Equivalent Fractions (B) Worksheet | Cazoom Maths Worksheets - Free Printable

Let's solve this Equivalent Fractions (B) worksheet step by step, explaining how to find the missing numbers in each section.

---

🔍 Key Concept: Equivalent Fractions

Two fractions are equivalent if they represent the same value. You can create an equivalent fraction by multiplying or dividing both the numerator and denominator by the same number.

For example:
$$
\frac{1}{2} = \frac{1 \times 3}{2 \times 3} = \frac{3}{6}
$$

We'll use this principle to fill in the blanks.

---

## ✔ Section A:

Each problem has the form:
$$
\frac{1}{a} = \frac{b}{c}
$$
We need to find the missing numerator or denominator so that the fractions are equivalent.

---

1. $ \frac{1}{2} = \frac{6}{?} $

Multiply numerator and denominator by 6:
$$
\frac{1 \times 6}{2 \times 6} = \frac{6}{12}
\Rightarrow \boxed{12}
$$

2. $ \frac{1}{3} = \frac{7}{?} $

Multiply numerator and denominator by 7:
$$
\frac{1 \times 7}{3 \times 7} = \frac{7}{21}
\Rightarrow \boxed{21}
$$

3. $ \frac{1}{6} = \frac{9}{?} $

Multiply numerator and denominator by 9:
$$
\frac{1 \times 9}{6 \times 9} = \frac{9}{54}
\Rightarrow \boxed{54}
$$

4. $ \frac{1}{7} = \frac{?}{14} $

We want denominator to be 14 → multiply by 2:
$$
\frac{1 \times 2}{7 \times 2} = \frac{2}{14}
\Rightarrow \boxed{2}
$$

5. $ \frac{1}{9} = \frac{5}{?} $

Multiply by 5:
$$
\frac{1 \times 5}{9 \times 5} = \frac{5}{45}
\Rightarrow \boxed{45}
$$

6. $ \frac{1}{8} = \frac{4}{?} $

Multiply by 4:
$$
\frac{1 \times 4}{8 \times 4} = \frac{4}{32}
\Rightarrow \boxed{32}
$$

7. $ \frac{1}{12} = \frac{3}{?} $

Multiply by 3:
$$
\frac{1 \times 3}{12 \times 3} = \frac{3}{36}
\Rightarrow \boxed{36}
$$

8. $ \frac{1}{8} = \frac{?}{32} $

Multiply by 4:
$$
\frac{1 \times 4}{8 \times 4} = \frac{4}{32}
\Rightarrow \boxed{4}
$$

9. $ \frac{1}{5} = \frac{9}{?} $

Multiply by 9:
$$
\frac{1 \times 9}{5 \times 9} = \frac{9}{45}
\Rightarrow \boxed{45}
$$

10. $ \frac{1}{11} = \frac{4}{?} $

Multiply by 4:
$$
\frac{1 \times 4}{11 \times 4} = \frac{4}{44}
\Rightarrow \boxed{44}
$$

11. $ \frac{1}{6} = \frac{12}{?} $

Multiply by 12:
$$
\frac{1 \times 12}{6 \times 12} = \frac{12}{72}
\Rightarrow \boxed{72}
$$

12. $ \frac{1}{7} = \frac{?}{49} $

Multiply by 7:
$$
\frac{1 \times 7}{7 \times 7} = \frac{7}{49}
\Rightarrow \boxed{7}
$$

13. $ \frac{1}{8} = \frac{3}{?} $

Multiply by 3:
$$
\frac{1 \times 3}{8 \times 3} = \frac{3}{24}
\Rightarrow \boxed{24}
$$

14. $ \frac{1}{6} = \frac{7}{?} $

Multiply by 7:
$$
\frac{1 \times 7}{6 \times 7} = \frac{7}{42}
\Rightarrow \boxed{42}
$$

15. $ \frac{1}{12} = \frac{10}{?} $

Multiply by 10:
$$
\frac{1 \times 10}{12 \times 10} = \frac{10}{120}
\Rightarrow \boxed{120}
$$

16. $ \frac{1}{9} = \frac{?}{63} $

Multiply by 7:
$$
\frac{1 \times 7}{9 \times 7} = \frac{7}{63}
\Rightarrow \boxed{7}
$$

---

## ✔ Section B:

Now we have more complex fractions.

