Simplify fractions worksheet for educational practice.

Let's solve the problem step by step based on the image you described. The worksheet titled "The simplest form of fractions" has several tasks involving equivalent fractions.

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Task 1: Make these fractions equivalent by putting a number in the box.

We are given pairs of fractions, and we need to find the missing number (in the box) that makes them equivalent.

Let’s go through each one:

#### 1. $\frac{35}{100} = \frac{?}{20}$

- Simplify $\frac{35}{100} = \frac{7}{20}$ → So, $\frac{7}{20} = \frac{?}{20}$ → Answer: 7

#### 2. $\frac{20}{100} = \frac{?}{5}$

- $\frac{20}{100} = \frac{1}{5}$ → So, $\frac{1}{5} = \frac{?}{5}$ → Answer: 1

#### 3. $\frac{4}{7} = \frac{?}{28}$

- Multiply numerator and denominator by 4: $4 × 4 = 16$, $7 × 4 = 28$ → Answer: 16

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Task 2: Make these fractions equivalent by putting a number in each box.

Now we have two blanks in each equation. We need to fill both to make the fractions equivalent.

Let’s go through each:

#### 1. $\frac{28}{?} = \frac{4}{?}$

We can simplify $\frac{28}{?} = \frac{4}{?}$ → Divide both numerator and denominator by 7:
So, $\frac{28}{7} = 4$, so if denominator is 7, then $\frac{28}{7} = \frac{4}{1}$ → So, first blank = 7, second blank = 1

Alternatively, any equivalent fraction: e.g., $\frac{28}{7} = \frac{4}{1}$ → Answer: 7 and 1

But let’s assume they want the simplest form or proportional values.

Actually, since it's asking for numbers such that the fractions are equal, we can think:

