 6 end fraction comma fraction numerator 23 over denominator negative 24 end fraction
    General
    Maths-

    8 Arrange the following rational numbers in ascending order fraction numerator 4 over denominator negative 5 end fraction comma fraction numerator negative 5 over denominator negative 12 end fraction comma fraction numerator 7 over denominator negative 18 end fraction and fraction numerator negative 2 over denominator 3 end fraction.

    Given rational numbers are fraction numerator 4 over denominator negative 5 end fraction comma fraction numerator negative 5 over denominator negative 12 end fraction comma fraction numerator 7 over denominator negative 18 end fraction and fraction numerator negative 2 over denominator 3 end fraction.
    Express the rational numbers with positive denominator by multiplying with -1.
    Here, fraction numerator 4 over denominator negative 5 end fraction equals fraction numerator 4 cross times negative 1 over denominator negative 5 cross times negative 1 end fraction equals fraction numerator negative 4 over denominator 5 end fraction and fraction numerator 7 over denominator negative 18 end fraction equals fraction numerator 7 cross times negative 1 over denominator negative 18 cross times negative 1 end fraction equals fraction numerator negative 7 over denominator 18 end fraction
    So, Now we have fraction numerator negative 4 over denominator 5 end fraction comma 5 over 12 comma fraction numerator negative 7 over denominator 18 end fraction and fraction numerator negative 2 over denominator 3 end fraction.
    By taking LCM of denominators 5,12,18 and 3, we get LCM as 180
    On multiplying fraction numerator negative 4 over denominator 5 end fraction with 36, we get fraction numerator negative 4 cross times 36 over denominator 5 cross times 36 end fraction equals fraction numerator negative 144 over denominator 180 end fraction
    On multiplying 5 over 12 with 15, we get fraction numerator 5 cross times 15 over denominator 12 cross times 15 end fraction equals 75 over 180
    On multiplying fraction numerator negative 7 over denominator 18 end fraction with 10, we get fraction numerator negative 7 cross times 10 over denominator 18 cross times 10 end fraction equals fraction numerator negative 70 over denominator 180 end fraction
    On multiplying fraction numerator negative 2 over denominator 3 end fraction with 60, we get fraction numerator negative 2 cross times 60 over denominator 3 cross times 60 end fraction equals fraction numerator negative 120 over denominator 180 end fraction
    On comparing the above fractions with same denominator,
    we have -144 < -120< -70 < 75
    Hence fraction numerator negative 144 over denominator 180 end fraction less than fraction numerator negative 120 over denominator 180 end fraction less than fraction numerator negative 70 over denominator 180 end fraction less than 75 over 180 equals fraction numerator negative 4 over denominator 5 end fraction less than fraction numerator negative 2 over denominator 3 end fraction less than fraction numerator negative 7 over denominator 18 end fraction less than 5 over 12
    So ascending order is fraction numerator 4 over denominator negative 5 end fraction comma fraction numerator negative 2 over denominator 3 end fraction comma fraction numerator 7 over denominator negative 18 end fraction comma 5 over 12

    8 Arrange the following rational numbers in ascending order fraction numerator 4 over denominator negative 5 end fraction comma fraction numerator negative 5 over denominator negative 12 end fraction comma fraction numerator 7 over denominator negative 18 end fraction and fraction numerator negative 2 over denominator 3 end fraction.

