Maths-
General
Easy

Question

Divide the sum of 13 over 5 and fraction numerator negative 12 over denominator 7 end fraction by the product fraction numerator negative 31 over denominator 7 end fraction and fraction numerator 1 over denominator negative 2 end fraction

Hint:

Perform the operations given in the question and get the final solution.

The correct answer is: 2/5


    To perform: fraction numerator 13 over 5 plus fraction numerator negative 12 over denominator 7 end fraction over denominator fraction numerator negative 31 over denominator 7 end fraction cross times fraction numerator 1 over denominator negative 2 end fraction end fraction
    Sum of 13 over 5 and fraction numerator negative 12 over denominator 7 end fraction equals 13 over 5 plus fraction numerator negative 12 over denominator 7 end fraction

    not stretchy rightwards double arrow fraction numerator 13 cross times 7 plus 5 cross times negative 12 over denominator 5 cross times 7 end fraction

    not stretchy rightwards double arrow fraction numerator 91 plus negative 60 over denominator 35 end fraction

    not stretchy rightwards double arrow 31 over 35…(i)
    Product of fraction numerator negative 31 over denominator 7 end fraction and fraction numerator 1 over denominator negative 2 end fraction equals fraction numerator negative 1 over denominator 2 end fraction equals fraction numerator negative 31 over denominator 7 end fraction cross times fraction numerator negative 1 over denominator 2 end fraction

    not stretchy rightwards double arrow fraction numerator 31 cross times 1 over denominator 7 cross times 2 end fraction

    not stretchy rightwards double arrow 31 over 14…(ii)
    On dividing, (i) by (ii)  we have

    thereforefraction numerator 13 over 5 plus fraction numerator negative 12 over denominator 7 end fraction over denominator fraction numerator negative 31 over denominator 7 end fraction cross times fraction numerator 1 over denominator negative 2 end fraction end fraction = 31 over 35 divided by 31 over 14

    not stretchy rightwards double arrow 31 over 35 cross times 14 over 31

    not stretchy rightwards double arrow 14 over 35 equals 2 over 5
    Hence fraction numerator 13 over 5 plus fraction numerator negative 12 over denominator 7 end fraction over denominator fraction numerator negative 31 over denominator 7 end fraction cross times fraction numerator 1 over denominator negative 2 end fraction end fraction equals 2 over 5

    Related Questions to study

    General
    Maths-

    Express 0.3178 in the form of p/q. Where p and q are integers.

    As 0.3178 is a terminating decimal so it can be expressed as p/q form.
    Step 1 of 2:
    Write down 0.3178 divided by 1:
    equals fraction numerator 0.3178 over denominator 1 end fraction
    Step 2 of 2:
    Multiplying numerator and denominator by 104(because there are 4 digits after the decimal point)
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals fraction numerator 0.3178 cross times 10 to the power of 4 over denominator 1 cross times 10 to the power of 4 end fraction end cell row cell equals 3178 over 10000 end cell end table
    Simplifying the fraction:
    equals 1589 over 5000
    Final Answer:
    Hence, the p/q form of 0.3178 is 1589 over 5000

    Express 0.3178 in the form of p/q. Where p and q are integers.

    Maths-General
    As 0.3178 is a terminating decimal so it can be expressed as p/q form.
    Step 1 of 2:
    Write down 0.3178 divided by 1:
    equals fraction numerator 0.3178 over denominator 1 end fraction
    Step 2 of 2:
    Multiplying numerator and denominator by 104(because there are 4 digits after the decimal point)
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell equals fraction numerator 0.3178 cross times 10 to the power of 4 over denominator 1 cross times 10 to the power of 4 end fraction end cell row cell equals 3178 over 10000 end cell end table
    Simplifying the fraction:
    equals 1589 over 5000
    Final Answer:
    Hence, the p/q form of 0.3178 is 1589 over 5000
    General
    Maths-

    One liter of petrol costs Rs. 70. What is the cost of 70 litres of petrol
     

    Cost of 1 litre petrol = 70 Rs
    thereforecost of 70 litres of petrol = 70 cross times70 = 4900 Rs

    One liter of petrol costs Rs. 70. What is the cost of 70 litres of petrol
     

    Maths-General
    Cost of 1 litre petrol = 70 Rs
    thereforecost of 70 litres of petrol = 70 cross times70 = 4900 Rs
    General
    Maths-

