Question

on your own
write the pair of fractions as a pair of fractions with a common denominator.

1. $\frac{1}{4}$ and $\frac{5}{6}$
2. $\frac{3}{5}$ and $\frac{4}{10}$

tell whether the fractions are equivalent. write = or ≠.

1. $\frac{3}{4}\bigcirc\frac{1}{2}$
2. $\frac{3}{4}\bigcirc\frac{6}{8}$
3. $\frac{1}{2}\bigcirc\frac{4}{8}$
4. $\frac{1}{3}\bigcirc\frac{2}{6}$
5. $\frac{1}{3}\bigcirc\frac{4}{12}$
6. $\frac{2}{6}\bigcirc\frac{4}{12}$

Explanation:

6.

• Step1: Find the least - common denominator (LCD) of 4 and 6

The multiples of 4 are 4, 8, 12, 16, ... and the multiples of 6 are 6, 12, 18, ... The LCD of 4 and 6 is 12.

• Step2: Rewrite the fractions with the common denominator

For $\frac{1}{4}$, multiply the numerator and denominator by 3: $\frac{1\times3}{4\times3}=\frac{3}{12}$.
For $\frac{5}{6}$, multiply the numerator and denominator by 2: $\frac{5\times2}{6\times2}=\frac{10}{12}$.

7.

• Step1: Find the least - common denominator (LCD) of 5 and 10

The multiples of 5 are 5, 10, 15, ... and the multiples of 10 are 10, 20, ... The LCD of 5 and 10 is 10.

• Step2: Rewrite the fractions with the common denominator

For $\frac{3}{5}$, multiply the numerator and denominator by 2: $\frac{3\times2}{5\times2}=\frac{6}{10}$.
$\frac{4}{10}$ already has a denominator of 10, so it remains as $\frac{4}{10}$.

8.

• Step1: Make the denominators the same

The LCD of 4 and 2 is 4. $\frac{1}{2}=\frac{1\times2}{2\times2}=\frac{2}{4}$. Since $\frac{3}{4}
eq\frac{2}{4}$, the answer is $
eq$.

9.

• Step1: Simplify $\frac{6}{8}$

$\frac{6}{8}=\frac{6\div2}{8\div2}=\frac{3}{4}$. So $\frac{3}{4}=\frac{6}{8}$, the answer is $=$.

10.

• Step1: Simplify $\frac{4}{8}$

$\frac{4}{8}=\frac{4\div4}{8\div4}=\frac{1}{2}$. So $\frac{1}{2}=\frac{4}{8}$, the answer is $=$.

12.

• Step1: Simplify $\frac{2}{6}$

$\frac{2}{6}=\frac{2\div2}{6\div2}=\frac{1}{3}$. So $\frac{1}{3}=\frac{2}{6}$, the answer is $=$.

13.

• Step1: Simplify $\frac{4}{12}$

$\frac{4}{12}=\frac{4\div4}{12\div4}=\frac{1}{3}$. So $\frac{1}{3}=\frac{4}{12}$, the answer is $=$.

14.

• Step1: Simplify $\frac{4}{12}$

$\frac{4}{12}=\frac{4\div2}{12\div2}=\frac{2}{6}$. So $\frac{2}{6}=\frac{4}{12}$, the answer is $=$.

Answer:

1. $\frac{3}{12}$ and $\frac{10}{12}$
2. $\frac{6}{10}$ and $\frac{4}{10}$
3. $

eq$

1. $=$
2. $=$
3. $=$
4. $=$
5. $=$