    Maths-General
    Given rational numbers are fraction numerator 4 over denominator negative 5 end fraction comma fraction numerator negative 5 over denominator negative 12 end fraction comma fraction numerator 7 over denominator negative 18 end fraction and fraction numerator negative 2 over denominator 3 end fraction.
    Express the rational numbers with positive denominator by multiplying with -1.
    Here, fraction numerator 4 over denominator negative 5 end fraction equals fraction numerator 4 cross times negative 1 over denominator negative 5 cross times negative 1 end fraction equals fraction numerator negative 4 over denominator 5 end fraction and fraction numerator 7 over denominator negative 18 end fraction equals fraction numerator 7 cross times negative 1 over denominator negative 18 cross times negative 1 end fraction equals fraction numerator negative 7 over denominator 18 end fraction
    So, Now we have fraction numerator negative 4 over denominator 5 end fraction comma 5 over 12 comma fraction numerator negative 7 over denominator 18 end fraction and fraction numerator negative 2 over denominator 3 end fraction.
    By taking LCM of denominators 5,12,18 and 3, we get LCM as 180
    On multiplying fraction numerator negative 4 over denominator 5 end fraction with 36, we get fraction numerator negative 4 cross times 36 over denominator 5 cross times 36 end fraction equals fraction numerator negative 144 over denominator 180 end fraction
    On multiplying 5 over 12 with 15, we get fraction numerator 5 cross times 15 over denominator 12 cross times 15 end fraction equals 75 over 180
    On multiplying fraction numerator negative 7 over denominator 18 end fraction with 10, we get fraction numerator negative 7 cross times 10 over denominator 18 cross times 10 end fraction equals fraction numerator negative 70 over denominator 180 end fraction
    On multiplying fraction numerator negative 2 over denominator 3 end fraction with 60, we get fraction numerator negative 2 cross times 60 over denominator 3 cross times 60 end fraction equals fraction numerator negative 120 over denominator 180 end fraction
    On comparing the above fractions with same denominator,
    we have -144 < -120< -70 < 75
    Hence fraction numerator negative 144 over denominator 180 end fraction less than fraction numerator negative 120 over denominator 180 end fraction less than fraction numerator negative 70 over denominator 180 end fraction less than 75 over 180 equals fraction numerator negative 4 over denominator 5 end fraction less than fraction numerator negative 2 over denominator 3 end fraction less than fraction numerator negative 7 over denominator 18 end fraction less than 5 over 12
    So ascending order is fraction numerator 4 over denominator negative 5 end fraction comma fraction numerator negative 2 over denominator 3 end fraction comma fraction numerator 7 over denominator negative 18 end fraction comma 5 over 12
    General
    Maths-

    Which of the two rational numbers is greater in the given pair fraction numerator 9 over denominator negative 13 end fraction and fraction numerator 7 over denominator negative 12 end fraction

    Given rational numbers are fraction numerator 9 over denominator negative 13 end fraction and fraction numerator 7 over denominator negative 12 end fraction.
    Here, fraction numerator 9 over denominator negative 13 end fraction equals fraction numerator 9 x minus 1 over denominator negative 13 x minus 1 end fraction equals fraction numerator negative 9 over denominator 13 end fraction and fraction numerator 7 over denominator negative 12 end fraction equals fraction numerator 7 cross times negative 1 over denominator negative 12 cross times negative 1 end fraction equals fraction numerator negative 7 over denominator 12 end fraction
    So we have fraction numerator negative 9 over denominator 13 end fraction and fraction numerator negative 7 over denominator 12 end fraction
    By taking LCM of denominators 13 and 12, we get LCM as 156
    On multiplying fraction numerator negative 9 over denominator 13 end fraction with 12, we get fraction numerator negative 9 cross times 12 over denominator 13 cross times 12 end fraction equals fraction numerator negative 108 over denominator 156 end fraction
    On multiplying fraction numerator negative 7 over denominator 12 end fraction with 13, we get fraction numerator negative 7 cross times 13 over denominator 12 cross times 13 end fraction equals fraction numerator negative 91 over denominator 156 end fraction
    On comparing the above fractions with same denominator,
    we have -91 > -108
    Hence fraction numerator negative 91 over denominator 156 end fraction greater than fraction numerator negative 108 over denominator 156 end fraction equals fraction numerator 7 over denominator negative 12 end fraction greater than fraction numerator 9 over denominator negative 13 end fraction

    Which of the two rational numbers is greater in the given pair fraction numerator 9 over denominator negative 13 end fraction and fraction numerator 7 over denominator negative 12 end fraction

