Which is larger, 3/5 or 5/8?

24/40 < 25/40, so 5/8 is larger

Write 2/3, 5/8 and 7/12 in ascending order.

16/24, 15/24, 14/24, so 7/12, 5/8, 2/3

Equivalent Fractions Worksheets with Answers (Free)

Q: What are equivalent fractions?

Equivalent fractions have the same value but different numerators and denominators, such as one half, two quarters and four eighths. You make them by multiplying or dividing the top and bottom by the same number.

Q: Do the equivalent fractions worksheets include answers?

Yes. Every question on a generated worksheet comes with a fully worked solution, and every example on this page shows each step.

Choose your year level

Equivalent fractions at each year level, matched to the textbook chapters most Victorian schools use: a free printable worksheet with answers, sample questions, and an auto-marked test teachers can share.

Free Year 7 equivalent fractions worksheet

10 questions, then the answers with worked solutions. Printable PDF, no sign-up.

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Auto-marked test for your class

Teachers: share one link and every student is marked straight away, with worked solutions.

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Printable practice exam

Mix in harder questions, with marks and a suggested time.

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Year 7 topics covered

Equivalent fractions and simplified fractions
Ordering fractions

Sample Year 7 equivalent fractions questions

Equivalent fractions and simplified fractions
Write $\dfrac{35}{56}$ in simplest form.
Show the answer
Key idea: Divide the numerator and denominator by their highest common factor.
1. Factors of $35$ : 1, 5, 7, 35. Factors of $56$ include $7$ ( $56 = 7 \times 8$ )
2. HCF $= 7$
3. $\dfrac{35 \div 7}{56 \div 7} = \dfrac{5}{8}$
Answer: $\dfrac{5}{8}$
Ordering fractions
Which is larger, $\dfrac{5}{8}$ or $\dfrac{3}{5}$ ?
Show the answer
Key idea: Write both fractions with a common denominator, then compare numerators.
1. Lowest common denominator of $8$ and $5$ is $40$
2. $\dfrac{5}{8} = \dfrac{25}{40}$ and $\dfrac{3}{5} = \dfrac{24}{40}$
3. $25 > 24$ , so $\dfrac{5}{8}$ is larger
Answer: $\dfrac{5}{8}$
Equivalent fractions and simplified fractions
Find the missing numbers:

(a) $\dfrac{3}{7} = \dfrac{}{35}$

(b) $\dfrac{3}{7} = \dfrac{12}{}$
Show the answer
Key idea: Equivalent fractions are made by multiplying the numerator and denominator by the same number.
1. (a) $7 \times 5 = 35$ , so multiply the numerator by $5$ too: $3 \times 5 = 15$
2. (b) $3 \times 4 = 12$ , so multiply the denominator by $4$ too: $7 \times 4 = 28$
Answer: (a) $15$ (b) $28$
Ordering fractions
Write in ascending order: $\dfrac{2}{3}, \dfrac{7}{12}, \dfrac{3}{4}, \dfrac{5}{6}$
Show the answer
Key idea: Ascending means smallest to largest. Use a common denominator of $12$ .
1. $\dfrac{2}{3} = \dfrac{8}{12}$ , $\dfrac{7}{12}$ , $\dfrac{3}{4} = \dfrac{9}{12}$ , $\dfrac{5}{6} = \dfrac{10}{12}$
2. Order the numerators: 7, 8, 9, 10
Answer: $\dfrac{7}{12}, \dfrac{2}{3}, \dfrac{3}{4}, \dfrac{5}{6}$

Free Year 8 equivalent fractions worksheet

10 questions, then the answers with worked solutions. Printable PDF, no sign-up.

Download the PDF

Auto-marked test for your class

Teachers: share one link and every student is marked straight away, with worked solutions.

Create a test

Printable practice exam

Mix in harder questions, with marks and a suggested time.

