Ratios and Proportions Worksheets

What are ratios and proportions?

A ratio compares two quantities: a recipe that uses 3 cups of flour for every 4 cups of milk has a flour to milk ratio of $3 : 4$. Two ratios are equivalent when one is the other scaled by the same number, just like equivalent fractions: $3 : 4 = 15 : 20$, because both parts were multiplied by 5. An equation stating that two ratios are equal is a proportion.

Each problem on these worksheets is a proportion with one missing term, such as $\_\_\_ : 20 = 3 : 4$. The given ratio is in lowest terms and uses numbers from 2 to 8, and the scale factor is a whole number from 2 to 6, so every answer is a whole number.

Worked examples

$\_\_\_ : 20 = 3 : 4$

Compare the terms that are both known: 4 became 20, so the scale factor is $20 \div 4 = 5$. Scale the other term the same way: $3 \times 5 = 15$. Answer: 15.

$12 : \_\_\_ = 2 : 5$

2 became 12, so the scale factor is 6, and the missing term is $5 \times 6 = 30$.

$\_\_\_ : 12 = 5 : 2$

2 became 12, a scale factor of 6, so the missing term is $5 \times 6 = 30$.

Another method: cross-multiplication

Write the proportion as fractions and cross-multiply: $\dfrac{x}{20} = \dfrac{3}{4}$ gives $4x = 60$, so $x = 15$. This works even when the scale factor is not a whole number.

Check your answers

Divide each side: $15 \div 20 = 0.75$ and $3 \div 4 = 0.75$. Equal values mean the ratios are equivalent.

Common mistakes

• Adding instead of multiplying. In $\_\_\_ : 20 = 3 : 4$, noticing that 20 is 16 more than 4 and answering $3 + 16 = 19$ is wrong. Ratios scale by multiplication.
• Mixing up the positions. The first terms correspond to each other, and so do the second terms. $3 : 4$ and $4 : 3$ are different ratios.
• Finding the scale factor from the wrong pair. The scale factor comes from the two terms in the same position that are both known.

Sample problems

These problems come from the same generator as the worksheet above. Press Generate for a fresh set.

Proportions

1. 20 : ___ = 5 : 4
2. 35 : ___ = 7 : 2
3. ___ : 6 = 7 : 2
4. ___ : 9 = 7 : 3
5. ___ : 40 = 3 : 8
6. 16 : ___ = 8 : 7

Tips for teachers and parents

• Real contexts make ratios concrete: doubling a recipe, reading a map scale, or mixing paint colours.
• Ask students to write the scale factor above the arrow between the two ratios; it makes the method visible.
• Proportions lead into percentages and, later, into solving equations such as $4x = 60$.

Related topics

• Fractions Basic Math 2
• Percentages Basic Math 2
• Solving Equations Algebra