    Insert 3 rational numbers between 3 and 4

    Given numbers are 3 and 4.
    So fraction numerator 3 plus 4 over denominator 2 end fraction equals 3 1 half
    not stretchy rightwards double arrow 3 comma 3 1 half comma 4
    Then, fraction numerator 3 plus 3.5 over denominator 2 end fraction equals 3 1 fourth comma fraction numerator 3.5 plus 4 over denominator 2 end fraction equals 3 3 over 4
    not stretchy rightwards double arrow 3 comma 3 1 fourth comma 3 1 half comma 3 3 over 4 comma 4
    Hence , required 3 rational numbers between 3 and 4 = 3 1 fourth comma 3 1 half comma 3 3 over 4

    Insert 3 rational numbers between 3 and 4

    Maths-General
    Given numbers are 3 and 4.
    So fraction numerator 3 plus 4 over denominator 2 end fraction equals 3 1 half
    not stretchy rightwards double arrow 3 comma 3 1 half comma 4
    Then, fraction numerator 3 plus 3.5 over denominator 2 end fraction equals 3 1 fourth comma fraction numerator 3.5 plus 4 over denominator 2 end fraction equals 3 3 over 4
    not stretchy rightwards double arrow 3 comma 3 1 fourth comma 3 1 half comma 3 3 over 4 comma 4
    Hence , required 3 rational numbers between 3 and 4 = 3 1 fourth comma 3 1 half comma 3 3 over 4
    parallel
    General
    Maths-

    Uma earns Rs. 16000 per month. She spends 1 fourth of her income on food, 3 over 10 of the remainder on house rent and 5 over 21 of the remainder on the education of children. How much money is left with her?

    Total money earned by Uma = 16000 Rs
    Money spent on food from her income = 1 fourth cross times 16000 equals 4000 Rs
    Amount left with her = 16000 minus 4000 equals 12000 Rs
    Money spent on house rent from the remaining money  = 3 over 10 cross times 12000 equals 3600Rs
    Amount left with her = 12000 - 3600 = 8400 Rs
    Money spent on education of children from the remaining money  = 5 over 21 cross times 8400 equals 2000 Rs
    Amount left with her = 8400 - 2000 = 6400 Rs
    Money still left with her = 6400 Rs

    Uma earns Rs. 16000 per month. She spends 1 fourth of her income on food, 3 over 10 of the remainder on house rent and 5 over 21 of the remainder on the education of children. How much money is left with her?

    Maths-General
    Total money earned by Uma = 16000 Rs
    Money spent on food from her income = 1 fourth cross times 16000 equals 4000 Rs
    Amount left with her = 16000 minus 4000 equals 12000 Rs
    Money spent on house rent from the remaining money  = 3 over 10 cross times 12000 equals 3600Rs
    Amount left with her = 12000 - 3600 = 8400 Rs
    Money spent on education of children from the remaining money  = 5 over 21 cross times 8400 equals 2000 Rs
    Amount left with her = 8400 - 2000 = 6400 Rs
    Money still left with her = 6400 Rs
    General
    Maths-

    Convert into decimal and identify whether it is a non-terminating and repeating decimal or a terminating decimal:6 over 24

    Let’s say x =6 over 24
    The given rational number is not in its simplified form. So, let’s first covert it in the simplified form
    x equals 1 fourth
    Upon dividing 1 by 4 we got
    x equals 1 fourth equals 0.25
    The resultant decimal is a terminating decimal
    Final Answer:
    As the resultant decimal has a finite number of digits following the decimal. Hence, the decimal value of 6 over 24  is 0.25 and it is a terminating decimal.

    Convert into decimal and identify whether it is a non-terminating and repeating decimal or a terminating decimal:6 over 24

    Maths-General
    Let’s say x =6 over 24
    The given rational number is not in its simplified form. So, let’s first covert it in the simplified form
    x equals 1 fourth
    Upon dividing 1 by 4 we got
    x equals 1 fourth equals 0.25
    The resultant decimal is a terminating decimal
    Final Answer:
    As the resultant decimal has a finite number of digits following the decimal. Hence, the decimal value of 6 over 24  is 0.25 and it is a terminating decimal.
    General
    Maths-

    In a school, 5 over 8𝑡ℎ of the students are boys, if there are 240 girls, find the number of boys in the school?

