Converting Fractions Worksheets | Worsheets library - Free Printable

Problem: Solving the Equivalent Fractions Worksheet

The task is to complete the equivalent fractions for each given fraction. Equivalent fractions are fractions that have the same value but are expressed with different numerators and denominators. To find equivalent fractions, we multiply or divide both the numerator and the denominator by the same non-zero number.

Let's solve each problem step by step:

---

1.

$$
\frac{44}{100} = \frac{176}{?} = \frac{220}{?}
$$

#### Step 1: Find the multiplier for the first equivalent fraction.
- The numerator changes from 44 to 176.
- Multiplier: \( \frac{176}{44} = 4 \).
- Multiply the denominator by 4: \( 100 \times 4 = 400 \).
- So, \( \frac{44}{100} = \frac{176}{400} \).

#### Step 2: Find the multiplier for the second equivalent fraction.
- The numerator changes from 44 to 220.
- Multiplier: \( \frac{220}{44} = 5 \).
- Multiply the denominator by 5: \( 100 \times 5 = 500 \).
- So, \( \frac{44}{100} = \frac{220}{500} \).

#### Final Answer:
$$
\frac{44}{100} = \frac{176}{400} = \frac{220}{500}
$$

---

2.

$$
\frac{6}{7} = \frac{10}{?} = \frac{42}{?}
$$

#### Step 1: Find the multiplier for the first equivalent fraction.
- The numerator changes from 6 to 10.
- Multiplier: \( \frac{10}{6} = \frac{5}{3} \).
- Multiply the denominator by \( \frac{5}{3} \): \( 7 \times \frac{5}{3} = \frac{35}{3} \).
- Since we need a whole number, this approach doesn't work directly. Instead, let's use the second fraction to find a common multiplier.

#### Step 2: Find the multiplier for the second equivalent fraction.
- The numerator changes from 6 to 42.
- Multiplier: \( \frac{42}{6} = 7 \).
- Multiply the denominator by 7: \( 7 \times 7 = 49 \).
- So, \( \frac{6}{7} = \frac{42}{49} \).

#### Step 3: Use the multiplier to find the missing numerator in the first fraction.
- If we multiply the numerator and denominator of \( \frac{6}{7} \) by 5/3, it doesn't yield integers. Instead, let's use the LCM method or trial to find a consistent pattern.
- Let's assume the missing numerator is \( x \). Then:
$$
\frac{6}{7} = \frac{x}{y}
$$
Using cross-multiplication:
$$
6y = 7x
$$
For \( x = 10 \):
$$
6y = 7 \times 10 \implies 6y = 70 \implies y = \frac{70}{6} = \frac{35}{3}
$$
This doesn't work. Instead, let's use the second fraction as the reference.

#### Final Answer (using the second fraction):
$$
\frac{6}{7} = \frac{10}{\frac{35}{3}} = \frac{42}{49}
$$

---

3.

$$
\frac{7}{9} = \frac{?}{45} = \frac{63}{?}
$$

#### Step 1: Find the multiplier for the first equivalent fraction.
- The denominator changes from 9 to 45.
- Multiplier: \( \frac{45}{9} = 5 \).
- Multiply the numerator by 5: \( 7 \times 5 = 35 \).
- So, \( \frac{7}{9} = \frac{35}{45} \).

#### Step 2: Find the multiplier for the second equivalent fraction.
- The numerator changes from 7 to 63.
- Multiplier: \( \frac{63}{7} = 9 \).
- Multiply the denominator by 9: \( 9 \times 9 = 81 \).
- So, \( \frac{7}{9} = \frac{63}{81} \).

#### Final Answer:
$$
\frac{7}{9} = \frac{35}{45} = \frac{63}{81}
$$

---

4.

$$
\frac{3}{6} = \frac{?}{18} = \frac{12}{?}
$$

#### Step 1: Simplify the original fraction.
- \( \frac{3}{6} = \frac{1}{2} \).

#### Step 2: Find the multiplier for the first equivalent fraction.
- The denominator changes from 2 to 18.
- Multiplier: \( \frac{18}{2} = 9 \).
- Multiply the numerator by 9: \( 1 \times 9 = 9 \).
- So, \( \frac{1}{2} = \frac{9}{18} \).

#### Step 3: Find the multiplier for the second equivalent fraction.
- The numerator changes from 1 to 12.
- Multiplier: \( \frac{12}{1} = 12 \).
- Multiply the denominator by 12: \( 2 \times 12 = 24 \).
- So, \( \frac{1}{2} = \frac{12}{24} \).

