Equivalent fractions worksheet with blank spaces for students to fill in missing numerators or denominators.

Let's solve each of these equivalent fraction problems step by step. The goal is to find the missing numerator or denominator so that the two fractions are equivalent (equal in value).

We use the principle:
If $\frac{a}{b} = \frac{c}{d}$, then $a \times d = b \times c$.

Alternatively, we can multiply or divide both the numerator and denominator by the same number to get an equivalent fraction.

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Column 1

1. $\frac{7}{8} = \frac{\square}{24}$
Multiply numerator and denominator by 3:
$7 \times 3 = 21$, $8 \times 3 = 24$ → 21

2. $\frac{7}{3} = \frac{14}{\square}$
Numerator doubled: $7 \times 2 = 14$, so denominator must also double: $3 \times 2 = 6$ → 6

3. $\frac{4}{9} = \frac{\square}{45}$
$9 \times 5 = 45$, so $4 \times 5 = 20$ → 20

4. $\frac{7}{2} = \frac{21}{\square}$
$7 \times 3 = 21$, so $2 \times 3 = 6$ → 6

5. $\frac{3}{4} = \frac{\square}{16}$
$4 \times 4 = 16$, so $3 \times 4 = 12$ → 12

6. $\frac{3}{2} = \frac{18}{\square}$
$3 \times 6 = 18$, so $2 \times 6 = 12$ → 12

7. $\frac{8}{1} = \frac{\square}{2}$
$1 \times 2 = 2$, so $8 \times 2 = 16$ → 16

8. $\frac{3}{6} = \frac{15}{\square}$
Simplify $\frac{3}{6} = \frac{1}{2}$, so $\frac{15}{x} = \frac{1}{2}$ → $x = 30$
Or: $3 \times 5 = 15$, so $6 \times 5 = 30$ → 30

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Column 2

1. $\frac{3}{4} = \frac{\square}{12}$
$4 \times 3 = 12$, so $3 \times 3 = 9$ → 9

2. $\frac{5}{8} = \frac{30}{\square}$
$5 \times 6 = 30$, so $8 \times 6 = 48$ → 48

3. $\frac{2}{8} = \frac{\square}{32}$
$8 \times 4 = 32$, so $2 \times 4 = 8$ → 8

4. $\frac{10}{8} = \frac{100}{\square}$
$10 \times 10 = 100$, so $8 \times 10 = 80$ → 80

5. $\frac{5}{3} = \frac{\square}{6}$
$3 \times 2 = 6$, so $5 \times 2 = 10$ → 10

6. $\frac{2}{1} = \frac{2}{\square}$
This is tricky. Left side is $2/1 = 2$. Right side is $2/x = 2$, so $x = 1$ → 1

7. $\frac{9}{4} = \frac{\square}{28}$
$4 \times 7 = 28$, so $9 \times 7 = 63$ → 63

8. $\frac{7}{1} = \frac{14}{\square}$
$7 \times 2 = 14$, so $1 \times 2 = 2$ → 2

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Column 3

1. $\frac{9}{7} = \frac{\square}{21}$
$7 \times 3 = 21$, so $9 \times 3 = 27$ → 27

2. $\frac{9}{4} = \frac{36}{\square}$
$9 \times 4 = 36$, so $4 \times 4 = 16$ → 16

3. $\frac{9}{7} = \frac{\square}{7}$
Denominator is same, so numerator must be same → 9

4. $\frac{2}{6} = \frac{12}{\square}$
$2 \times 6 = 12$, so $6 \times 6 = 36$ → 36

5. $\frac{7}{9} = \frac{\square}{36}$
$9 \times 4 = 36$, so $7 \times 4 = 28$ → 28

6. $\frac{5}{9} = \frac{40}{\square}$
$5 \times 8 = 40$, so $9 \times 8 = 72$ → 72

7. $\frac{10}{5} = \frac{\square}{50}$
$10 \times 10 = 100$, $5 \times 10 = 50$ → 100

8. $\frac{9}{5} = \frac{72}{\square}$
$9 \times 8 = 72$, so $5 \times 8 = 40$ → 40

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✔ Final Answers (Filling in the blanks):

```
7/8 = 21/24
7/3 = 14/6
4/9 = 20/45
7/2 = 21/6
3/4 = 12/16
3/2 = 18/12
8/1 = 16/2
3/6 = 15/30

3/4 = 9/12
5/8 = 30/48
2/8 = 8/32
10/8 = 100/80
5/3 = 10/6
2/1 = 2/1
9/4 = 63/28
7/1 = 14/2

9/7 = 27/21
9/4 = 36/16
9/7 = 9/7
2/6 = 12/36
7/9 = 28/36
5/9 = 40/72
10/5 = 100/50
9/5 = 72/40
```

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🟩 Summary of Missing Values:

| Problem | Answer |
|--------|--------|
| 1 | 21 |
| 2 | 6 |
| 3 | 20 |
| 4 | 6 |
| 5 | 12 |
| 6 | 12 |
| 7 | 16 |
| 8 | 30 |
| 9 | 9 |
| 10 | 48 |
| 11 | 8 |
| 12 | 80 |
| 13 | 10 |
| 14 | 1 |
| 15 | 63 |
| 16 | 2 |
| 17 | 27 |
| 18 | 16 |
| 19 | 9 |
| 20 | 36 |
| 21 | 28 |
| 22 | 72 |
| 23 | 100 |
| 24 | 40 |

✔ All solved! Let me know if you'd like a printable version or explanation for any specific one.