    Let the total number of students = x
    Number of girls = 240
    So, number of boys = x - 240…(i)
    Given that 5 over 8 to the power of t h end exponent of the total students are boys. That is,5 over 8 x …(ii)
    On equating (i) and (ii) , we get 5 over 8 x equals x minus 240
    Multiply by 8 on both sides.
    We have 5 x equals 8 left parenthesis x minus 240 right parenthesis
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 5 x equals 8 x minus 1920 end cell row cell not stretchy rightwards double arrow 8 x minus 5 x equals 1920 end cell end table
    not stretchy rightwards double arrow 3 x equals 1920
    not stretchy rightwards double arrow x equals 1920 over 3 equals 640
    Hence total number of students = 640
    From (ii), we get total number of boys equals 5 over 8 x equals 5 over 8 left parenthesis 640 right parenthesis equals 400
    So, number of boys in the school = 400

    In a school, 5 over 8𝑡ℎ of the students are boys, if there are 240 girls, find the number of boys in the school?

    Maths-General
    Let the total number of students = x
    Number of girls = 240
    So, number of boys = x - 240…(i)
    Given that 5 over 8 to the power of t h end exponent of the total students are boys. That is,5 over 8 x …(ii)
    On equating (i) and (ii) , we get 5 over 8 x equals x minus 240
    Multiply by 8 on both sides.
    We have 5 x equals 8 left parenthesis x minus 240 right parenthesis
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell not stretchy rightwards double arrow 5 x equals 8 x minus 1920 end cell row cell not stretchy rightwards double arrow 8 x minus 5 x equals 1920 end cell end table
    not stretchy rightwards double arrow 3 x equals 1920
    not stretchy rightwards double arrow x equals 1920 over 3 equals 640
    Hence total number of students = 640
    From (ii), we get total number of boys equals 5 over 8 x equals 5 over 8 left parenthesis 640 right parenthesis equals 400
    So, number of boys in the school = 400
    parallel
    General
    Maths-

    If 24 pairs of trousers of equal size can be prepared with 54 m of cloth, what length of cloth is required for each pair of trousers?

    Let the cloth required for one trouser = x meters
    Then the cloth required for 24 equal size trousers =  54 m
    That is, 24x = 54
    On dividing both the sides by 24, we get fraction numerator 24 x over denominator 24 end fraction equals 54 over 24
    not stretchy rightwards double arrow 1 x equals 9 over 4 equals 2.25 straight m
    Hence, cloth required for one trouser x equals 9 over 4

    If 24 pairs of trousers of equal size can be prepared with 54 m of cloth, what length of cloth is required for each pair of trousers?

    Maths-General
    Let the cloth required for one trouser = x meters
    Then the cloth required for 24 equal size trousers =  54 m
    That is, 24x = 54
    On dividing both the sides by 24, we get fraction numerator 24 x over denominator 24 end fraction equals 54 over 24
    not stretchy rightwards double arrow 1 x equals 9 over 4 equals 2.25 straight m
    Hence, cloth required for one trouser x equals 9 over 4
    General
    Maths-

    Convert into decimal and identify whether it is a non-terminating and repeating decimal or a terminating decimal:24 over 11

    Let’s say x =24 over 11
    Upon dividing 24 by 11 we got
    x equals 24 over 11 equals 2.181818 horizontal ellipsis
    The resultant decimal is a non-terminating and repeating decimal.
    Final Answer:
    As the resultant decimal has an infinite number of digits following the decimal and these digits are repeated after a fixed interval. Hence, the decimal value of 24 over 11 is 2.18 with bottom parenthesis below and it is a non-terminating and repeating decimal.

    Convert into decimal and identify whether it is a non-terminating and repeating decimal or a terminating decimal:24 over 11

    Maths-General
    Let’s say x =24 over 11
    Upon dividing 24 by 11 we got
    x equals 24 over 11 equals 2.181818 horizontal ellipsis
    The resultant decimal is a non-terminating and repeating decimal.
    Final Answer:
    As the resultant decimal has an infinite number of digits following the decimal and these digits are repeated after a fixed interval. Hence, the decimal value of 24 over 11 is 2.18 with bottom parenthesis below and it is a non-terminating and repeating decimal.
    General
    Maths-

    By what rational number fraction numerator negative 8 over denominator 39 end fraction should  be multiplied to obtain 5 over 26 ?

    Complete step by step solution:
    Given rational number = fraction numerator negative 8 over denominator 39 end fraction and let the other rational number be x
    On multiplication, we get the result to be 5 over 26
    That is, we have fraction numerator negative 8 over denominator 39 end fraction x equals 5 over 26
    On dividing both sides by fraction numerator negative 8 over denominator 39 end fraction,

    we get x equals 5 over 26 divided by fraction numerator negative 8 over denominator 39 end fraction

    not stretchy rightwards double arrow x equals 5 over 26 cross times fraction numerator 39 over denominator negative 8 end fraction equals fraction numerator negative 15 over denominator 16 end fraction
    not stretchy rightwards double arrow x equals fraction numerator negative 15 over denominator 16 end fraction
    So, fraction numerator negative 15 over denominator 16 end fraction must be multiplied with fraction numerator negative 8 over denominator 39 end fraction  to get 5 over 26.