---

1. $ \frac{2}{3} = \frac{4}{?} $

Multiply numerator and denominator by 2:
$$
\frac{2 \times 2}{3 \times 2} = \frac{4}{6}
\Rightarrow \boxed{6}
$$

2. $ \frac{4}{5} = \frac{12}{?} $

Multiply numerator and denominator by 3:
$$
\frac{4 \times 3}{5 \times 3} = \frac{12}{15}
\Rightarrow \boxed{15}
$$

3. $ \frac{3}{4} = \frac{21}{?} $

Multiply numerator and denominator by 7:
$$
\frac{3 \times 7}{4 \times 7} = \frac{21}{28}
\Rightarrow \boxed{28}
$$

4. $ \frac{2}{5} = \frac{10}{?} $

Multiply by 5:
$$
\frac{2 \times 5}{5 \times 5} = \frac{10}{25}
\Rightarrow \boxed{25}
$$

5. $ \frac{2}{9} = \frac{16}{?} $

Multiply numerator and denominator by 8:
$$
\frac{2 \times 8}{9 \times 8} = \frac{16}{72}
\Rightarrow \boxed{72}
$$

6. $ \frac{9}{10} = \frac{18}{?} $

Multiply by 2:
$$
\frac{9 \times 2}{10 \times 2} = \frac{18}{20}
\Rightarrow \boxed{20}
$$

7. $ \frac{4}{7} = \frac{16}{?} $

Multiply by 4:
$$
\frac{4 \times 4}{7 \times 4} = \frac{16}{28}
\Rightarrow \boxed{28}
$$

8. $ \frac{3}{11} = \frac{27}{?} $

Multiply by 9:
$$
\frac{3 \times 9}{11 \times 9} = \frac{27}{99}
\Rightarrow \boxed{99}
$$

9. $ \frac{7}{8} = \frac{?}{56} $

We want denominator 56 → 8 × 7 = 56 → multiply numerator by 7:
$$
\frac{7 \times 7}{8 \times 7} = \frac{49}{56}
\Rightarrow \boxed{49}
$$

10. $ \frac{2}{3} = \frac{?}{36} $

3 × 12 = 36 → multiply numerator by 12:
$$
\frac{2 \times 12}{3 \times 12} = \frac{24}{36}
\Rightarrow \boxed{24}
$$

11. $ \frac{5}{6} = \frac{?}{48} $

6 × 8 = 48 → multiply numerator by 8:
$$
\frac{5 \times 8}{6 \times 8} = \frac{40}{48}
\Rightarrow \boxed{40}
$$

12. $ \frac{3}{7} = \frac{?}{84} $

7 × 12 = 84 → multiply numerator by 12:
$$
\frac{3 \times 12}{7 \times 12} = \frac{36}{84}
\Rightarrow \boxed{36}
$$

13. $ \frac{1}{20} = \frac{?}{160} $

20 × 8 = 160 → multiply numerator by 8:
$$
\frac{1 \times 8}{20 \times 8} = \frac{8}{160}
\Rightarrow \boxed{8}
$$

14. $ \frac{3}{50} = \frac{?}{150} $

50 × 3 = 150 → multiply numerator by 3:
$$
\frac{3 \times 3}{50 \times 3} = \frac{9}{150}
\Rightarrow \boxed{9}
$$

15. $ \frac{11}{30} = \frac{?}{120} $

30 × 4 = 120 → multiply numerator by 4:
$$
\frac{11 \times 4}{30 \times 4} = \frac{44}{120}
\Rightarrow \boxed{44}
$$

16. $ \frac{9}{25} = \frac{?}{100} $

25 × 4 = 100 → multiply numerator by 4:
$$
\frac{9 \times 4}{25 \times 4} = \frac{36}{100}
\Rightarrow \boxed{36}
$$

---

## ✔ Section C:

Now we're finding multiple equivalent fractions in a chain.

---

First Chain: $ \frac{2}{3} = \frac{?}{9} = \frac{12}{?} = \frac{?}{21} $

1. $ \frac{2}{3} = \frac{?}{9} $

3 × 3 = 9 → multiply numerator by 3:
$$
\frac{2 \times 3}{3 \times 3} = \frac{6}{9}
\Rightarrow \boxed{6}
$$

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

2 × 6 = 12 → multiply denominator by 6:
$$
\frac{2 \times 6}{3 \times 6} = \frac{12}{18}
\Rightarrow \boxed{18}
$$

3. $ \frac{2}{3} = \frac{?}{21} $

3 × 7 = 21 → multiply numerator by 7:
$$
\frac{2 \times 7}{3 \times 7} = \frac{14}{21}
\Rightarrow \boxed{14}
$$

