Question

Which of the following fractions is equivalent to $\frac{16}{36}$?

• A. $\frac{9}{18}$
• B. $\frac{12}{28}$
• C. $\frac{24}{54}$
• D. $\frac{15}{45}$

Answer 1

The correct option is C $\frac{24}{54}$

Two fractions are said to be equivalent if their simplest form are equal.

Let's simplify each given fraction using GCF method

$\frac{16}{36}$
Factors of 16 = 1, 2, 4, 8, 16
Factors of 36 = 1, 2, 3, 4, 6, 9, 12, 18, 36
GCF (16, 36) = 4
$\frac{16}{36}$ = $\frac{4\times 4}{4\times 9}$ =$\frac{4}{9}$

1)$\frac{9}{18}$
Factors of 9 = 1, 3, 9
Factors of 18 = 1, 2, 3, 9, 18
GCF (9, 18) = 9
$\frac{9}{18}$ = $\frac{1\times 9}{2\times 9}$ =$\frac{1}{2}$

2) $\frac{12}{28}$
Factors of 12 = 1, 2, 3, 4, 6 , 12
Factors of 28 = 1, 2, 4, 7, 14, 28
GCF (12, 28) = 4
$\frac{12}{28}$ = $\frac{4\times 3}{4\times 7}$ =$\frac{1}{7}$

3) $\frac{24}{54}$
Factors of 24 = 1, 2, 3, 4, 6 , 8, 12, 24
Factors of 54 = 1, 2, 3, 6, 9, 18, 27 and 54.
GCF (24, 54) = 6
$\frac{24}{54}$ = $\frac{6\times 4}{6\times 9}$ =$\frac{4}{9}$

4) $\frac{15}{45}$
Factors of 15 = 1, 3,5, 15
Factors of 45 = 1, 3, 5,9, 15, 45
GCF (15,45) = 15
$\frac{15}{45}$ = $\frac{1\times 15}{3\times 15}$ =$\frac{1}{3}$

$\therefore$ The simplest form of $\frac{16}{36}$ and$\frac{24}{54}$ equals to $\frac{4}{9}$.
Hence, $\frac{16}{36}$ and$\frac{24}{54}$ are equivalent fractions.
Option C is the correct answer