What exactly is in the download?

A 31-question, 54-mark sheet with branded header, objectives, skills, instructions, name and date fields, page numbering, footer branding, copyright, worksheet ID TN-MATH-GR8-33206, version v2.0 and a QR code back to this page.

Does it print correctly on US Letter?

Yes. Switch paper size in the download panel — margins and typography are identical, so nothing reflows or clips.

Is the answer key included?

This version prints answers inline, followed by the full solutions and teacher pack pages.

Worksheet · TN-MATH-GR8-33206 · v2.0

Equivalent Fractions — Worksheet with Answers

A single-focus worksheet on equivalent fractions for Grade 8 Math. Nothing else from fractions is mixed in — every question, from warm-up to reflection, assesses this one objective and builds towards mastery.

CoreCommon Core30 min54 marksAnswers included

Self-marking copy with worked solutions.

Grade

Grade 8

Subject

Math

Topic

Fractions

Subtopic

Equivalent Fractions

Curriculum

Common Core

Difficulty

Core

Time

30 min

Questions

Total marks

Worksheet ID

TN-MATH-GR8-33206

Version

v2.0

Format

A4 · US Letter

Preview & download

Print-ready · high-resolution PDF · minimal ink

FreeMathWorksheet

Worksheet with Answers

TN-MATH-GR8-33206 · v2.0

Equivalent Fractions

Grade 8 · Math · Fractions · Common Core

Grade

Grade 8

Subject

Math

Topic

Fractions

Subtopic

Equivalent Fractions

Curriculum

Common Core

Difficulty

Core

Time

30 minutes

Total marks

Student name

Teacher name

Date

Learning objectives

Recognise equivalent fractions accurately in math contexts.
Explain the underlying rule of equivalent fractions in the student's own words.
Apply equivalent fractions to multi-step and unfamiliar problems.
Justify a chosen method and identify errors in another student's work.

Skills assessed

Fluency and recall
Method and setting out
Reasoning and justification
Problem solving in context
Self-assessment

Instructions

Write your name, your teacher's name and the date in the header.
Answer every question in the space provided. Continue on the back if needed.
Show all working — method marks are awarded even when the final answer is wrong.
Aim to finish in about 30 minutes.
Complete the reflection box at the end before you hand the sheet in.

Warm-up

Bloom: Remember · 4 marks

Answer quickly. These check you are ready for the topic.

1.Fill in the missing number: 6/8 = □/48
[1]
Answer36
2.Fill in the missing number: 2/3 = □/18
[1]
Answer12
3.Fill in the missing number: 1/4 = □/16
[1]
Answer4
4.Fill in the missing number: 2/4 = □/12
[1]
Answer6

Recall

Bloom: Remember · 4 marks

Complete from memory. No calculator, no notes.

1.Fill in the missing number: 6/7 = □/21
[1]
Answer18
2.Fill in the missing number: 1/2 = □/12
[1]
Answer6
3.Fill in the missing number: 6/8 = □/48
[1]
Answer36
4.Fill in the missing number: 6/9 = □/27
[1]
Answer18

FreeMathWorksheet · Grade 8 Math

Equivalent Fractions

Basic Practice

Bloom: Understand · 5 marks

Work through each item. Show the step you used.

1.Fill in the missing number: 3/6 = □/18
[1]
Answer9
2.Fill in the missing number: 1/3 = □/18
[1]
Answer6
3.Fill in the missing number: 4/8 = □/32
[1]
Answer16
4.Fill in the missing number: 5/7 = □/35
[1]
Answer25
5.Fill in the missing number: 1/5 = □/25
[1]
Answer5

Guided Practice

Bloom: Understand · 8 marks

The first step is given. Finish the reasoning.

1.Write 16/20 in its simplest form, and state the factor you divided by.
[2]
Answer4/5 (divided by 4)
2.Write 10/40 in its simplest form, and state the factor you divided by.
[2]
Answer1/4 (divided by 10)
3.Write 15/30 in its simplest form, and state the factor you divided by.
[2]
Answer1/2 (divided by 15)
4.Write 10/12 in its simplest form, and state the factor you divided by.
[2]
Answer5/6 (divided by 2)

FreeMathWorksheet · Grade 8 Math

Equivalent Fractions

Independent Practice

Bloom: Apply · 10 marks

No scaffolding. Set out your full method.