    Maths-General
    Given rational numbers are fraction numerator 9 over denominator negative 13 end fraction and fraction numerator 7 over denominator negative 12 end fraction.
    Here, fraction numerator 9 over denominator negative 13 end fraction equals fraction numerator 9 x minus 1 over denominator negative 13 x minus 1 end fraction equals fraction numerator negative 9 over denominator 13 end fraction and fraction numerator 7 over denominator negative 12 end fraction equals fraction numerator 7 cross times negative 1 over denominator negative 12 cross times negative 1 end fraction equals fraction numerator negative 7 over denominator 12 end fraction
    So we have fraction numerator negative 9 over denominator 13 end fraction and fraction numerator negative 7 over denominator 12 end fraction
    By taking LCM of denominators 13 and 12, we get LCM as 156
    On multiplying fraction numerator negative 9 over denominator 13 end fraction with 12, we get fraction numerator negative 9 cross times 12 over denominator 13 cross times 12 end fraction equals fraction numerator negative 108 over denominator 156 end fraction
    On multiplying fraction numerator negative 7 over denominator 12 end fraction with 13, we get fraction numerator negative 7 cross times 13 over denominator 12 cross times 13 end fraction equals fraction numerator negative 91 over denominator 156 end fraction
    On comparing the above fractions with same denominator,
    we have -91 > -108
    Hence fraction numerator negative 91 over denominator 156 end fraction greater than fraction numerator negative 108 over denominator 156 end fraction equals fraction numerator 7 over denominator negative 12 end fraction greater than fraction numerator 9 over denominator negative 13 end fraction
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    General
    Maths-

    Find the circumference of the circle whose diameter is 21 cm.

    It is given that diameter of circle =  21 cm
    rightwards double arrowRadius = fraction numerator d i a m e t e r over denominator 2 end fraction
    21 over 2 cm
    Circumference = 2 pi r
    = 2 (3.14)  21 over 2
    (thereforestraight pi = 3.14 )
    = (3.14) 21
    = 65.94 cm

    Find the circumference of the circle whose diameter is 21 cm.

    Maths-General
    It is given that diameter of circle =  21 cm
    rightwards double arrowRadius = fraction numerator d i a m e t e r over denominator 2 end fraction
    21 over 2 cm
    Circumference = 2 pi r
    = 2 (3.14)  21 over 2
    (thereforestraight pi = 3.14 )
    = (3.14) 21
    = 65.94 cm
    General
    Maths-

    Express fraction numerator negative 48 over denominator 60 end fraction as a rational number with denominator 5

    Given rational number = fraction numerator negative 48 over denominator 60 end fraction
    The greatest common divisor of 48 and 60 is 12.
    Now, divide numerator and denominator of fraction numerator negative 48 over denominator 60 end fraction by 12,
    we get fraction numerator negative 48 divided by 12 over denominator 60 divided by 12 end fraction equals fraction numerator negative 4 over denominator 5 end fraction
    fraction numerator negative 48 over denominator 60 end fraction expressed as rational number with denominator 5 is fraction numerator negative 4 over denominator 5 end fraction.

    Express fraction numerator negative 48 over denominator 60 end fraction as a rational number with denominator 5

    Maths-General
    Given rational number = fraction numerator negative 48 over denominator 60 end fraction
    The greatest common divisor of 48 and 60 is 12.
    Now, divide numerator and denominator of fraction numerator negative 48 over denominator 60 end fraction by 12,
    we get fraction numerator negative 48 divided by 12 over denominator 60 divided by 12 end fraction equals fraction numerator negative 4 over denominator 5 end fraction
    fraction numerator negative 48 over denominator 60 end fraction expressed as rational number with denominator 5 is fraction numerator negative 4 over denominator 5 end fraction.
    General
    Maths-

    Arrange the numbers fraction numerator negative 3 over denominator 5 end fraction comma fraction numerator 7 over denominator negative 10 end fraction and fraction numerator negative 5 over denominator 8 end fraction in ascending order