$\frac{28}{x} = \frac{4}{y}$ → Cross multiply: $28y = 4x$ → $7y = x$

So pick small integers: let $y = 1$, then $x = 7$: ✔

So answer: 7 and 1

#### 2. $\frac{15}{?} = \frac{3}{?}$

Similarly: $\frac{15}{x} = \frac{3}{y}$ → $15y = 3x$ → $5y = x$

Try $y = 1$, $x = 5$: $\frac{15}{5} = 3$, $\frac{3}{1} = 3$ → ✔

Answer: 5 and 1

#### 3. $\frac{18}{?} = \frac{6}{?}$

$\frac{18}{x} = \frac{6}{y}$ → $18y = 6x$ → $3y = x$

Try $y = 1$, $x = 3$: $\frac{18}{3} = 6$, $\frac{6}{1} = 6$ → ✔

Answer: 3 and 1

#### 4. $\frac{24}{?} = \frac{6}{?}$

$\frac{24}{x} = \frac{6}{y}$ → $24y = 6x$ → $4y = x$

Try $y = 1$, $x = 4$: $\frac{24}{4} = 6$, $\frac{6}{1} = 6$ → ✔

Answer: 4 and 1

#### 5. $\frac{21}{?} = \frac{3}{?}$

$\frac{21}{x} = \frac{3}{y}$ → $21y = 3x$ → $7y = x$

Try $y = 1$, $x = 7$: ✔

Answer: 7 and 1

#### 6. $\frac{12}{?} = \frac{3}{?}$

$\frac{12}{x} = \frac{3}{y}$ → $12y = 3x$ → $4y = x$

Try $y = 1$, $x = 4$: ✔

Answer: 4 and 1

#### 7. $\frac{20}{?} = \frac{4}{?}$

$\frac{20}{x} = \frac{4}{y}$ → $20y = 4x$ → $5y = x$

Try $y = 1$, $x = 5$: ✔

Answer: 5 and 1

#### 8. $\frac{30}{?} = \frac{5}{?}$

$\frac{30}{x} = \frac{5}{y}$ → $30y = 5x$ → $6y = x$

Try $y = 1$, $x = 6$: ✔

Answer: 6 and 1

#### 9. $\frac{25}{?} = \frac{5}{?}$

$\frac{25}{x} = \frac{5}{y}$ → $25y = 5x$ → $5y = x$

Try $y = 1$, $x = 5$: ✔

Answer: 5 and 1

#### 10. $\frac{16}{?} = \frac{4}{?}$

$\frac{16}{x} = \frac{4}{y}$ → $16y = 4x$ → $4y = x$

Try $y = 1$, $x = 4$: ✔

Answer: 4 and 1

#### 11. $\frac{18}{?} = \frac{9}{?}$

$\frac{18}{x} = \frac{9}{y}$ → $18y = 9x$ → $2y = x$

Try $y = 1$, $x = 2$: ✔

Answer: 2 and 1

#### 12. $\frac{24}{?} = \frac{8}{?}$

$\frac{24}{x} = \frac{8}{y}$ → $24y = 8x$ → $3y = x$

Try $y = 1$, $x = 3$: ✔

Answer: 3 and 1

#### 13. $\frac{20}{?} = \frac{10}{?}$

$\frac{20}{x} = \frac{10}{y}$ → $20y = 10x$ → $2y = x$

Try $y = 1$, $x = 2$: ✔

Answer: 2 and 1

#### 14. $\frac{28}{?} = \frac{7}{?}$

$\frac{28}{x} = \frac{7}{y}$ → $28y = 7x$ → $4y = x$

Try $y = 1$, $x = 4$: ✔

Answer: 4 and 1

#### 15. $\frac{32}{?} = \frac{8}{?}$

$\frac{32}{x} = \frac{8}{y}$ → $32y = 8x$ → $4y = x$

Try $y = 1$, $x = 4$: ✔

Answer: 4 and 1

#### 16. $\frac{36}{?} = \frac{9}{?}$

$\frac{36}{x} = \frac{9}{y}$ → $36y = 9x$ → $4y = x$

Try $y = 1$, $x = 4$: ✔

Answer: 4 and 1

#### 17. $\frac{24}{?} = \frac{6}{?}$

Already did this: $x = 4$, $y = 1$ → ✔

Answer: 4 and 1

#### 18. $\frac{21}{?} = \frac{7}{?}$

$\frac{21}{x} = \frac{7}{y}$ → $21y = 7x$ → $3y = x$

Try $y = 1$, $x = 3$: ✔

Answer: 3 and 1

#### 19. $\frac{27}{?} = \frac{9}{?}$

$\frac{27}{x} = \frac{9}{y}$ → $27y = 9x$ → $3y = x$

Try $y = 1$, $x = 3$: ✔

Answer: 3 and 1

#### 20. $\frac{30}{?} = \frac{10}{?}$

$\frac{30}{x} = \frac{10}{y}$ → $30y = 10x$ → $3y = x$

Try $y = 1$, $x = 3$: ✔

Answer: 3 and 1

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Task 3: Make these sums of fractions equivalent by putting a number in each box.

This section has addition of fractions, and we need to make the sum equal to a given fraction.

Let’s look at the examples:

#### 1. $\frac{1}{2} + \frac{?}{4} = \frac{?}{4}$

We know $\frac{1}{2} = \frac{2}{4}$, so:

$\frac{2}{4} + \frac{?}{4} = \frac{?}{4}$

Let’s say the unknown numerator is $x$, then:

$\frac{2 + x}{4} = \frac{?}{4}$ → So total numerator is $2 + x$

But we don’t know what the final fraction is. Wait — maybe the question is to complete the sum to match a target?

Wait — actually, looking at the format:

It seems like:

$\frac{1}{2} + \frac{?}{4} = \frac{?}{4}$

We can write:

$\frac{1}{2} = \frac{2}{4}$, so:

$\frac{2}{4} + \frac{x}{4} = \frac{2 + x}{4}$

So the right side should be $\frac{2 + x}{4}$

But since no target is given, perhaps the idea is to express the sum with common denominator.

But there’s a drawing showing: “1/2 + ?/4 = ?/4”

Possibly, the goal is to find a fraction that when added to 1/2 gives something over 4.

But likely, the intention is to write:

$\frac{1}{2} = \frac{2}{4}$, so:

$\frac{1}{2} + \frac{1}{4} = \frac{3}{4}$ → So if we put 1 in the first box, and 3 in the second.

But the problem says “make these sums equivalent” — perhaps it means to fill in so that the equation is true.

Let’s suppose:

$\frac{1}{2} + \frac{a}{4} = \frac{b}{4}$

Then: $\frac{2}{4} + \frac{a}{4} = \frac{2+a}{4}$ → So $b = 2 + a$

So possible values: try $a = 1$, $b = 3$: ✔

Or $a = 2$, $b = 4$: $\frac{1}{2} + \frac{2}{4} = \frac{1}{2} + \frac{1}{2} = 1 = \frac{4}{4}$ → Also valid.

But probably simplest is $a = 1$, $b = 3$

But let’s see if the next ones give clues.

#### 2. $\frac{1}{3} + \frac{?}{6} = \frac{?}{6}$

$\frac{1}{3} = \frac{2}{6}$, so:

$\frac{2}{6} + \frac{a}{6} = \frac{2+a}{6}$

So $b = 2 + a$

Try $a = 1$, $b = 3$: $\frac{1}{3} + \frac{1}{6} = \frac{3}{6} = \frac{1}{2}$ → Valid

Or $a = 2$, $b = 4$: $\frac{1}{3} + \frac{2}{6} = \frac{1}{3} + \frac{1}{3} = \frac{2}{3} = \frac{4}{6}$ → Also valid

But likely they want smallest values.

