1. Changing recurring decimals into fractions and vice versa.
Grade 7
Recurring decimals
Changing recurring decimals into fractions and vice versa.
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2. Lesson Plan Lesson Overview Progression of Learning
Objective(s)
Changing recurring decimals into fractions and vice versa
Grade 7
Prior Knowledge
Solving equations
Multiplying by powers of 10
Division without a calculator
Duration
Content can be covered with sufficient practice time within 70 minutes
Resources
Print slides: 4, 7, 11, 13, 16
Equipment
Progression of Learning
What are the students learning?
How are the students learning? (Activities & Differentiation)
How to write recurring decimals (where to place the dots)
Give students slide 4 printed. Show slide 5 to illustrate how to write recurring decimals. 10
Division to convert fraction into decimal to determine is recurring or terminating decimal
Show slide 6 and guide students through division to see if decimal to recurring or terminating. Students to record their work on slide 4.
Changing recurring decimals into fractions
Give students slide 7 printed. Using slide 8 to 10 guide the students through the process of converting recurring decimals into fractions.
Give students slide 11 printed for further practice. Use slide 12 to mark answers with students. 20
Changing recurring decimals into fractions in contextualised problems
Give students slide 13. Allow students to attempt question on their own for 2 minutes. Review question together and model answer.
Changing recurring decimals into fractions in exam questions (from specimen papers)
Give students slide 16. This includes 7 exam questions related to objective. Students need to use notes from lesson to answer the questions. Ensure that all steps are shown. Relate to mark scheme to show how the marks are allocated. 30
Next Steps
Assessment
PLC/Reformed Specification/Target7/Number/Recurring Decimals

3. Recurring Fraction Decimal Solve Equation
Key vocabulary
Recurring
Fraction
Decimal
Solve
Equation
Student Sheet 1

4. How to write recurring decimals…
Change the following fractions into decimals and identify whether the answer is a recurring decimal or terminating decimal:
1) ) 5 6 … … …
Student Sheet 1

5. How to write recurring decimals
… Can be written as 0. 3 The dot shows which digit is recurring
… Can be written as
Two digits both recur
… Can be written as
The whole section between 7 and 4 recurs
… Can be written as
The whole section between 6 and 4 recurs

6. Change recurring decimals into fractions
Change the following fractions into decimals and identify whether the answer is a recurring decimal or terminating decimal:
1) ) 5 6
Is the same as 3÷8
Is the same as 5÷6
3 is a recurring
=0.8 3 8)
- 0
3 0
6 0
4 0
8x3=24
8x7=56
8x5=40
….. 6)
- 0
5 0
2 0 2
6x8=48
6x3=18
Terminating decimal
Recurring decimal

7. Change recurring decimals into fractions
0. 8
Student Sheet 2

8. Change recurring decimals into fractions
Change into a fraction
Let X = ……
Only one number is recurring so multiply by 10
10X = ……
- X = ……
9X = 8
X = 8 9
Subtract the two
Divide both sides by 9
0. 8 = 8 9

9. Change recurring decimals into fractions
Change into a fraction
Let X = ……
Two numbers are recurring so multiply by 100 and
100X = ……
- X = ……
99X = 79
X =
Subtract the two
Divide both sides by 99 =

10. Change recurring decimals into fractions
Change into a fraction
Let X = X = X=
1000X = ……
- 10X = ……
990X = 135
X = = = 3 22
Subtract the two
Divide both sides by 990
÷ 9
÷ 5
Simplify the fraction
= 3 22

11. Practice Student Sheet 3 Convert 4 9 into a decimal
Change into a fraction
Change the following fractions into decimals and state whether they are recurring decimals or terminating decimals
(i) (ii)
Convert into a decimal
Change into a fraction
(i) (ii) 3 16
Student Sheet 3

12. Practice - Solutions = 0. 𝟒 = 𝟗𝟏 𝟗𝟗 Convert 4 9 into a decimal
Change into a fraction
Change the following fractions into decimals and state whether they are recurring decimals or terminating decimals
(i) (ii)
Convert into a decimal
Change into a fraction
(i) (ii) 3 16
= 0. 𝟒
= 𝟗𝟏 𝟗𝟗
= 0.15
Terminating decimal
= 0.3 𝟕
Recurring decimal
= 0. 𝟕 𝟓
= 𝟒𝟏 𝟗𝟎
= 0. 𝟐 1 𝟔
Recurring decimal =
Terminating decimal

13. Problem Solving and Reasoning
Prove that the recurring decimal =
The recurring decimal can be written as the fraction
Write the decimal as a fraction in its simplest form
Student Sheet 4

14. Problem Solving and Reasoning
Prove that the recurring decimal =
Let X = ……
Two numbers are recurring so multiply by 100 and
100X = ……
- X = ……
99X = 72
X = =
Subtract the two
Divide both sides by 99
÷ 9
8 11
Simplify the fraction

15. Problem Solving and Reasoning
The recurring decimal can be written as the fraction Write the decimal as a fraction in its simplest form
can be written as
0.5 = =
= = =

16. Exam Question – Specimen Papers
Student Sheet 5

20. Exam Question – Specimen Papers

21. Exam Question – Specimen Papers

22. Exam Question – Specimen Papers