    Given rational numbers are fraction numerator negative 3 over denominator 5 end fraction comma fraction numerator 7 over denominator negative 10 end fraction and fraction numerator negative 5 over denominator 8 end fraction.
    Express the rational numbers with positive denominator by multiplying with -1.
    Here, fraction numerator 7 over denominator negative 10 end fraction equals fraction numerator 7 cross times negative 1 over denominator negative 10 cross times negative 1 end fraction equals fraction numerator negative 7 over denominator 10 end fraction
    So, Now we have fraction numerator negative 3 over denominator 5 end fraction comma fraction numerator negative 7 over denominator 10 end fraction and fraction numerator negative 5 over denominator 8 end fraction.
    By taking LCM of denominators 5,10 and 8, we get LCM as 40
    On multiplying fraction numerator negative 3 over denominator 5 end fraction with 8, we get fraction numerator negative 3 cross times 8 over denominator 5 cross times 8 end fraction equals fraction numerator negative 24 over denominator 40 end fraction
    On multiplying fraction numerator negative 7 over denominator 10 end fraction with 4, we get fraction numerator negative 7 cross times 4 over denominator 10 cross times 4 end fraction equals fraction numerator negative 28 over denominator 40 end fraction
    On multiplying fraction numerator negative 5 over denominator 8 end fraction with 5, we get fraction numerator negative 5 cross times 5 over denominator 8 cross times 5 end fraction equals fraction numerator negative 25 over denominator 40 end fraction
    On comparing the above fractions with same denominator,
    we have  -28 < -25 < -24
    Hence fraction numerator negative 28 over denominator 40 end fraction less than fraction numerator negative 25 over denominator 40 end fraction less than fraction numerator negative 24 over denominator 40 end fraction equals fraction numerator 7 over denominator negative 10 end fraction less than fraction numerator negative 5 over denominator 8 end fraction less than fraction numerator negative 3 over denominator 5 end fraction
    So ascending order is fraction numerator 7 over denominator negative 10 end fraction comma fraction numerator negative 5 over denominator 8 end fraction comma fraction numerator negative 3 over denominator 5 end fraction.

    Arrange the numbers fraction numerator negative 3 over denominator 5 end fraction comma fraction numerator 7 over denominator negative 10 end fraction and fraction numerator negative 5 over denominator 8 end fraction in ascending order

    Maths-General
    Given rational numbers are fraction numerator negative 3 over denominator 5 end fraction comma fraction numerator 7 over denominator negative 10 end fraction and fraction numerator negative 5 over denominator 8 end fraction.
    Express the rational numbers with positive denominator by multiplying with -1.
    Here, fraction numerator 7 over denominator negative 10 end fraction equals fraction numerator 7 cross times negative 1 over denominator negative 10 cross times negative 1 end fraction equals fraction numerator negative 7 over denominator 10 end fraction
    So, Now we have fraction numerator negative 3 over denominator 5 end fraction comma fraction numerator negative 7 over denominator 10 end fraction and fraction numerator negative 5 over denominator 8 end fraction.
    By taking LCM of denominators 5,10 and 8, we get LCM as 40
    On multiplying fraction numerator negative 3 over denominator 5 end fraction with 8, we get fraction numerator negative 3 cross times 8 over denominator 5 cross times 8 end fraction equals fraction numerator negative 24 over denominator 40 end fraction
    On multiplying fraction numerator negative 7 over denominator 10 end fraction with 4, we get fraction numerator negative 7 cross times 4 over denominator 10 cross times 4 end fraction equals fraction numerator negative 28 over denominator 40 end fraction
    On multiplying fraction numerator negative 5 over denominator 8 end fraction with 5, we get fraction numerator negative 5 cross times 5 over denominator 8 cross times 5 end fraction equals fraction numerator negative 25 over denominator 40 end fraction
    On comparing the above fractions with same denominator,
    we have  -28 < -25 < -24
    Hence fraction numerator negative 28 over denominator 40 end fraction less than fraction numerator negative 25 over denominator 40 end fraction less than fraction numerator negative 24 over denominator 40 end fraction equals fraction numerator 7 over denominator negative 10 end fraction less than fraction numerator negative 5 over denominator 8 end fraction less than fraction numerator negative 3 over denominator 5 end fraction
    So ascending order is fraction numerator 7 over denominator negative 10 end fraction comma fraction numerator negative 5 over denominator 8 end fraction comma fraction numerator negative 3 over denominator 5 end fraction.
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