Solve 5/8 = x/28.
- The denominator scale factor is 28 ÷ 8 = 3.5.
- Scale the numerator: x = 5 × 3.5 = 17.5.
- Check: 17.5 ÷ 28 = 0.625 = 5 ÷ 8.
Solving proportions
Match the quantities on both sides.
A proportion is an equality of ratios
Write corresponding quantities in the same order. If 3 notebooks cost $7.50, then 3 notebooks / $7.50 = 8 notebooks / x dollars. Mixing notebooks/dollars with dollars/notebooks does not preserve the comparison.
See the quantities change.
Predict before changing a value. The written explanation below remains available without JavaScript.
Choose an efficient strategy
Scale both terms, find the unit rate, or solve the equation. Since one notebook costs $2.50, eight cost $20. A non-whole-number scale factor is allowed.
Cross products come from equality
For a/b = c/d with nonzero b and d, multiplying both sides by bd gives ad = bc. Cross multiplication is an equation step, not permission to ignore units or assume a situation is proportional.
Khan Academy
Pause the explanation before a calculation. Predict the next step and explain which quantities are being compared.
Khan AcademyWatch · pause · explain
Writing proportions
Check that corresponding quantities are in the same order.
Open on YouTube →Worked examples
Six tickets cost $45. At the same rate, what do 14 tickets cost?
- One ticket costs 45 ÷ 6 = $7.50.
- 14 × 7.50 = $105.
- Check: 45/6 = 105/14 = 7.5 dollars per ticket.
Try it before checking.
Solve 4/7 = x/21.
A first hint
21 is 3 times 7.
Compare your reasoning
x = 4 × 3 = 12. Check: 12/21 = 4/7.
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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Explain a little more.
Solve the ticket example using both scaling and an equation. Explain why they agree.
Use this thinking in the If… project →