Math Fraction Worksheets for Kids | Learning Printable - Free Printable

Problem Overview:

The task involves finding equivalent fractions for given fractions. Equivalent fractions are fractions that represent the same value but are expressed with different numerators and denominators. To solve this, we need to use the concept of multiplying or dividing both the numerator and the denominator by the same non-zero number.

Solution:

#### Step 1: Understand the Concept of Equivalent Fractions
Two fractions are equivalent if they can be simplified or expanded to have the same value. For example:
- \( \frac{1}{2} \) is equivalent to \( \frac{2}{4} \) because \( \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \).
- Similarly, \( \frac{1}{3} \) is equivalent to \( \frac{2}{6} \) because \( \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \).

#### Step 2: Solve Each Row

##### Row 1:
1. \( \frac{1}{2} = \frac{\square}{4} \)
- To find the missing numerator, notice that the denominator 2 is multiplied by 2 to get 4. Therefore, the numerator 1 must also be multiplied by 2.
- \( \frac{1 \times 2}{2 \times 2} = \frac{2}{4} \).
- Answer: \( \frac{1}{2} = \frac{2}{4} \).

2. \( \frac{1}{3} = \frac{\square}{6} \)
- The denominator 3 is multiplied by 2 to get 6. Therefore, the numerator 1 must also be multiplied by 2.
- \( \frac{1 \times 2}{3 \times 2} = \frac{2}{6} \).
- Answer: \( \frac{1}{3} = \frac{2}{6} \).

3. \( \frac{2}{6} = \frac{\square}{12} \)
- The denominator 6 is multiplied by 2 to get 12. Therefore, the numerator 2 must also be multiplied by 2.
- \( \frac{2 \times 2}{6 \times 2} = \frac{4}{12} \).
- Answer: \( \frac{2}{6} = \frac{4}{12} \).

##### Row 2:
1. \( \frac{1}{2} = \frac{\square}{8} \)
- The denominator 2 is multiplied by 4 to get 8. Therefore, the numerator 1 must also be multiplied by 4.
- \( \frac{1 \times 4}{2 \times 4} = \frac{4}{8} \).
- Answer: \( \frac{1}{2} = \frac{4}{8} \).

2. \( \frac{1}{3} = \frac{\square}{12} \)
- The denominator 3 is multiplied by 4 to get 12. Therefore, the numerator 1 must also be multiplied by 4.
- \( \frac{1 \times 4}{3 \times 4} = \frac{4}{12} \).
- Answer: \( \frac{1}{3} = \frac{4}{12} \).

3. \( \frac{2}{6} = \frac{\square}{3} \)
- The denominator 6 is divided by 2 to get 3. Therefore, the numerator 2 must also be divided by 2.
- \( \frac{2 \div 2}{6 \div 2} = \frac{1}{3} \).
- Answer: \( \frac{2}{6} = \frac{1}{3} \).

##### Row 3:
1. \( \frac{2}{4} = \frac{\square}{8} \)
- The denominator 4 is multiplied by 2 to get 8. Therefore, the numerator 2 must also be multiplied by 2.
- \( \frac{2 \times 2}{4 \times 2} = \frac{4}{8} \).
- Answer: \( \frac{2}{4} = \frac{4}{8} \).

2. \( \frac{4}{8} = \frac{\square}{2} \)
- The denominator 8 is divided by 4 to get 2. Therefore, the numerator 4 must also be divided by 4.
- \( \frac{4 \div 4}{8 \div 4} = \frac{1}{2} \).
- Answer: \( \frac{4}{8} = \frac{1}{2} \).

3. \( \frac{4}{12} = \frac{\square}{3} \)
- The denominator 12 is divided by 4 to get 3. Therefore, the numerator 4 must also be divided by 4.
- \( \frac{4 \div 4}{12 \div 4} = \frac{1}{3} \).
- Answer: \( \frac{4}{12} = \frac{1}{3} \).

##### Row 4:
1. \( \frac{2}{4} = \frac{\square}{2} \)
- The denominator 4 is divided by 2 to get 2. Therefore, the numerator 2 must also be divided by 2.
- \( \frac{2 \div 2}{4 \div 2} = \frac{1}{2} \).
- Answer: \( \frac{2}{4} = \frac{1}{2} \).

2. \( \frac{4}{8} = \frac{\square}{4} \)
- The denominator 8 is divided by 2 to get 4. Therefore, the numerator 4 must also be divided by 2.
- \( \frac{4 \div 2}{8 \div 2} = \frac{2}{4} \).
- Answer: \( \frac{4}{8} = \frac{2}{4} \).

3. \( \frac{4}{12} = \frac{\square}{6} \)
- The denominator 12 is divided by 2 to get 6. Therefore, the numerator 4 must also be divided by 2.
- \( \frac{4 \div 2}{12 \div 2} = \frac{2}{6} \).
- Answer: \( \frac{4}{12} = \frac{2}{6} \).

Final Answer:

\[
\boxed{
\begin{array}{ccc}
\frac{1}{2} = \frac{2}{4} & \frac{1}{3} = \frac{2}{6} & \frac{2}{6} = \frac{4}{12} \\
\frac{1}{2} = \frac{4}{8} & \frac{1}{3} = \frac{4}{12} & \frac{2}{6} = \frac{1}{3} \\
\frac{2}{4} = \frac{4}{8} & \frac{4}{8} = \frac{1}{2} & \frac{4}{12} = \frac{1}{3} \\
\frac{2}{4} = \frac{1}{2} & \frac{4}{8} = \frac{2}{4} & \frac{4}{12} = \frac{2}{6}
\end{array}
}
\]