So:
$$
\frac{2}{3} = \frac{6}{9} = \frac{12}{18} = \frac{14}{21}
$$

---

Second Chain: $ \frac{3}{5} = \frac{?}{25} = \frac{36}{?} = \frac{24}{?} $

1. $ \frac{3}{5} = \frac{?}{25} $

5 × 5 = 25 → multiply numerator by 5:
$$
\frac{3 \times 5}{5 \times 5} = \frac{15}{25}
\Rightarrow \boxed{15}
$$

2. $ \frac{3}{5} = \frac{36}{?} $

3 × 12 = 36 → multiply denominator by 12:
$$
\frac{3 \times 12}{5 \times 12} = \frac{36}{60}
\Rightarrow \boxed{60}
$$

3. $ \frac{3}{5} = \frac{24}{?} $

3 × 8 = 24 → multiply denominator by 8:
$$
\frac{3 \times 8}{5 \times 8} = \frac{24}{40}
\Rightarrow \boxed{40}
$$

So:
$$
\frac{3}{5} = \frac{15}{25} = \frac{36}{60} = \frac{24}{40}
$$

---

Third Chain: $ \frac{6}{7} = \frac{?}{14} = \frac{36}{?} = \frac{?}{56} $

1. $ \frac{6}{7} = \frac{?}{14} $

7 × 2 = 14 → multiply numerator by 2:
$$
\frac{6 \times 2}{7 \times 2} = \frac{12}{14}
\Rightarrow \boxed{12}
$$

2. $ \frac{6}{7} = \frac{36}{?} $

6 × 6 = 36 → multiply denominator by 6:
$$
\frac{6 \times 6}{7 \times 6} = \frac{36}{42}
\Rightarrow \boxed{42}
$$

3. $ \frac{6}{7} = \frac{?}{56} $

7 × 8 = 56 → multiply numerator by 8:
$$
\frac{6 \times 8}{7 \times 8} = \frac{48}{56}
\Rightarrow \boxed{48}
$$

So:
$$
\frac{6}{7} = \frac{12}{14} = \frac{36}{42} = \frac{48}{56}
$$

---

Fourth Chain: $ \frac{11}{20} = \frac{?}{40} = \frac{66}{?} = \frac{132}{?} $

1. $ \frac{11}{20} = \frac{?}{40} $

20 × 2 = 40 → multiply numerator by 2:
$$
\frac{11 \times 2}{20 \times 2} = \frac{22}{40}
\Rightarrow \boxed{22}
$$

2. $ \frac{11}{20} = \frac{66}{?} $

11 × 6 = 66 → multiply denominator by 6:
$$
\frac{11 \times 6}{20 \times 6} = \frac{66}{120}
\Rightarrow \boxed{120}
$$

3. $ \frac{11}{20} = \frac{132}{?} $

11 × 12 = 132 → multiply denominator by 12:
$$
\frac{11 \times 12}{20 \times 12} = \frac{132}{240}
\Rightarrow \boxed{240}
$$

So:
$$
\frac{11}{20} = \frac{22}{40} = \frac{66}{120} = \frac{132}{240}
$$

---

## ✔ Final Answer Summary:

Section A:

```
1/2 = 6/12 1/3 = 7/21 1/6 = 9/54 1/7 = 2/14
1/9 = 5/45 1/8 = 4/32 1/12 = 3/36 1/8 = 4/32
1/5 = 9/45 1/11 = 4/44 1/6 = 12/72 1/7 = 7/49
1/8 = 3/24 1/6 = 7/42 1/12 = 10/120 1/9 = 7/63
```

Section B:

```
2/3 = 4/6 4/5 = 12/15 3/4 = 21/28 2/5 = 10/25
2/9 = 16/72 9/10 = 18/20 4/7 = 16/28 3/11 = 27/99
7/8 = 49/56 2/3 = 24/36 5/6 = 40/48 3/7 = 36/84
1/20 = 8/160 3/50 = 9/150 11/30 = 44/120 9/25 = 36/100
```

Section C:

```
2/3 = 6/9 = 12/18 = 14/21
3/5 = 15/25 = 36/60 = 24/40
6/7 = 12/14 = 36/42 = 48/56
11/20 = 22/40 = 66/120 = 132/240
```

✔ All problems solved using multiplication of numerator and denominator by the same factor to maintain equivalence.

Let me know if you'd like this as a printable PDF or with visual diagrams!