Simplify 18 : 30.
- The greatest common factor of 18 and 30 is 6.
- 18 ÷ 6 = 3; 30 ÷ 6 = 5.
- 18 : 30 = 3 : 5. Check: 3 × 6 = 18 and 5 × 6 = 30.
Equivalent ratios
Scale both quantities together.
Keep the multiplicative relationship
Equivalent ratios compare quantities in the same relative amounts. Multiply or divide every term by the same positive factor. From 2 : 3, multiplying both terms by 4 gives 8 : 12.
See the quantities change.
Predict before changing a value. The written explanation below remains available without JavaScript.
Addition usually changes the relationship
Adding 2 to both terms of 2 : 3 gives 4 : 5. These are not equivalent: 2/3 differs from 4/5. Scaling repeats or partitions the entire batch.
Simplify without losing meaning
Divide whole-number terms by their greatest common factor. For decimal terms, multiply both by a power of ten first, then simplify. The original quantities and units still matter.
Khan Academy
Pause the explanation before a calculation. Predict the next step and explain which quantities are being compared.
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Equivalent ratios
Identify the factor applied to both quantities.
Open on YouTube →Worked examples
Find a ratio equivalent to 1.2 : 1.8 using whole numbers.
- Multiply both terms by 10: 12 : 18.
- Divide both by 6: 2 : 3.
- Both changes apply the same factor to each term.
Try it before checking.
Complete 4 : 7 = 20 : ___.
A first hint
The first quantity was multiplied by 5.
Compare your reasoning
7 × 5 = 35, so 4 : 7 = 20 : 35.
Practise the skill.
Fresh questions · useful feedback
Build fluency, one decision at a time.
Work through eight questions. Two independent correct answers introduce a harder version; supported answers bring the next question back to the foundation. You can use hints at any time.
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This round saves on this device. It is practice, not a school mark.
Explain a little more.
Is every ratio equivalent to one with first term 1? Discuss nonzero and zero first terms.
Use this thinking in the If… project →