Question

equivalent fractions
write two fractions equivalent to the given fraction.

1. \\(\frac{3}{4}\\)
2. \\(\frac{7}{8}\\)
3. \\(\frac{12}{5}\\)
4. \\(\frac{1}{2}\\)
5. \\(\frac{8}{9}\\)
6. \\(\frac{2}{3}\\)

Explanation:

Let's solve each problem one by one. The key concept is that to find equivalent fractions, we multiply the numerator and the denominator by the same non - zero number.

Problem 4: $\boldsymbol{\frac{3}{4}}$

Step 1: Multiply numerator and denominator by 2

To get an equivalent fraction, we multiply both the numerator and the denominator of $\frac{3}{4}$ by 2.
The formula for equivalent fractions is $\frac{a}{b}=\frac{a\times k}{b\times k}$, where $k
eq0$.
For $k = 2$, we have $\frac{3\times2}{4\times2}=\frac{6}{8}$.

Step 2: Multiply numerator and denominator by 3

For $k=3$, we calculate $\frac{3\times3}{4\times3}=\frac{9}{12}$.
So two equivalent fractions of $\frac{3}{4}$ are $\frac{6}{8}$ and $\frac{9}{12}$.

Problem 5: $\boldsymbol{\frac{7}{8}}$

Step 1: Multiply numerator and denominator by 2

Using the formula $\frac{a}{b}=\frac{a\times k}{b\times k}$ with $a = 7$, $b = 8$ and $k = 2$.
We get $\frac{7\times2}{8\times2}=\frac{14}{16}$.

Step 2: Multiply numerator and denominator by 3

For $k = 3$, we have $\frac{7\times3}{8\times3}=\frac{21}{24}$.
So two equivalent fractions of $\frac{7}{8}$ are $\frac{14}{16}$ and $\frac{21}{24}$.

Problem 6: $\boldsymbol{\frac{12}{5}}$

Step 1: Multiply numerator and denominator by 2

Applying the formula $\frac{a}{b}=\frac{a\times k}{b\times k}$ with $a = 12$, $b = 5$ and $k = 2$.
We obtain $\frac{12\times2}{5\times2}=\frac{24}{10}$.

Step 2: Multiply numerator and denominator by 3

For $k = 3$, we calculate $\frac{12\times3}{5\times3}=\frac{36}{15}$.
So two equivalent fractions of $\frac{12}{5}$ are $\frac{24}{10}$ and $\frac{36}{15}$.

Problem 7: $\boldsymbol{\frac{1}{2}}$

Step 1: Multiply numerator and denominator by 2

Using the formula $\frac{a}{b}=\frac{a\times k}{b\times k}$ with $a = 1$, $b = 2$ and $k = 2$.
We get $\frac{1\times2}{2\times2}=\frac{2}{4}$.

Step 2: Multiply numerator and denominator by 3

For $k = 3$, we have $\frac{1\times3}{2\times3}=\frac{3}{6}$.
So two equivalent fractions of $\frac{1}{2}$ are $\frac{2}{4}$ and $\frac{3}{6}$.

Problem 8: $\boldsymbol{\frac{8}{9}}$

Step 1: Multiply numerator and denominator by 2

Applying the formula $\frac{a}{b}=\frac{a\times k}{b\times k}$ with $a = 8$, $b = 9$ and $k = 2$.
We obtain $\frac{8\times2}{9\times2}=\frac{16}{18}$.

Step 2: Multiply numerator and denominator by 3

For $k = 3$, we calculate $\frac{8\times3}{9\times3}=\frac{24}{27}$.
So two equivalent fractions of $\frac{8}{9}$ are $\frac{16}{18}$ and $\frac{24}{27}$.

Problem 9: $\boldsymbol{\frac{2}{3}}$

Step 1: Multiply numerator and denominator by 2

Using the formula $\frac{a}{b}=\frac{a\times k}{b\times k}$ with $a = 2$, $b = 3$ and $k = 2$.
We get $\frac{2\times2}{3\times2}=\frac{4}{6}$.

Step 2: Multiply numerator and denominator by 3

For $k = 3$, we have $\frac{2\times3}{3\times3}=\frac{6}{9}$.
So two equivalent fractions of $\frac{2}{3}$ are $\frac{4}{6}$ and $\frac{6}{9}$.

