Ratio and proportion: solved examples

Worked examples of ratio and proportion, from easy to hard, with every step written out. Try each one yourself first, then check the working.

✓ Every answer here is computed and checked by the math engine

Easy

Example 1. Simplify the ratio $45 : 27$ .
1. Divide both parts by 9. $45 : 27 = 5 : 3$
Answer: $5 : 3$
Example 2. Simplify the ratio $2 : 6$ .
1. Divide both parts by 2. $2 : 6 = 1 : 3$
Answer: $1 : 3$
Example 3. Simplify the ratio $16 : 18$ .
1. Divide both parts by 2. $16 : 18 = 8 : 9$
Answer: $8 : 9$

Example 4. Share $152$ in the ratio $5 : 3$ . How big is the larger share?
1. Find one part. $152 \div 8 = 19$
2. Multiply by the larger number of parts. $5 \times 19 = 95$
Answer: $95$
Example 5. Share $16$ in the ratio $1 : 3$ . How big is the larger share?
1. Find one part. $16 \div 4 = 4$
2. Multiply by the larger number of parts. $3 \times 4 = 12$
Answer: $12$
Example 6. Share $34$ in the ratio $8 : 9$ . How big is the larger share?
1. Find one part. $34 \div 17 = 2$
2. Multiply by the larger number of parts. $9 \times 2 = 18$
Answer: $18$

Example 7. Find $x$ if $9 : 9 = 54 : x$ .
1. 54 is 6 times 9, so multiply 9 by 6. $x = 9 \times 6 = 54$
Answer: $54$
Example 8. Find $x$ if $2 : 5 = 16 : x$ .
1. 16 is 8 times 2, so multiply 5 by 8. $x = 5 \times 8 = 40$
Answer: $40$
Example 9. Find $x$ if $2 : 6 = 18 : x$ .
1. 18 is 9 times 2, so multiply 6 by 9. $x = 6 \times 9 = 54$
Answer: $54$

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