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Number foundations

Fractions & decimals: parts of a whole

See equivalent fractions, combine equal-sized parts, and move confidently between fractions and decimal notation.

BeginnerAbout 14 min3 worked examples
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01 / THE STARTING POINT

Before you begin

What you need: Multiplication, division and common multiples.

  • Explain numerator and denominator
  • Add and multiply fractions correctly
  • Convert terminating decimals to simplified fractions
02 / BUILD THE CONCEPT

Understand the idea

The denominator sets the piece size

In a/b, b tells how many equal parts make one whole and a tells how many of those parts are counted. The denominator cannot be zero. An improper fraction can represent more than one whole.

Equivalent fractions name the same value

Multiplying numerator and denominator by the same nonzero number preserves the value. This lets us rewrite 1/2 as 2/4 or 4/8, with smaller but more numerous pieces.

Decimals use powers of ten

0.375 means 375 thousandths: 375/1000 = 3/8. A fraction in lowest terms has a terminating decimal exactly when its positive denominator has no prime factors other than 2 and 5.

03 / A DIFFERENT WAY TO SEE IT

Same amount, different pieces

3/4
6/8
Three quarters and six eighths cover exactly the same portion of a whole.
04 / FROM IDEA TO ANSWER

A method you can reuse

KEEP THIS HANDY

a/b + c/d = (ad + bc)/(bd)

Use a common denominator; using the LCM often keeps the numbers smaller.
  1. For addition or subtraction, rewrite with a common denominator.
  2. Combine numerators and keep that denominator. For multiplication, multiply numerators and denominators.
  3. Reduce the result by its HCF. For division, multiply by the reciprocal of the nonzero divisor.
A useful insight

Cancel common factors before multiplying fractions. In (3/7) × (14/9), cancel 14 with 7 and 3 with 9 to get 2/3.

05 / WATCH THE METHOD WORK

Worked examples

Read the question first. Try a step yourself, then compare your reasoning.

EXAMPLE 01

Add unlike fractions

Find 3/4 + 5/8.

  1. The LCM of 4 and 8 is 8.
  2. 3/4 = 6/8, so the sum is 6/8 + 5/8.
  3. 11/8 is already in lowest terms.
Answer11/8 = 1⅜
EXAMPLE 02

Convert a decimal

Write 0.375 as a fraction.

  1. Three decimal places means 375/1000.
  2. The HCF of 375 and 1000 is 125.
  3. Divide both by 125.
Answer3/8
EXAMPLE 03

Divide by a fraction

Calculate 2/3 ÷ 4/5.

  1. The reciprocal of 4/5 is 5/4.
  2. 2/3 × 5/4 = 10/12.
  3. Divide numerator and denominator by 2.
Answer5/6
06 / YOUR TURN

Check your understanding

Quick questions, with explanations. These are for self-study and do not affect your account score.

0 of 3 questions checked

QUESTION 1Find 1/3 + 1/6.

See the explanation

1/2. Use sixths: 2/6 + 1/6 = 3/6 = 1/2.

QUESTION 2Which fraction equals 0.08?

See the explanation

2/25. 0.08 = 8/100 = 2/25.

QUESTION 3Calculate 3/5 × 10/9.

See the explanation

2/3. 30/45 simplifies by 15 to 2/3.

07 / TAKE THE NEXT STEP

Put your understanding to work

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EXPLORE THE NUMBERS

Add Fractions Calculator

Change the inputs and follow the working.

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Fractions and Decimals Practice Quiz 1

Move on to a timed quiz with detailed results.

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Fractions and Decimals Practice Quiz 2

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Fractions and Decimals Practice Quiz 3

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