Final Answers

1. $\frac{6}{8}$, $\frac{9}{12}$
2. $\frac{14}{16}$, $\frac{21}{24}$
3. $\frac{24}{10}$, $\frac{36}{15}$
4. $\frac{2}{4}$, $\frac{3}{6}$
5. $\frac{16}{18}$, $\frac{24}{27}$
6. $\frac{4}{6}$, $\frac{6}{9}$

Answer:

Let's solve each problem one by one. The key concept is that to find equivalent fractions, we multiply the numerator and the denominator by the same non - zero number.

Problem 4: $\boldsymbol{\frac{3}{4}}$

Step 1: Multiply numerator and denominator by 2

To get an equivalent fraction, we multiply both the numerator and the denominator of $\frac{3}{4}$ by 2.
The formula for equivalent fractions is $\frac{a}{b}=\frac{a\times k}{b\times k}$, where $k
eq0$.
For $k = 2$, we have $\frac{3\times2}{4\times2}=\frac{6}{8}$.

Step 2: Multiply numerator and denominator by 3

For $k=3$, we calculate $\frac{3\times3}{4\times3}=\frac{9}{12}$.
So two equivalent fractions of $\frac{3}{4}$ are $\frac{6}{8}$ and $\frac{9}{12}$.

Problem 5: $\boldsymbol{\frac{7}{8}}$

Step 1: Multiply numerator and denominator by 2

Using the formula $\frac{a}{b}=\frac{a\times k}{b\times k}$ with $a = 7$, $b = 8$ and $k = 2$.
We get $\frac{7\times2}{8\times2}=\frac{14}{16}$.

Step 2: Multiply numerator and denominator by 3

For $k = 3$, we have $\frac{7\times3}{8\times3}=\frac{21}{24}$.
So two equivalent fractions of $\frac{7}{8}$ are $\frac{14}{16}$ and $\frac{21}{24}$.

Problem 6: $\boldsymbol{\frac{12}{5}}$

Step 1: Multiply numerator and denominator by 2

Applying the formula $\frac{a}{b}=\frac{a\times k}{b\times k}$ with $a = 12$, $b = 5$ and $k = 2$.
We obtain $\frac{12\times2}{5\times2}=\frac{24}{10}$.

Step 2: Multiply numerator and denominator by 3

For $k = 3$, we calculate $\frac{12\times3}{5\times3}=\frac{36}{15}$.
So two equivalent fractions of $\frac{12}{5}$ are $\frac{24}{10}$ and $\frac{36}{15}$.

Problem 7: $\boldsymbol{\frac{1}{2}}$

Step 1: Multiply numerator and denominator by 2

Using the formula $\frac{a}{b}=\frac{a\times k}{b\times k}$ with $a = 1$, $b = 2$ and $k = 2$.
We get $\frac{1\times2}{2\times2}=\frac{2}{4}$.

Step 2: Multiply numerator and denominator by 3

For $k = 3$, we have $\frac{1\times3}{2\times3}=\frac{3}{6}$.
So two equivalent fractions of $\frac{1}{2}$ are $\frac{2}{4}$ and $\frac{3}{6}$.

Problem 8: $\boldsymbol{\frac{8}{9}}$

Step 1: Multiply numerator and denominator by 2

Applying the formula $\frac{a}{b}=\frac{a\times k}{b\times k}$ with $a = 8$, $b = 9$ and $k = 2$.
We obtain $\frac{8\times2}{9\times2}=\frac{16}{18}$.

Step 2: Multiply numerator and denominator by 3

For $k = 3$, we calculate $\frac{8\times3}{9\times3}=\frac{24}{27}$.
So two equivalent fractions of $\frac{8}{9}$ are $\frac{16}{18}$ and $\frac{24}{27}$.

Problem 9: $\boldsymbol{\frac{2}{3}}$

Step 1: Multiply numerator and denominator by 2

Using the formula $\frac{a}{b}=\frac{a\times k}{b\times k}$ with $a = 2$, $b = 3$ and $k = 2$.
We get $\frac{2\times2}{3\times2}=\frac{4}{6}$.

Step 2: Multiply numerator and denominator by 3

For $k = 3$, we have $\frac{2\times3}{3\times3}=\frac{6}{9}$.
So two equivalent fractions of $\frac{2}{3}$ are $\frac{4}{6}$ and $\frac{6}{9}$.

Final Answers

1. $\frac{6}{8}$, $\frac{9}{12}$
2. $\frac{14}{16}$, $\frac{21}{24}$
3. $\frac{24}{10}$, $\frac{36}{15}$
4. $\frac{2}{4}$, $\frac{3}{6}$
5. $\frac{16}{18}$, $\frac{24}{27}$
6. $\frac{4}{6}$, $\frac{6}{9}$