Maths-
General
Easy

Question

𝑉𝑒𝑟𝑖𝑓𝑦 open parentheses fraction numerator negative 9 over denominator 5 end fraction plus fraction numerator 10 over denominator negative 3 end fraction close parentheses plus fraction numerator negative 21 over denominator 4 end fraction equals fraction numerator negative 9 over denominator 5 end fraction plus open parentheses fraction numerator 10 over denominator negative 3 end fraction plus fraction numerator negative 21 over denominator 4 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 9 over denominator 5 end fraction plus fraction numerator 10 over denominator negative 3 end fraction close parentheses plus fraction numerator negative 21 over denominator 4 end fraction equals fraction numerator negative 9 over denominator 5 end fraction plus open parentheses fraction numerator 10 over denominator negative 3 end fraction plus fraction numerator negative 21 over denominator 4 end fraction close parentheses
    Express the rational numbers with positive denominator by multiplying with -1.

    Here, fraction numerator 10 over denominator negative 3 end fraction equals fraction numerator 10 x minus 1 over denominator negative 3 x minus 1 end fraction equals fraction numerator negative 10 over denominator 3 end fraction
    Consider the LHS part, we have open parentheses fraction numerator negative 9 over denominator 5 end fraction plus fraction numerator negative 10 over denominator 3 end fraction close parentheses plus fraction numerator negative 21 over denominator 4 end fraction …(i)
    Determine the LCM of the denominators of rational numbers inside the brackets.
    LCM of 5 and 3 = 15
    On multiplying fraction numerator negative 9 over denominator 5 end fraction with 3, we get fraction numerator negative 9 cross times 3 over denominator 5 cross times 3 end fraction equals fraction numerator negative 27 over denominator 15 end fraction
    On multiplying fraction numerator negative 10 over denominator 3 end fraction with 5, we get fraction numerator negative 10 cross times 5 over denominator 3 cross times 5 end fraction equals fraction numerator negative 50 over denominator 15 end fraction
    On adding, we get fraction numerator negative 27 over denominator 15 end fraction plus fraction numerator negative 50 over denominator 15 end fraction equals fraction numerator negative 77 over denominator 15 end fraction
    On substituting this in (i), we get fraction numerator negative 77 over denominator 15 end fraction plus fraction numerator negative 21 over denominator 4 end fraction
    Determine the LCM of the denominators of rational numbers.
    LCM of 15 and 4 = 60
    On multiplying fraction numerator negative 77 over denominator 15 end fraction with 4, we get fraction numerator negative 77 cross times 4 over denominator 15 cross times 4 end fraction equals fraction numerator negative 308 over denominator 60 end fraction
    On multiplying fraction numerator negative 21 over denominator 4 end fraction with 15, we get fraction numerator negative 21 cross times 15 over denominator 4 cross times 15 end fraction equals fraction numerator negative 315 over denominator 60 end fraction
    On adding, we get fraction numerator negative 308 over denominator 60 end fraction plus fraction numerator negative 315 over denominator 60 end fraction equals fraction numerator negative 623 over denominator 60 end fraction
    Thus we have LHS to be open parentheses fraction numerator negative 9 over denominator 5 end fraction plus fraction numerator negative 10 over denominator 3 end fraction close parentheses plus fraction numerator negative 21 over denominator 4 end fraction equals fraction numerator negative 623 over denominator 60 end fraction
    Consider the RHS part, we have fraction numerator negative 9 over denominator 5 end fraction plus open parentheses fraction numerator negative 10 over denominator 3 end fraction plus fraction numerator negative 21 over denominator 4 end fraction close parentheses…(ii)
    Determine the LCM of the denominators of rational numbers inside the brackets.
    LCM of 3 and 4 = 12
    On multiplying fraction numerator negative 10 over denominator 3 end fraction with 4, we get fraction numerator negative 10 cross times 4 over denominator 3 cross times 4 end fraction equals fraction numerator negative 40 over denominator 12 end fraction
    On multiplying fraction numerator negative 21 over denominator 4 end fraction with 3, we get fraction numerator negative 21 cross times 3 over denominator 4 cross times 3 end fraction equals fraction numerator negative 63 over denominator 12 end fraction
    On adding, we get fraction numerator negative 40 over denominator 12 end fraction plus fraction numerator negative 63 over denominator 12 end fraction equals fraction numerator negative 103 over denominator 12 end fraction
    On substituting this in (ii), we get fraction numerator negative 9 over denominator 5 end fraction plus fraction numerator negative 103 over denominator 12 end fraction
    Determine the LCM of the denominators of rational numbers.
    LCM of 5 and 12 = 60
    On multiplying fraction numerator negative 9 over denominator 5 end fraction with 12, we get fraction numerator negative 9 cross times 12 over denominator 5 cross times 12 end fraction equals fraction numerator negative 108 over denominator 60 end fraction
    On multiplying fraction numerator negative 103 over denominator 12 end fraction with 5, we get fraction numerator negative 103 cross times 5 over denominator 12 cross times 5 end fraction equals fraction numerator negative 515 over denominator 60 end fraction
    On adding, we get fraction numerator negative 108 over denominator 60 end fraction plus fraction numerator negative 515 over denominator 60 end fraction equals fraction numerator negative 623 over denominator 60 end fraction
    Thus we have RHS to be fraction numerator negative 9 over denominator 5 end fraction plus open parentheses fraction numerator negative 10 over denominator 9 end fraction plus fraction numerator negative 21 over denominator 4 end fraction close parentheses equals fraction numerator negative 623 over denominator 60 end fraction
    So we get LHS = RHS = fraction numerator negative 623 over denominator 60 end fraction
    Hence verified.

    Related Questions to study

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.