Fractions of shapes
Equivalent fractions
Two fractions can have the same value even though they look different. These are called equivalent fractions.
What equivalent means
Equivalent fractions cover the same amount of a whole. On two strips of the same length, they shade exactly the same part. Example: 2/5 and 4/10 shade the same amount, so 2/5 = 4/10.
Fifths and tenths
If you split each fifth into 2 equal parts, the strip now has 10 parts — tenths. So 1/5 = 2/10, 2/5 = 4/10 and 3/5 = 6/10.
Using fraction strips
Line up two fraction strips of the same length. If the shaded parts match, the fractions are equivalent.
Worked examples
Fifths to tenths
- Start with 2/5 on a strip of 5 equal parts.
- Split each fifth into 2, making 10 equal parts.
- The 2 shaded fifths become 4 shaded tenths.
Answer: 2/5 = 4/10
A half as tenths
- A half of a strip is 5 of its 10 equal parts.
- So one half is the same as five tenths.
Answer: 1/2 = 5/10
A half as quarters
- Split a half into 2 equal parts to make quarters.
- One half is the same as two quarters.
Answer: 1/2 = 2/4
Where you see this in real life
- Seeing that half a chocolate bar is the same as 2 of its 4 pieces.
- Sharing that half a pizza is the same as 5 of 10 slices.
- Swapping coins of equal value, like 2 fives for one ten.
Key words
- Equivalent
- Having the same value, even if written differently.
- Fraction strip
- A strip split into equal parts, used to compare fractions.
- Numerator
- The top number — how many parts you have.
- Denominator
- The bottom number — how many equal parts in the whole.