Build an exam

Year 8 topics covered

Equivalent fractions

Sample Year 8 equivalent fractions questions

Equivalent fractions
Write $\dfrac{84}{126}$ in simplest form.
Show the answer
Key idea: Divide the numerator and denominator by their highest common factor.
1. $84 = 2^2 \times 3 \times 7$ and $126 = 2 \times 3^2 \times 7$ , so the HCF is $2 \times 3 \times 7 = 42$
2. $\dfrac{84 \div 42}{126 \div 42} = \dfrac{2}{3}$
Answer: $\dfrac{2}{3}$
Equivalent fractions
Find the missing numbers to make the fractions equivalent:
$\frac{3}{8} = \frac{\Box}{40} = \frac{27}{\Box}$
Show the answer
Key idea: Equivalent fractions are made by multiplying the numerator and denominator by the same number.
1. $8 \times 5 = 40$ , so the numerator is $3 \times 5 = 15$
2. $3 \times 9 = 27$ , so the denominator is $8 \times 9 = 72$
Answer: $\dfrac{3}{8} = \dfrac{15}{40} = \dfrac{27}{72}$
Equivalent fractions
(a) Write $4\frac{3}{7}$ as an improper fraction.

(b) Write $\dfrac{47}{6}$ as a mixed number.
Show the answer
Key idea: A whole number of $1$ equals $\frac{7}{7}$ sevenths or $\frac{6}{6}$ sixths, so convert using multiplication and division.
1. (a) $4 \times 7 + 3 = 31$ , so $4\frac{3}{7} = \dfrac{31}{7}$
2. (b) $47 \div 6 = 7$ remainder $5$ , so $\dfrac{47}{6} = 7\frac{5}{6}$
Answer: (a) $\dfrac{31}{7}$ (b) $7\frac{5}{6}$
Equivalent fractions
Write these fractions in ascending order:
$\frac{3}{4}, \frac{5}{8}, \frac{7}{12}, \frac{2}{3}$
Show the answer
Key idea: Write each fraction with the lowest common denominator, then compare numerators.
1. The LCD of 4, 8, 12, 3 is $24$
2. $\dfrac{3}{4} = \dfrac{18}{24}$ , $\dfrac{5}{8} = \dfrac{15}{24}$ , $\dfrac{7}{12} = \dfrac{14}{24}$ , $\dfrac{2}{3} = \dfrac{16}{24}$
3. In order of numerators: 14, 15, 16, 18
Answer: $\dfrac{7}{12}, \dfrac{5}{8}, \dfrac{2}{3}, \dfrac{3}{4}$

Equivalent fractions, explained

One idea sits under all of it: multiply or divide the top and bottom by the same number and the value does not change.

1. What equivalent fractions are

Equivalent fractions are equal in value even though the numbers are different. Shade $2$ of $3$ equal parts, or $4$ of $6$ , or $8$ of $12$ , and the same amount is shaded:

$\frac{2}{3} = \frac{4}{6} = \frac{8}{12}$

2. Making equivalent fractions

Multiply the numerator and denominator by the same number. Multiplying by $\frac{4}{4}$ is multiplying by $1$ , so the value stays the same:

$\frac{3}{5} = \frac{3 \times 4}{5 \times 4} = \frac{12}{20}$

Never add the same number to the top and bottom: $\frac{1}{2}$ and $\frac{2}{3}$ are not equal.

3. Finding a missing number

Work out what the known numerator or denominator was multiplied or divided by, then do the same to the other one. In $\frac{3}{4} = \frac{?}{28}$ , the denominator was multiplied by $7$ :

$\frac{3}{4} = \frac{3 \times 7}{4 \times 7} = \frac{21}{28}$

In $\frac{15}{25} = \frac{3}{?}$ , the numerator was divided by $5$ , so the missing number is $25 \div 5 = 5$ .

4. Simplifying to simplest form

Divide the numerator and denominator by their highest common factor (HCF). For $\frac{24}{36}$ the HCF is $12$ :

$\frac{24}{36} = \frac{24 \div 12}{36 \div 12} = \frac{2}{3}$

A fraction is in simplest form when the only common factor of the top and bottom is $1$ . Dividing by a smaller common factor works too, but you may need more than one step.