1.Write 10/12 in its simplest form, and state the factor you divided by.
[2]
Answer5/6 (divided by 2)
2.Write 12/18 in its simplest form, and state the factor you divided by.
[2]
Answer2/3 (divided by 6)
3.Write 12/30 in its simplest form, and state the factor you divided by.
[2]
Answer2/5 (divided by 6)
4.Write 3/21 in its simplest form, and state the factor you divided by.
[2]
Answer1/7 (divided by 3)
5.Write 18/54 in its simplest form, and state the factor you divided by.
[2]
Answer1/3 (divided by 18)

Challenge Questions

Bloom: Analyse · 9 marks

Harder items. Attempt every one, even partially.

1.Are 1/4 and 3/13 equivalent? Justify your answer with a calculation.
[3]
AnswerNo — the denominators were not scaled by the same factor.
2.Are 2/3 and 18/28 equivalent? Justify your answer with a calculation.
[3]
AnswerNo — the denominators were not scaled by the same factor.
3.Are 1/7 and 6/43 equivalent? Justify your answer with a calculation.
[3]
AnswerNo — the denominators were not scaled by the same factor.

FreeMathWorksheet · Grade 8 Math

Equivalent Fractions

Real-life Application

Bloom: Apply · 6 marks

Use the skill in context. State units in your answer.

1.A recipe uses 2/9 of a litre of milk. A baker makes 2 batches. Write the total as a fraction with denominator 18, then simplify it.
[3]
Answer4/9 litres = 4/9 (simplified where possible)
2.A recipe uses 3/7 of a litre of milk. A baker makes 2 batches. Write the total as a fraction with denominator 14, then simplify it.
[3]
Answer6/7 litres = 6/7 (simplified where possible)

Critical Thinking

Bloom: Evaluate · 8 marks

Explain your reasoning in full sentences.

1.Explain why a student's method for equivalent fractions is or is not efficient.
[4]
AnswerAccept any correct response that applies the equivalent fractions rule accurately.
2.Compare and justify a student's method for equivalent fractions is or is not efficient.
[4]
AnswerAccept any correct response that applies the equivalent fractions rule accurately.

Reflection

Bloom: Create · 0 marks

Not marked. Answer honestly — this guides your next worksheet.

1.Reflect on how confident you feel with equivalent fractions and what you will practise next.
[—]
AnswerStudent response — not marked.
2.Describe how confident you feel with equivalent fractions and what you will practise next.
[—]
AnswerStudent response — not marked.

FreeMathWorksheet

Answer key · Equivalent Fractions

Warm-up

1.36[1]
1. 8 × 6 = 48, so the denominator was multiplied by 6.
2. Multiply the numerator by the same factor: 6 × 6 = 36.
2.12[1]
1. 3 × 6 = 18, so the denominator was multiplied by 6.
2. Multiply the numerator by the same factor: 2 × 6 = 12.
3.4[1]
1. 4 × 4 = 16, so the denominator was multiplied by 4.
2. Multiply the numerator by the same factor: 1 × 4 = 4.
4.6[1]
1. 4 × 3 = 12, so the denominator was multiplied by 3.
2. Multiply the numerator by the same factor: 2 × 3 = 6.

Recall

1.18[1]
1. 7 × 3 = 21, so the denominator was multiplied by 3.
2. Multiply the numerator by the same factor: 6 × 3 = 18.
2.6[1]
1. 2 × 6 = 12, so the denominator was multiplied by 6.
2. Multiply the numerator by the same factor: 1 × 6 = 6.
3.36[1]
1. 8 × 6 = 48, so the denominator was multiplied by 6.
2. Multiply the numerator by the same factor: 6 × 6 = 36.
4.18[1]
1. 9 × 3 = 27, so the denominator was multiplied by 3.
2. Multiply the numerator by the same factor: 6 × 3 = 18.

