Question 1

What is cross-multiplication and why does it work?

Accepted Answer

Cross-multiplication converts a proportion a/b = c/d into the equation a×d = b×c by multiplying both sides by b×d. This clears the denominators: (a/b)×b×d = (c/d)×b×d → a×d = b×c. It works because multiplying equals by equals preserves equality. Cross-multiplication is valid only for proportions (equalities of two fractions), not for other fraction expressions.

Question 2

How do I solve a proportion when the unknown is in the denominator?

Accepted Answer

Cross-multiply just the same. If 5/x = 3/9: cross-multiply to get 5×9 = 3×x → 45 = 3x → x = 15. Or if a/b = c/x: cross-multiply → a×x = b×c → x = (b×c)/a. The position of the unknown in numerator or denominator doesn't change the cross-multiplication method.

Question 3

What is the difference between a proportion and a ratio?

Accepted Answer

A ratio (e.g., 3:4) compares two quantities. A proportion (e.g., 3/4 = 6/8) states that two ratios are equal. A ratio is a single comparison; a proportion is an equation between two ratios. Checking if 6:8 is equivalent to 3:4 is a proportion problem: 6/8 = 3/4 → cross-multiply → 6×4 = 8×3 → 24 = 24 ✓.

Question 4

What is a direct proportion vs an inverse proportion?

Accepted Answer

Direct proportion: as one quantity increases, the other increases proportionally (y = kx). Example: more hours worked → more pay. If 3 hours earns $45, then 7 hours earns $45×(7/3) = $105. Inverse proportion: as one quantity increases, the other decreases (y = k/x). Example: more workers → fewer days to complete a job. Both can be solved with proportions but the setup differs.

Question 5

How do I use proportions for unit conversions?

Accepted Answer

Set up a proportion where both ratios use the same unit relationship. To convert 45 miles to kilometres (1 mile = 1.609 km): 1/1.609 = 45/x → x = 45 × 1.609 = 72.4 km. Always put the same units in corresponding positions (both numerators the same unit, both denominators the same unit). Keeping units consistent is the key to avoiding conversion errors.

Question 6

Can proportions be used for percent calculations?

Accepted Answer

Yes. "What is 35% of 200?" becomes the proportion 35/100 = x/200. Cross-multiply: 100x = 7000 → x = 70. "15 is what percent of 60?" becomes x/100 = 15/60. Cross-multiply: 60x = 1500 → x = 25%. "40 is 80% of what number?" becomes 80/100 = 40/x → 80x = 4000 → x = 50. All three percentage question types reduce to simple proportions.

Proportion Calculator

Formula

Proportion Calculator

Related Calculators

Disclaimer

Frequently Asked Questions