5. Checking whether two fractions are equivalent

Simplify both fractions. If they reduce to the same fraction, they are equivalent:

$\frac{6}{9} = \frac{2}{3} \frac{10}{15} = \frac{2}{3}$

So $\frac{6}{9}$ and $\frac{10}{15}$ are equivalent. You can also cross-multiply: $6 \times 15 = 90$ and $9 \times 10 = 90$ , and equal products mean equal fractions.

6. Comparing and ordering fractions

Rewrite the fractions with a common denominator, then compare the numerators. To compare $\frac{5}{6}$ and $\frac{7}{9}$ , use $18$ :

$\frac{5}{6} = \frac{15}{18} \frac{7}{9} = \frac{14}{18}$

Since $15 > 14$ , $\frac{5}{6}$ is larger. The same method puts a whole list of fractions in order.

Quick check: 10 questions

Try each one, then open the answer.

Find the missing number: $\frac{1}{2} = \frac{?}{8}$ .
Answer
$4$
Write two fractions equivalent to $\frac{3}{4}$ .
Answer
For example, $\frac{6}{8}$ and $\frac{9}{12}$
Find the missing number: $\frac{2}{5} = \frac{?}{35}$ .
Answer
$14$
Simplify $\frac{15}{20}$ .
Answer
$\frac{3}{4}$
Simplify $\frac{36}{48}$ using the HCF.
Answer
The HCF is $12$ , so $\frac{3}{4}$
Find the missing number: $\frac{21}{?} = \frac{3}{8}$ .
Answer
$56$
Are $\frac{12}{18}$ and $\frac{20}{30}$ equivalent?
Answer
Yes, both simplify to $\frac{2}{3}$
Write $\frac{84}{126}$ in simplest form.
Answer
The HCF is $42$ , so $\frac{2}{3}$
Which is larger, $\frac{3}{5}$ or $\frac{5}{8}$ ?
Answer
$\frac{24}{40} < \frac{25}{40}$ , so $\frac{5}{8}$ is larger
Write $\frac{2}{3}$ , $\frac{5}{8}$ and $\frac{7}{12}$ in ascending order.
Answer
$\frac{16}{24}$ , $\frac{15}{24}$ , $\frac{14}{24}$ , so $\frac{7}{12}, \frac{5}{8}, \frac{2}{3}$

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Six questions across Foundation, Standard and Extension, with full worked solutions, written to the Australian Curriculum.

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Questions

What are equivalent fractions?

Equivalent fractions have the same value but different numerators and denominators, such as one half, two quarters and four eighths. You make them by multiplying or dividing the top and bottom by the same number.

How do you write a fraction in simplest form?

Divide the numerator and denominator by their highest common factor. When the only common factor left is 1, the fraction is in simplest form.

Do the equivalent fractions worksheets include answers?

Yes. Every question on a generated worksheet comes with a fully worked solution, and every example on this page shows each step.

Equivalent fractions worksheets with answers

Choose your year level

Equivalent fractions, explained

1. What equivalent fractions are

2. Making equivalent fractions

3. Finding a missing number

4. Simplifying to simplest form

5. Checking whether two fractions are equivalent

6. Comparing and ordering fractions

Quick check: 10 questions

Generate a free maths worksheet

Practice built from mistakes.

Questions

What are equivalent fractions?

How do you write a fraction in simplest form?

Do the equivalent fractions worksheets include answers?

More skill worksheets

Better maths marks start with the next wrong answer.

Choose your year level

Equivalent fractions, explained

1. What equivalent fractions are

2. Making equivalent fractions

3. Finding a missing number

4. Simplifying to simplest form

5. Checking whether two fractions are equivalent

6. Comparing and ordering fractions

Quick check: 10 questions

Generate a free maths worksheet

Practice built from mistakes.

Topic worksheets with worked examples

Questions

What are equivalent fractions?

How do you write a fraction in simplest form?

Do the equivalent fractions worksheets include answers?

More skill worksheets

Better maths marks start with the next wrong answer.