Question

which correctly rename 7/8 and 5/6 using a common denominator 42/48 and 40/48? 42/48 and 30/48? 14/16 and 15/18? or 28/24 and 20/24?

Answer 1

a) and c) as correctly rename  $\dfrac{7}{8}$  and  $\dfrac{5}{6}$.

Step-by-step explanation:

We have,

$\dfrac{7}{8}$  and $\dfrac{5}{6}$

To check options:

a)  $\dfrac{42}{48}$ and  $\dfrac{40}{48}$

= $\dfrac{6\times 7}{6\times 8}$ and  $\dfrac{8\times 5}{8\times 6}$

=$\dfrac{7}{8}$  and  $\dfrac{5}{6}$

=$\dfrac{7}{8}$  and  $\dfrac{5}{6}$, is the correct option.

b)  $\dfrac{42}{48}$  and  $\dfrac{30}{48}$

=  $\dfrac{6\times 7}{6\times 8}$  and  $\dfrac{6\times 5}{6\times 8}$

=  $\dfrac{7}{8}$  and  $\dfrac{5}{8}$

=  $\dfrac{7}{8} and \dfrac{5}{8}$ ≠  $\dfrac{7}{8}$ and  $\dfrac{5}{6}$, is the incorrect option.

c)  $\dfrac{14}{16}$  and $\dfrac{15}{18}$

= $\dfrac{2\times 7}{2\times 8}$ and $\dfrac{3\times 5}{3\times 6}$

= $\dfrac{7}{8}$ and $\dfrac{5}{6}$

= $\dfrac{7}{8}$ and  $\dfrac{5}{6}$ =  $\dfrac{7}{8}$  and  $\dfrac{5}{6}$ , is the correct.

d)  $\dfrac{28}{24}$  and  $\dfrac{20}{24}$

=$\dfrac{4\times 7}{4\times 6}$ and  $\dfrac{4\times 5}{4\times 6}$

=  $\dfrac{7}{6}$ and  $\dfrac{5}{6}$

=  $\dfrac{7}{6}$  and  $\dfrac{5}{6}$ ≠  $\dfrac{7}{8}$ and  $\dfrac{5}{6}$ , is the incorrect.

Hence, a) and c) as correctly rename   $\dfrac{7}{8}$ and  $\dfrac{5}{6}$.