    By what rational number fraction numerator negative 8 over denominator 39 end fraction should  be multiplied to obtain 5 over 26 ?

    Maths-General
    Complete step by step solution:
    Given rational number = fraction numerator negative 8 over denominator 39 end fraction and let the other rational number be x
    On multiplication, we get the result to be 5 over 26
    That is, we have fraction numerator negative 8 over denominator 39 end fraction x equals 5 over 26
    On dividing both sides by fraction numerator negative 8 over denominator 39 end fraction,

    we get x equals 5 over 26 divided by fraction numerator negative 8 over denominator 39 end fraction

    not stretchy rightwards double arrow x equals 5 over 26 cross times fraction numerator 39 over denominator negative 8 end fraction equals fraction numerator negative 15 over denominator 16 end fraction
    not stretchy rightwards double arrow x equals fraction numerator negative 15 over denominator 16 end fraction
    So, fraction numerator negative 15 over denominator 16 end fraction must be multiplied with fraction numerator negative 8 over denominator 39 end fraction  to get 5 over 26.

    parallel
    General
    Maths-

    By what rational number fraction numerator negative 8 over denominator 39 end fraction should  be multiplied to obtain 5 over 26 ?

    Complete step by step solution:
    Given rational number = fraction numerator negative 8 over denominator 39 end fraction and let the other rational number be x
    On multiplication, we get the result to be 5 over 26
    That is, we have fraction numerator negative 8 over denominator 39 end fraction x equals 5 over 26
    On dividing both sides by fraction numerator negative 8 over denominator 39 end fraction,

    we get x equals 5 over 26 divided by fraction numerator negative 8 over denominator 39 end fraction

    not stretchy rightwards double arrow x equals 5 over 26 cross times fraction numerator 39 over denominator negative 8 end fraction equals fraction numerator negative 15 over denominator 16 end fraction
    not stretchy rightwards double arrow x equals fraction numerator negative 15 over denominator 16 end fraction
    So, fraction numerator negative 15 over denominator 16 end fraction must be multiplied with fraction numerator negative 8 over denominator 39 end fraction  to get 5 over 26.

    By what rational number fraction numerator negative 8 over denominator 39 end fraction should  be multiplied to obtain 5 over 26 ?

    Maths-General
    Complete step by step solution:
    Given rational number = fraction numerator negative 8 over denominator 39 end fraction and let the other rational number be x
    On multiplication, we get the result to be 5 over 26
    That is, we have fraction numerator negative 8 over denominator 39 end fraction x equals 5 over 26
    On dividing both sides by fraction numerator negative 8 over denominator 39 end fraction,

    we get x equals 5 over 26 divided by fraction numerator negative 8 over denominator 39 end fraction

    not stretchy rightwards double arrow x equals 5 over 26 cross times fraction numerator 39 over denominator negative 8 end fraction equals fraction numerator negative 15 over denominator 16 end fraction
    not stretchy rightwards double arrow x equals fraction numerator negative 15 over denominator 16 end fraction
    So, fraction numerator negative 15 over denominator 16 end fraction must be multiplied with fraction numerator negative 8 over denominator 39 end fraction  to get 5 over 26.

    General
    Maths-

    Convert into decimal and identify whether it is a non-terminating and repeating decimal or a terminating decimal:59 over 8

    Let’s say x =59 over 8
    Upon dividing 59 by 8 we got
    x equals 59 over 8 equals 7.375
    The resultant decimal is a terminating decimal
    Final Answer:
    As the resultant decimal has a finite number of digits following the decimal. Hence, the decimal value of 59 over 8  is 7.375 and it is a terminating decimal.

    Convert into decimal and identify whether it is a non-terminating and repeating decimal or a terminating decimal:59 over 8

    Maths-General
    Let’s say x =59 over 8
    Upon dividing 59 by 8 we got
    x equals 59 over 8 equals 7.375
    The resultant decimal is a terminating decimal
    Final Answer:
    As the resultant decimal has a finite number of digits following the decimal. Hence, the decimal value of 59 over 8  is 7.375 and it is a terminating decimal.
    General
    Maths-

    A sim earns Rs. 40000 per month. He spends 2 over 5 of his income on food, 5 over 12 of the remaining on education of children and 3 over 7 of the remainder on the house rent. How much money is still left with him?

