Question

which of the following expressions are equivalent to $-\frac{4}{7}-\frac{8}{9}+\frac{4}{7}+\frac{9}{8}$? choose 2 answers: a $(-\frac{4}{7}-\frac{4}{7})+(\frac{8}{9}+\frac{9}{8})$ b $-\frac{8}{9}+\frac{9}{8}$ c $(\frac{4}{7}-\frac{4}{7})+(\frac{9}{8}-\frac{8}{9})$ d $0$

Explanation:

Step1: Rearrange the terms

$-\frac{4}{7}+\frac{4}{7}-\frac{8}{9}+\frac{9}{8}$

Step2: Simplify the fractions with same - denominator

$(-\frac{4}{7}+\frac{4}{7})+(-\frac{8}{9}+\frac{9}{8})$
$=0 + (-\frac{8\times8}{9\times8}+\frac{9\times9}{8\times9})$
$=-\frac{64}{72}+\frac{81}{72}$
$=\frac{-64 + 81}{72}=\frac{17}{72}$

Now let's check each option:

• Option A: $(-\frac{4}{7}-\frac{4}{7})+(\frac{8}{9}+\frac{9}{8})=-\frac{8}{7}+\frac{64 + 81}{72}=-\frac{8}{7}+\frac{145}{72}

eq\frac{17}{72}$

• Option B: $-\frac{8}{9}+\frac{9}{8}=-\frac{64}{72}+\frac{81}{72}=\frac{17}{72}$
• Option C: $(\frac{4}{7}-\frac{4}{7})+(\frac{9}{8}-\frac{8}{9})=0+(\frac{9}{8}-\frac{8}{9})=\frac{17}{72}$
• Option D: $0

eq\frac{17}{72}$

Answer:

B. $-\frac{8}{9}+\frac{9}{8}$, C. $(\frac{4}{7}-\frac{4}{7})+(\frac{9}{8}-\frac{8}{9})$