Basic Practice

1.9[1]
1. 6 × 3 = 18, so the denominator was multiplied by 3.
2. Multiply the numerator by the same factor: 3 × 3 = 9.
2.6[1]
1. 3 × 6 = 18, so the denominator was multiplied by 6.
2. Multiply the numerator by the same factor: 1 × 6 = 6.
3.16[1]
1. 8 × 4 = 32, so the denominator was multiplied by 4.
2. Multiply the numerator by the same factor: 4 × 4 = 16.
4.25[1]
1. 7 × 5 = 35, so the denominator was multiplied by 5.
2. Multiply the numerator by the same factor: 5 × 5 = 25.
5.5[1]
1. 5 × 5 = 25, so the denominator was multiplied by 5.
2. Multiply the numerator by the same factor: 1 × 5 = 5.

Guided Practice

1.4/5 (divided by 4)[2]
1. Find the highest common factor of 16 and 20: HCF = 4.
2. Divide both parts by 4 to get 4/5.
2.1/4 (divided by 10)[2]
1. Find the highest common factor of 10 and 40: HCF = 10.
2. Divide both parts by 10 to get 1/4.
3.1/2 (divided by 15)[2]
1. Find the highest common factor of 15 and 30: HCF = 15.
2. Divide both parts by 15 to get 1/2.
4.5/6 (divided by 2)[2]
1. Find the highest common factor of 10 and 12: HCF = 2.
2. Divide both parts by 2 to get 5/6.

Independent Practice

1.5/6 (divided by 2)[2]
1. Find the highest common factor of 10 and 12: HCF = 2.
2. Divide both parts by 2 to get 5/6.
2.2/3 (divided by 6)[2]
1. Find the highest common factor of 12 and 18: HCF = 6.
2. Divide both parts by 6 to get 2/3.
3.2/5 (divided by 6)[2]
1. Find the highest common factor of 12 and 30: HCF = 6.
2. Divide both parts by 6 to get 2/5.
4.1/7 (divided by 3)[2]
1. Find the highest common factor of 3 and 21: HCF = 3.
2. Divide both parts by 3 to get 1/7.
5.1/3 (divided by 18)[2]
1. Find the highest common factor of 18 and 54: HCF = 18.
2. Divide both parts by 18 to get 1/3.

Challenge Questions

1.No — the denominators were not scaled by the same factor.[3]
1. Numerator scale factor: 3 ÷ 1 = 3.
2. Denominator scale factor: 13 ÷ 4 ≠ 3.
3. Because the factors differ, the fractions are not equivalent.
2.No — the denominators were not scaled by the same factor.[3]
1. Numerator scale factor: 18 ÷ 2 = 9.
2. Denominator scale factor: 28 ÷ 3 ≠ 9.
3. Because the factors differ, the fractions are not equivalent.
3.No — the denominators were not scaled by the same factor.[3]
1. Numerator scale factor: 6 ÷ 1 = 6.
2. Denominator scale factor: 43 ÷ 7 ≠ 6.
3. Because the factors differ, the fractions are not equivalent.

Real-life Application

1.4/9 litres = 4/9 (simplified where possible)[3]
1. Each batch needs 2/9 l, so 2 batches need 2 × 2 = 4 lots of 1/9.
2. That is 4/9 litres.
3. Convert to a mixed number if the numerator exceeds the denominator.
2.6/7 litres = 6/7 (simplified where possible)[3]
1. Each batch needs 3/7 l, so 2 batches need 3 × 2 = 6 lots of 1/7.
2. That is 6/7 litres.
3. Convert to a mixed number if the numerator exceeds the denominator.

Critical Thinking

1.Accept any correct response that applies the equivalent fractions rule accurately.[4]
1. Recall the definition that underpins equivalent fractions.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Accept any correct response that applies the equivalent fractions rule accurately.[4]
1. Recall the definition that underpins equivalent fractions.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

Reflection

1.Student response — not marked.[0]
1. Recall the definition that underpins equivalent fractions.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.
2.Student response — not marked.[0]
1. Recall the definition that underpins equivalent fractions.
2. Apply it to the values or wording given in the question.
3. State the final answer clearly, with units or terminology where relevant.

FreeMathWorksheet

Teacher pack · Equivalent Fractions

Marking scheme

Band	Marks	Descriptor
Mastered	46–54	Applies equivalent fractions fluently, including in unfamiliar contexts, with clear justification.
Secure	35–45	Reliable in routine questions; reasoning is mostly complete.
Developing	22–34	Secure in scaffolded items, inconsistent once support is removed.
Emerging	0–21	Needs re-teaching of the core rule before progressing.