    Total money earned by Asim = 40000 Rs
    Money spent on food from his income = 2 over 5 cross times 40000 equals 16000 Rs
    Amount left with him = 40000 - 16000 = 24000 Rs
    Money spent on education of children from the remaining money  = 5 over 12 cross times 24000 equals 10000 Rs
    Amount left with him = 24000 - 10000 = 14000 Rs
    Money spent on house rent from the remaining money  = 3 over 7 cross times 14000 equals 6000 Rs
    Amount left with him = 14000 - 6000 = 8000 Rs
    Money still left with him = 8000 Rs

    A sim earns Rs. 40000 per month. He spends 2 over 5 of his income on food, 5 over 12 of the remaining on education of children and 3 over 7 of the remainder on the house rent. How much money is still left with him?

    Maths-General
    Total money earned by Asim = 40000 Rs
    Money spent on food from his income = 2 over 5 cross times 40000 equals 16000 Rs
    Amount left with him = 40000 - 16000 = 24000 Rs
    Money spent on education of children from the remaining money  = 5 over 12 cross times 24000 equals 10000 Rs
    Amount left with him = 24000 - 10000 = 14000 Rs
    Money spent on house rent from the remaining money  = 3 over 7 cross times 14000 equals 6000 Rs
    Amount left with him = 14000 - 6000 = 8000 Rs
    Money still left with him = 8000 Rs
    parallel
    General
    Maths-

    Find the cost of 32 over 5 m of cloth at Rs 363 over 4.  per meter.
     

    Given that the cost of 1 m of cloth equals 36 3 over 4 equals 147 over 4 Rs
    ∴ Cost of 3 2 over 5 m equals 17 over 5 m equals 147 over 4 cross times 17 over 5
    equals fraction numerator 147 cross times 17 over denominator 4 cross times 5 end fraction
    equals 2499 over 20
    = 124.93 Rs
    Hence cost of 17 over 5 meter = 2499 over 20 Rs

    Find the cost of 32 over 5 m of cloth at Rs 363 over 4.  per meter.
     

    Maths-General
    Given that the cost of 1 m of cloth equals 36 3 over 4 equals 147 over 4 Rs
    ∴ Cost of 3 2 over 5 m equals 17 over 5 m equals 147 over 4 cross times 17 over 5
    equals fraction numerator 147 cross times 17 over denominator 4 cross times 5 end fraction
    equals 2499 over 20
    = 124.93 Rs
    Hence cost of 17 over 5 meter = 2499 over 20 Rs
    General
    Maths-

    Find the area of circular ring whose external and internal radii are 10cm and 3 cm respectively

    It is given that External radii, r1 = 10 cm
    Internal radii, r2 = 3 cm
    Area of circular ring = Area of outer ring – Area of inner ring
    straight pi (r1)2  - straight pi r2
    22 over 7 × (r1)2  -  22 over 7 × (r2)2
    22 over 7 × (102 – 32)
    22 over 7 × 91  =  286 cm2

    Find the area of circular ring whose external and internal radii are 10cm and 3 cm respectively

    Maths-General
    It is given that External radii, r1 = 10 cm
    Internal radii, r2 = 3 cm
    Area of circular ring = Area of outer ring – Area of inner ring
    straight pi (r1)2  - straight pi r2
    22 over 7 × (r1)2  -  22 over 7 × (r2)2
    22 over 7 × (102 – 32)
    22 over 7 × 91  =  286 cm2
    General
    Maths-

    The circumference of a circle is 123.2 cm. Calculate (i) the radius of the circle in cm. (ii) the area of the circle, correct to nearest cm2

    It is given that Circumference of the circle = 123.2 cm
    (i). Circumference of the circle = 2 straight pi r
    123.2  =  2 ×  22 over 7 × r
    19.6  = r
    (ii) Area of circle = straight pi r2
    = 22 over 7 × (19.6)2
    = 1207.36 cm2

    The circumference of a circle is 123.2 cm. Calculate (i) the radius of the circle in cm. (ii) the area of the circle, correct to nearest cm2

    Maths-General
    It is given that Circumference of the circle = 123.2 cm
    (i). Circumference of the circle = 2 straight pi r
    123.2  =  2 ×  22 over 7 × r
    19.6  = r
    (ii) Area of circle = straight pi r2
    = 22 over 7 × (19.6)2
    = 1207.36 cm2
    parallel

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