Build Equivalent Fractions
Create a fraction with smaller equal parts that represents the same amount.
Supplied materials
- Paper and a pencil, or say your answers aloud.
Learn the idea
Equivalent fractions describe the same amount of the same whole. If every original part is split into the same number of smaller equal parts, both the selected-part count and the total-part count grow by that factor.
For example, split each fifth into two equal parts. One fifth becomes two tenths, so 3/5 becomes 6/10. Multiplying just the numerator or just the denominator would usually change the amount.
- Draw a rectangle divided into five equal strips and shade three.
- Divide every strip into two equal pieces.
- Count six shaded pieces out of ten total pieces.
- For the check, imagine splitting every third into four equal pieces.
See the method in action
3/5 = 6/10 because 3 × 2 = 6 and 5 × 2 = 10. The new pieces are half as big, so twice as many represent the same shaded amount.
Check your reasoning
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See the answer and explanation
8/12
Multiply both counts by four: 2 × 4 = 8 and 3 × 4 = 12. Eight twelfths covers the same amount as two thirds.
Take it further
Check 2/3 = 4/6 by splitting each third into two pieces instead. Draw both partitions of the same-sized rectangle and compare the shaded areas.
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Check the subject sources
These LifeStarter passages, scenarios and exercises are authored for this Academy with AI assistance and review. External resources keep their publishers’ terms. A grade label suggests a starting level; it does not establish alignment with your school’s complete requirements.