You will learn
- Write tenths and hundredths as decimals.
- Know 1/2, 1/4, 3/4 and 1/5 as decimals.
- Convert fractions with denominators 10 and 100.
- Use equivalent fractions.
Version 0.2 · expanded edition · expert review pending Standards alignment: pending verification. Written in the style of common primary school assessments. No exam result is promised.
Student lesson
- Tenths and hundredths are fractions with denominator 10 or 100.
- Know 1/2, 1/4, 3/4 and 1/5 as decimals.
- Use equivalent fractions to get denominator 10 or 100.
- Simplify a decimal fraction.
Words to know
1/2, 1/4, 3/4 …
Equal in value.
A number with a point.
Parts in the whole.
1. Discover: half a unit
Half a metre is 50 cm, which is 0.5 m. Why?
2. Understand: fractions and decimals
- 1/2 = 5/10 = 0.5.
- 1/4 = 25/100 = 0.25.
- 3/4 = 75/100 = 0.75.
- 1/5 = 2/10 = 0.2; 3/5 = 6/10 = 0.6.
- 1/10 = 0.1.
Make the denominator 10 or 100, then read the decimal.
Idea 1: Tenths
1/10 = 0.1. 7/10 = 0.7. 2/5 = 4/10 = 0.4.
Idea 2: Hundredths
1/4 = 25/100 = 0.25. 3/4 = 0.75.
Idea 3: Back to fractions
0.8 = 8/10 = 4/5 in lowest terms.
Why 100? 4 × 25 = 100, so quarters become hundredths.
3. Worked examples
Example 1 (I show you): To decimal
1/4
- 1/4 = 25/100.
Answer: 0.25
Example 2 (We do it together): To decimal
2/5
- 2/5 = 4/10.
Answer: 0.4
Example 3 (You try): To fraction
0.8
Show the steps and answer
- 8/10 ÷ 2.
Answer: 4/5
Did you know?
1/2 = 0.5 is one of the most useful facts in maths.
Why this matters
Fractions and decimals are two names for the same number.
4. Explore: convert
You need paper.
- Write 1/4.
- Multiply top and bottom by 25.
- Read 25/100 as 0.25.
- Do the same for 3/5.
Think about it: what did you notice?
0.25 and 0.6.
5. Practise
Say it in a sentence
Use these starters when you talk about the lesson. Say them out loud.
- I multiply the denominator by ___ to get ___.
- So the numerator becomes ___.
- As a decimal it is ___.
- In lowest terms it is ___.
Guided practice
Question 1. 1/2?
0.5.
Question 2. 3/4?
0.75.
Question 3. 3/5?
0.6.
Independent practice
Level 1: Start
- 1/10
- 1/4
- 7/10
- 2/5
- 0.8 as a fraction (lowest terms)
Level 2: Grow
- 1/5 as a decimal
- 3/10 as a decimal
- 0.5 as a fraction in lowest terms
Level 3: Stretch
- 9/20 as a decimal
- 0.12 as a fraction in lowest terms
- Ben says 1/4 = 0.4 because of the 4. What is wrong?
Answers are in the answer key below. Try first, then check.
6. Apply: everyday mathematics
A jug is 3/4 full. Write 3/4 as a decimal.
Show a sample answer
0.75.
Another one. A tank is 3/4 full. Write this as a decimal.
Show a sample answer
3/4 = 75/100 = 0.75
7. Common mistakes
Fix: Make the denominator 100: 25/100.
Fix: Convert to tenths or hundredths first.
Fix: Divide by the greatest common factor.
8. Lesson summary and revision card
- I can write tenths and hundredths as decimals.
- I know 1/2, 1/4, 3/4 and 1/5 as decimals.
- I can convert fractions with denominator 10 and 100.
- I can use equivalent fractions.
9. Check and master
Answer all 14 questions. You will see feedback after each one.
Your result appears here after you answer every question.
10. Key takeaways
- Benchmarks: 0.5, 0.25, 0.75.
- Make 10 or 100.
- Convert back and simplify.
11. Next lesson
Next lesson: Decimals in money and measurement. Keep going with the next idea in this course.
Exam practice
These questions are written in the style of common school and international primary assessments. Try them on your own, without looking back. Then check your answers in the marking guide. The marks are shown in brackets.
- Write 1/10 as a decimal. [1 mark]
- Write 1/4 as a decimal. [2 marks]
- Write 7/10 as a decimal. [1 mark]
- Write 2/5 as a decimal. [2 marks]
- Write 0.8 as a fraction in lowest terms. [3 marks]
Total: 9 marks.
Marking guide and model answers
- 0.1 [1]
- 1/4 = 25/100 [1]; 0.25 [1]
- 0.7 [1]
- 2/5 = 4/10 [1]; 0.4 [1]
- 8/10 [1]; divide by 2 [1]; 4/5 [1]
Score guide: 8 to 9 = secure. 6 to 7 = nearly there, revise the parts you missed. Under 6 = work through the lesson again with a grown-up.
Printable worksheet
- 1/10
- 1/4
- 7/10
- 2/5
- 0.8 as a fraction (lowest)
- 1/2 =
- 1/4 =
- 3/4 =
- 3/5 =
- 0.8 in lowest terms is
Homework
Make a chart of ten fractions and their decimals.