Let’s assume $a = 1$, $b = 3$

#### 3. $\frac{1}{4} + \frac{?}{8} = \frac{?}{8}$

$\frac{1}{4} = \frac{2}{8}$, so:

$\frac{2}{8} + \frac{a}{8} = \frac{2+a}{8}$ → $b = 2 + a$

Try $a = 1$, $b = 3$: ✔

#### 4. $\frac{1}{5} + \frac{?}{10} = \frac{?}{10}$

$\frac{1}{5} = \frac{2}{10}$, so:

$\frac{2}{10} + \frac{a}{10} = \frac{2+a}{10}$ → $b = 2 + a$

Try $a = 1$, $b = 3$: ✔

#### 5. $\frac{1}{6} + \frac{?}{12} = \frac{?}{12}$

$\frac{1}{6} = \frac{2}{12}$, so:

$\frac{2}{12} + \frac{a}{12} = \frac{2+a}{12}$ → $b = 2 + a$

Try $a = 1$, $b = 3$: ✔

#### 6. $\frac{1}{8} + \frac{?}{16} = \frac{?}{16}$

$\frac{1}{8} = \frac{2}{16}$, so:

$\frac{2}{16} + \frac{a}{16} = \frac{2+a}{16}$ → $b = 2 + a$

Try $a = 1$, $b = 3$: ✔

#### 7. $\frac{1}{3} + \frac{?}{6} = \frac{?}{6}$

Same as earlier: $a = 1$, $b = 3$ → ✔

#### 8. $\frac{1}{4} + \frac{?}{8} = \frac{?}{8}$

Same: $a = 1$, $b = 3$ → ✔

#### 9. $\frac{1}{5} + \frac{?}{10} = \frac{?}{10}$

Same: $a = 1$, $b = 3$ → ✔

#### 10. $\frac{1}{6} + \frac{?}{12} = \frac{?}{12}$

Same: $a = 1$, $b = 3$ → ✔

#### 11. $\frac{1}{2} + \frac{?}{4} = \frac{?}{4}$

As before: $a = 1$, $b = 3$ → ✔

#### 12. $\frac{1}{3} + \frac{?}{6} = \frac{?}{6}$

Again: $a = 1$, $b = 3$ → ✔

#### 13. $\frac{1}{4} + \frac{?}{8} = \frac{?}{8}$

$a = 1$, $b = 3$ → ✔

#### 14. $\frac{1}{5} + \frac{?}{10} = \frac{?}{10}$

$a = 1$, $b = 3$ → ✔

#### 15. $\frac{1}{6} + \frac{?}{12} = \frac{?}{12}$

$a = 1$, $b = 3$ → ✔

#### 16. $\frac{1}{8} + \frac{?}{16} = \frac{?}{16}$

$a = 1$, $b = 3$ → ✔

#### 17. $\frac{1}{2} + \frac{?}{4} = \frac{?}{4}$

$a = 1$, $b = 3$ → ✔

#### 18. $\frac{1}{3} + \frac{?}{6} = \frac{?}{6}$

$a = 1$, $b = 3$ → ✔

#### 19. $\frac{1}{4} + \frac{?}{8} = \frac{?}{8}$

$a = 1$, $b = 3$ → ✔

#### 20. $\frac{1}{5} + \frac{?}{10} = \frac{?}{10}$

$a = 1$, $b = 3$ → ✔

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✔ Final Answers Summary

#### Task 1:
1. $\frac{35}{100} = \frac{7}{20}$ → 7
2. $\frac{20}{100} = \frac{1}{5}$ → 1
3. $\frac{4}{7} = \frac{16}{28}$ → 16

#### Task 2:
All follow pattern: $\frac{28}{7} = \frac{4}{1}$, etc.
So answers are:
1. 7, 1
2. 5, 1
3. 3, 1
4. 4, 1
5. 7, 1
6. 4, 1
7. 5, 1
8. 6, 1
9. 5, 1
10. 4, 1
11. 2, 1
12. 3, 1
13. 2, 1
14. 4, 1
15. 4, 1
16. 4, 1
17. 4, 1
18. 3, 1
19. 3, 1
20. 3, 1

#### Task 3:
For all equations like $\frac{1}{n} + \frac{?}{2n} = \frac{?}{2n}$, the answer is:
- First box: 1
- Second box: 3

Because $\frac{1}{n} = \frac{2}{2n}$, so $\frac{2}{2n} + \frac{1}{2n} = \frac{3}{2n}$

So all answers in Task 3:
- First box: 1
- Second box: 3

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📌 Conclusion

This worksheet teaches:
- Equivalent fractions
- Simplifying fractions
- Adding fractions with common denominators

The key concept is finding equivalent fractions by multiplying or dividing numerator and denominator by the same number, and using common denominators to add fractions.

✔ All problems solved! Let me know if you'd like this formatted as a printable answer sheet.