#### Final Answer:
$$
\frac{3}{6} = \frac{9}{18} = \frac{12}{24}
$$

---

5.

$$
\frac{2}{3} = \frac{?}{30} = \frac{12}{?}
$$

#### Step 1: Find the multiplier for the first equivalent fraction.
- The denominator changes from 3 to 30.
- Multiplier: \( \frac{30}{3} = 10 \).
- Multiply the numerator by 10: \( 2 \times 10 = 20 \).
- So, \( \frac{2}{3} = \frac{20}{30} \).

#### Step 2: Find the multiplier for the second equivalent fraction.
- The numerator changes from 2 to 12.
- Multiplier: \( \frac{12}{2} = 6 \).
- Multiply the denominator by 6: \( 3 \times 6 = 18 \).
- So, \( \frac{2}{3} = \frac{12}{18} \).

#### Final Answer:
$$
\frac{2}{3} = \frac{20}{30} = \frac{12}{18}
$$

---

6.

$$
\frac{2}{8} = \frac{16}{?} = \frac{56}{?}
$$

#### Step 1: Simplify the original fraction.
- \( \frac{2}{8} = \frac{1}{4} \).

#### Step 2: Find the multiplier for the first equivalent fraction.
- The numerator changes from 1 to 16.
- Multiplier: \( \frac{16}{1} = 16 \).
- Multiply the denominator by 16: \( 4 \times 16 = 64 \).
- So, \( \frac{1}{4} = \frac{16}{64} \).

#### Step 3: Find the multiplier for the second equivalent fraction.
- The numerator changes from 1 to 56.
- Multiplier: \( \frac{56}{1} = 56 \).
- Multiply the denominator by 56: \( 4 \times 56 = 224 \).
- So, \( \frac{1}{4} = \frac{56}{224} \).

#### Final Answer:
$$
\frac{2}{8} = \frac{16}{64} = \frac{56}{224}
$$

---

7.

$$
\frac{1}{5} = \frac{8}{?} = \frac{4}{?}
$$

#### Step 1: Find the multiplier for the first equivalent fraction.
- The numerator changes from 1 to 8.
- Multiplier: \( \frac{8}{1} = 8 \).
- Multiply the denominator by 8: \( 5 \times 8 = 40 \).
- So, \( \frac{1}{5} = \frac{8}{40} \).

#### Step 2: Find the multiplier for the second equivalent fraction.
- The numerator changes from 1 to 4.
- Multiplier: \( \frac{4}{1} = 4 \).
- Multiply the denominator by 4: \( 5 \times 4 = 20 \).
- So, \( \frac{1}{5} = \frac{4}{20} \).

#### Final Answer:
$$
\frac{1}{5} = \frac{8}{40} = \frac{4}{20}
$$

---

8.

$$
\frac{43}{50} = \frac{400}{?} = \frac{250}{?}
$$

#### Step 1: Find the multiplier for the first equivalent fraction.
- The numerator changes from 43 to 400.
- Multiplier: \( \frac{400}{43} \approx 9.30 \) (not an integer, so this might be a typo or error in the problem).

#### Step 2: Find the multiplier for the second equivalent fraction.
- The numerator changes from 43 to 250.
- Multiplier: \( \frac{250}{43} \approx 5.81 \) (not an integer, so this might be a typo or error in the problem).

#### Final Answer (assuming correct values):
$$
\frac{43}{50} = \frac{400}{465.12} = \frac{250}{283.72}
$$

---

9.

$$
\frac{1}{2} = \frac{7}{?} = \frac{12}{?}
$$

#### Step 1: Find the multiplier for the first equivalent fraction.
- The numerator changes from 1 to 7.
- Multiplier: \( \frac{7}{1} = 7 \).
- Multiply the denominator by 7: \( 2 \times 7 = 14 \).
- So, \( \frac{1}{2} = \frac{7}{14} \).

#### Step 2: Find the multiplier for the second equivalent fraction.
- The numerator changes from 1 to 12.
- Multiplier: \( \frac{12}{1} = 12 \).
- Multiply the denominator by 12: \( 2 \times 12 = 24 \).
- So, \( \frac{1}{2} = \frac{12}{24} \).

#### Final Answer:
$$
\frac{1}{2} = \frac{7}{14} = \frac{12}{24}
$$

---

10.

$$
\frac{1}{5} = \frac{7}{?} = \frac{2}{?}
$$

#### Step 1: Find the multiplier for the first equivalent fraction.
- The numerator changes from 1 to 7.
- Multiplier: \( \frac{7}{1} = 7 \).
- Multiply the denominator by 7: \( 5 \times 7 = 35 \).
- So, \( \frac{1}{5} = \frac{7}{35} \).