Answer key and marking scheme
| Question | Expected response | Marks |
|---|---|---|
| 1/10 | 0.1 | 2 |
| 1/4 | 0.25 | 2 |
| 7/10 | 0.7 | 2 |
| 2/5 | 0.4 | 2 |
| 0.8 as a fraction (lowest) | 4/5 | 2 |
| Total | 10 |
Practice answers: Worksheet: 1 0.1; 2 0.25; 3 0.7; 4 0.4; 5 4/5.
Quiz answers: 1 A, 2 B, 3 C, 4 A, 5 B, 6 A, 7 B, 8 C, 9 A, 10 B, 11 C, 12 A, Challenge 1 C, Challenge 2 C.
Extra worksheet answers (items 6 onward): 6 0.5; 7 0.25; 8 0.75; 9 0.6; 10 4/5.
Independent practice answers. Level 1: 1 0.1; 2 0.25; 3 0.7; 4 0.4; 5 4/5. Level 2: 1 0.2; 2 0.3; 3 1/2. Level 3: 1 0.45; 2 3/25; 3 1/4 = 25/100 = 0.25. 0.4 is 4/10 = 2/5..
Mastery and remediation
| Objective | Bronze (Developing) | Silver (Proficient) | Gold (Advanced) |
|---|---|---|---|
| O1 Write tenths and hundredths as decimals | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O2 Know 1/2, 1/4, 3/4 and 1/5 as decimals | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O3 Convert fractions with denominators 10 and 100 | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
| O4 Use equivalent fractions | Shows this with help from an adult or a picture | Does this independently and explains how they know | Explains it clearly and uses it in a new situation |
Proposed Courseversity thresholds for this page: Bronze = at least 8 of 12 core questions correct; Silver = all 12; Gold = all 12 plus both challenge questions. A badge is never a full record of progress.
If a learner struggles
- Find the misconception: Writing 1/4 as 1.4. Make the denominator 100: 25/100.
- Explain another way: use real objects first, then pictures.
- Show a simpler example: Shade hundred grids.
- Guided practice: work through one example together and let the learner try the next one.
- Reassess: use the quiz again or the worksheet.
- Move on when the learner shows Silver-level evidence independently.
For parents and guardians
In this lesson your child converts between simple fractions and decimals. You do not need to be good at mathematics to help.
- Say halves and quarters as decimals.
- Ask: can you make the denominator 10 or 100?
- Use money: 25 cents is a quarter.
- Ask “how do you know?” after each answer, and listen.
- Praise effort, not only right answers. Mistakes are how we learn.
- Ten to fifteen minutes a day is better than one long session.
Teacher package
1–5. Objectives, prerequisites, materials, preparation, duration
Lesson objectives. Learners will: write tenths and hundredths as decimals; know 1/2, 1/4, 3/4 and 1/5 as decimals; convert fractions with denominators 10 and 100; use equivalent fractions.
Prerequisite knowledge. Lessons 2 and 4.
Materials. Counters (stones, seeds or bottle tops), paper, pencils, board or chalkboard. Low-resource options: use stones, seeds, sticks, bottle tops or drawings in the sand or on the board instead of printed materials.
Preparation. Gather the counters and draw the example pictures on the board before the lesson.
Suggested duration. 45–60 minutes. It can be split into two shorter sessions.
6–9. Teaching procedure, explanation notes, guided and independent activities
Introduction (5 min). Start with the Discover situation and let learners suggest ideas before you teach.
Explanation (10 min). Teach the Understand section with real objects first, then pictures, then symbols and words.
Guided activity (10 min). You need paper. Learners follow the Explore steps in pairs.
Independent activity (10 min). Learners complete the independent practice and the worksheet.
Assessment and reflection (5 min). Ask each learner to say one thing they learned and how they know it.
Key questions. Can I make the denominator 10 or 100?
Teacher explanation notes. Use the concrete, pictorial, abstract order: real objects first, then pictures, then symbols and words. Return to real objects whenever a learner needs support.
10–12. Differentiation, formative assessment, common misconceptions
Support. Use real objects and work with a partner; say each step aloud together. Extension. Ask learners to make up their own example and explain it to a partner.
Formative assessment. Listen to learner explanations, ask “how do you know?”, and check the independent work.
Misconceptions. Writing 1/4 as 1.4. Make the denominator 100: 25/100.
13–15. Assessment questions, answer keys, marking scheme
Use the quiz and worksheet on this page. The 9-mark exam practice scheme, the 10-mark scheme and all answers are in the answer sections above. Re-check every answer and the marking scheme before publication.
16–19. Remediation, enrichment, homework, teacher reflection
Remediation. Shade hundred grids. Enrichment. Invite learners to find or create three more examples at home or in the classroom and explain them. Homework. See above.
Teacher reflection. After teaching, record: which concepts learners understood; which misconceptions occurred; which activities worked; which learners need more practice; and what to improve next time.
Sources and standards
Alignment is pending verification and no external endorsement is claimed. Reference starting points named in the Courseversity standard: Common Core State Standards for Mathematics, Cambridge Primary and the IB Primary Years Programme. Specific standard codes will be added once checked against the official documents.
Research used to shape this lesson. Common Core 4.NF.C.5 and 4.NF.C.6; Cambridge Primary Mathematics Stage 5 (fractions and decimals). These sources informed the lesson; no official alignment is claimed.