Ratios & Proportions - ACT Math

An equation that shows two ratios are equal. Two ratios set equal form a proportion.

3:4. Divide both terms by their GCD of 6.

$3:4$. Divide both terms by their GCD of 6.

x = 4. Cross-multiply: $x \times 12 = 6 \times 8$, so $x = 4$.

$x=7.5$. Cross multiply: $8x=60$, so $x=7.5$.

1:5. Divide both numbers by their GCD of 10.

2x = 12. Cross multiply: $2 \cdot x = 3 \cdot 4$.

4:1. Divide both numbers by their GCD of 4.

1:2. Divide both terms by their GCD of 50.

k = 12. Cross-multiply: $9 \times 16 = 12 \times k$, so $k = 12$.

$x = 1$. Cross-multiply: $x \times 15 = 3 \times 5$, so $x = 1$

y = 14. Cross-multiply: $7 \times 28 = y \times 14$, so $y = 14$.

x = 10. Cross-multiply: $5 \times 20 = x \times 10$, so $x = 10$.

2:3. Divide both terms by their GCD of 10.

x = 6. Cross-multiply: $3 \times 8 = 4 \times x$, so $x = 6$.

A rate is a special type of ratio comparing different units. Rates compare quantities with different units of measurement.

y = 15. Cross-multiply: $5 \times 30 = y \times 10$, so $y = 15$.

x = 12. Cross-multiply: $4 \times 36 = x \times 12$, so $x = 12$.

Ratios that express the same relationship. Different ratios that represent the same comparison.

1:2. Divide both terms by their GCD of 4.

A rate with a denominator of one. The second quantity equals 1 in a unit rate.

3:4. Divide both terms by their GCD of 3.

x = 25. Cross-multiply: $15 \times 75 = x \times 45$, so $x = 25$.

3:4. Divide both terms by their GCD of 25.

2:5. Divide both terms by their GCD of 4.

2:5. Divide both terms by their GCD of 5.

1:3. Divide both terms by their GCD of 14.

1:5. Convert to whole numbers: $5:25$, then divide by 5.

3:4. Divide both terms by their GCD of 15.