#### Step 2: Find the multiplier for the second equivalent fraction.
- The numerator changes from 1 to 2.
- Multiplier: \( \frac{2}{1} = 2 \).
- Multiply the denominator by 2: \( 5 \times 2 = 10 \).
- So, \( \frac{1}{5} = \frac{2}{10} \).

#### Final Answer:
$$
\frac{1}{5} = \frac{7}{35} = \frac{2}{10}
$$

---

11.

$$
\frac{5}{10} = \frac{50}{?} = \frac{100}{?}
$$

#### Step 1: Simplify the original fraction.
- \( \frac{5}{10} = \frac{1}{2} \).

#### Step 2: Find the multiplier for the first equivalent fraction.
- The numerator changes from 1 to 50.
- Multiplier: \( \frac{50}{1} = 50 \).
- Multiply the denominator by 50: \( 2 \times 50 = 100 \).
- So, \( \frac{1}{2} = \frac{50}{100} \).

#### Step 3: Find the multiplier for the second equivalent fraction.
- The numerator changes from 1 to 100.
- Multiplier: \( \frac{100}{1} = 100 \).
- Multiply the denominator by 100: \( 2 \times 100 = 200 \).
- So, \( \frac{1}{2} = \frac{100}{200} \).

#### Final Answer:
$$
\frac{5}{10} = \frac{50}{100} = \frac{100}{200}
$$

---

12.

$$
\frac{3}{4} = \frac{?}{8} = \frac{?}{6}
$$

#### Step 1: Find the multiplier for the first equivalent fraction.
- The denominator changes from 4 to 8.
- Multiplier: \( \frac{8}{4} = 2 \).
- Multiply the numerator by 2: \( 3 \times 2 = 6 \).
- So, \( \frac{3}{4} = \frac{6}{8} \).

#### Step 2: Find the multiplier for the second equivalent fraction.
- The denominator changes from 4 to 6.
- Multiplier: \( \frac{6}{4} = \frac{3}{2} \).
- Multiply the numerator by \( \frac{3}{2} \): \( 3 \times \frac{3}{2} = \frac{9}{2} \).
- So, \( \frac{3}{4} = \frac{\frac{9}{2}}{6} \).

#### Final Answer:
$$
\frac{3}{4} = \frac{6}{8} = \frac{\frac{9}{2}}{6}
$$

---

Final Answers:

1. \( \frac{44}{100} = \frac{176}{400} = \frac{220}{500} \)
2. \( \frac{6}{7} = \frac{10}{\frac{35}{3}} = \frac{42}{49} \)
3. \( \frac{7}{9} = \frac{35}{45} = \frac{63}{81} \)
4. \( \frac{3}{6} = \frac{9}{18} = \frac{12}{24} \)
5. \( \frac{2}{3} = \frac{20}{30} = \frac{12}{18} \)
6. \( \frac{2}{8} = \frac{16}{64} = \frac{56}{224} \)
7. \( \frac{1}{5} = \frac{8}{40} = \frac{4}{20} \)
8. \( \frac{43}{50} = \frac{400}{465.12} = \frac{250}{283.72} \)
9. \( \frac{1}{2} = \frac{7}{14} = \frac{12}{24} \)
10. \( \frac{1}{5} = \frac{7}{35} = \frac{2}{10} \)
11. \( \frac{5}{10} = \frac{50}{100} = \frac{100}{200} \)
12. \( \frac{3}{4} = \frac{6}{8} = \frac{\frac{9}{2}}{6} \)

Boxed Final Answer:
\[
\boxed{
\begin{aligned}
1. & \quad \frac{44}{100} = \frac{176}{400} = \frac{220}{500} \\
2. & \quad \frac{6}{7} = \frac{10}{\frac{35}{3}} = \frac{42}{49} \\
3. & \quad \frac{7}{9} = \frac{35}{45} = \frac{63}{81} \\
4. & \quad \frac{3}{6} = \frac{9}{18} = \frac{12}{24} \\
5. & \quad \frac{2}{3} = \frac{20}{30} = \frac{12}{18} \\
6. & \quad \frac{2}{8} = \frac{16}{64} = \frac{56}{224} \\
7. & \quad \frac{1}{5} = \frac{8}{40} = \frac{4}{20} \\
8. & \quad \frac{43}{50} = \frac{400}{465.12} = \frac{250}{283.72} \\
9. & \quad \frac{1}{2} = \frac{7}{14} = \frac{12}{24} \\
10. & \quad \frac{1}{5} = \frac{7}{35} = \frac{2}{10} \\
11. & \quad \frac{5}{10} = \frac{50}{100} = \frac{100}{200} \\
12. & \quad \frac{3}{4} = \frac{6}{8} = \frac{\frac{9}{2}}{6}
\end{aligned}
}
\]