0.5 × 2/3 + 1 = □ (as a fraction in its simplest form) Answer in simplest form

4/3. 0.5 = 1/2; 1/2 × 2/3 = 1/3; add 1: 4/3.

1/3 + 2/3 ÷ 2 = ? A. 2/3 B. 1/2 C. 5/6 D. 5/3 Choose the right answer

A. 2/3. Divide before adding: 2/3 ÷ 2 = 2/3 × 1/2; then add 1/3: 2/3.

(8 − 1/8) × 1 = □ (as a decimal)

7.875. 1/8 = 0.125. Brackets first, 8 − 0.125 = 7.875; then times 1: 7.875.

Working with numbers · Ages 12–13

Fractions and decimals mixed

One form for all first, then times before plus.

How to do it

Method

One form for all first, then times before plus

0.5 + 34 × 2 = 12 + 32 = 2

Another way

All as decimals

0.5 + 0.75 × 2 = 0.5 + 1.5 = 2

In full

When fractions and decimals meet, choose one form for all of them first: a decimal turns into a fraction easily (0.75 = 34), but a fraction like 13 never ends as a decimal, so keep fractions then. Then times and divide before plus and minus. 0.5 + 34 × 2 = 12 + 32 = 2; or all as decimals: 0.5 + 0.75 × 2 = 0.5 + 1.5 = 2. Dividing by a fraction is multiplying by its reciprocal.

Worked examples

Have a go first, then open each one for the answer and the working.

Example 1
0.5 × 23 + 1 = (as a fraction in its simplest form)
Answer in simplest form
Show the answer and working
Answer: 43
0.5 = 12; 12 × 23 = 13; add 1: 43.
Example 2
13 + 23 ÷ 2 = ?
- A. 23
- B. 12
- C. 56
- D. 53
Choose the right answer
Show the answer and working
Answer: A. 23
Divide before adding: 23 ÷ 2 = 23 × 12; then add 13: 23.
Example 3
(8 − 18) × 1 = (as a decimal)
Show the answer and working
Answer: 7.875
18 = 0.125. Brackets first, 8 − 0.125 = 7.875; then times 1: 7.875.

Practice questions to try

Try these 5; the answers are at the end. For a whole worksheet, see VIP worksheets below.

1.Write 0.35 as a fraction in its simplest form: 0.35 =
Fill in each blank
Answer:
2.34 + 13 ÷ 2 = ?
- A. 1112
- B. 1324
- C. 1724
- D. 1712
Choose the right answer
Answer:
3.0.2 × 29 + 3 = (as a fraction in its simplest form)
Answer in simplest form
Answer:
4.(8 − 18) × 1.5 = (as a decimal)
Answer:
5.23 ÷ 49 = 23 × 94
True or false?
Answer:

All the answers

1. 7, 20
2. A. 1112
3. 13745
4. 11.8125
5. True

Free worksheet: Fractions and decimals mixedWorking out, multiple choice and word problems, with answers and working, to print or save as a PDF

VIP practice notes and papers

Aimed at tests and exams: questions on this topic, new every time, to print or save as a PDF.

Practice notes: The key point, worked examples step by step, then questions of the same kind to follow, hints fading
Practice paper: Set out in parts like a school paper, marked, with answers and full working

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