Teacher notes

Set the warm-up as a five-minute starter; it diagnoses readiness for equivalent fractions before you teach.
Guided practice is the pivot point — circulate here rather than during independent practice.
Mark the reasoning questions with the marking scheme bands, not raw totals, so progress is comparable across variants.
Students who band Emerging should repeat the Easy variant of this same subtopic before moving on within Fractions.

Common student mistakes

Adding the same number to both parts instead of multiplying.
Dividing only the numerator, or stopping before the fraction is fully simplified.
Assuming any two fractions with bigger numbers are automatically equivalent.
Multiplying the denominator as well as the numerator when scaling a quantity.
Confusing equivalent fractions with a neighbouring idea in fractions.

Teaching tips

Model one worked example of equivalent fractions under a visualiser before handing the sheet out.
Ask students to predict which question they will find hardest, then check the prediction afterwards.
Pair Developing students with Secure students for the guided practice block only.
Use the answer key as a self-marking station rather than collecting the sheets in.

Extension activities

Challenge worksheet on equivalent fractions with justification-only questions.
Design your own equivalent fractions question and write the mark scheme for it.
Link equivalent fractions to the next subtopic in Fractions and explain the connection.
Ten-minute timed practice to convert accuracy into fluency.

Question progression

Recognition → understanding → application → reasoning → mastery. The ladder adapts to Grade 8, and every rung stays on equivalent fractions only.

01Warm-up
Answer quickly. These check you are ready for the topic.
Remember4 questions4 marks
02Recall
Complete from memory. No calculator, no notes.
Remember4 questions4 marks
03Basic Practice
Work through each item. Show the step you used.
Understand5 questions5 marks
04Guided Practice
The first step is given. Finish the reasoning.
Understand4 questions8 marks
05Independent Practice
No scaffolding. Set out your full method.
Apply5 questions10 marks
06Challenge Questions
Harder items. Attempt every one, even partially.
Analyse3 questions9 marks
07Real-life Application
Use the skill in context. State units in your answer.
Apply2 questions6 marks
08Critical Thinking
Explain your reasoning in full sentences.
Evaluate2 questions8 marks
09Reflection
Not marked. Answer honestly — this guides your next worksheet.
Create2 questions0 marks

Answer key & solutions

Every worksheet auto-generates a complete key with step-by-step solutions, the marking scheme and teacher notes. It prints as separate pages so the student copy stays clean.

Teacher notes

Set the warm-up as a five-minute starter; it diagnoses readiness for equivalent fractions before you teach.
Guided practice is the pivot point — circulate here rather than during independent practice.
Mark the reasoning questions with the marking scheme bands, not raw totals, so progress is comparable across variants.
Students who band Emerging should repeat the Easy variant of this same subtopic before moving on within Fractions.

Common student mistakes

Adding the same number to both parts instead of multiplying.
Dividing only the numerator, or stopping before the fraction is fully simplified.
Assuming any two fractions with bigger numbers are automatically equivalent.
Multiplying the denominator as well as the numerator when scaling a quantity.
Confusing equivalent fractions with a neighbouring idea in fractions.

Teaching tips

Model one worked example of equivalent fractions under a visualiser before handing the sheet out.
Ask students to predict which question they will find hardest, then check the prediction afterwards.
Pair Developing students with Secure students for the guided practice block only.
Use the answer key as a self-marking station rather than collecting the sheets in.

Extension activities

Challenge worksheet on equivalent fractions with justification-only questions.
Design your own equivalent fractions question and write the mark scheme for it.
Link equivalent fractions to the next subtopic in Fractions and explain the connection.
Ten-minute timed practice to convert accuracy into fluency.

Switch version

Same subtopic · same objectives · different job

Frequently asked

What exactly is in the download?: A 31-question, 54-mark sheet with branded header, objectives, skills, instructions, name and date fields, page numbering, footer branding, copyright, worksheet ID TN-MATH-GR8-33206, version v2.0 and a QR code back to this page.
Does it print correctly on US Letter?: Yes. Switch paper size in the download panel — margins and typography are identical, so nothing reflows or clips.
Is the answer key included?: This version prints answers inline, followed by the full solutions and teacher pack pages.

Related resources

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