Find the compounded ratio of 15:8 and 18:5
Understand the Problem
The question asks to find the compounded ratio of 15:8 and 18:5. A compounded ratio is found by multiplying the corresponding terms of the ratios.
Answer
27:4
Answer for screen readers
27:4
Steps to Solve
- Write the ratios as fractions
Write the ratios 15:8 and 18:5 as fractions: $\frac{15}{8}$ and $\frac{18}{5}$
- Multiply the fractions
Multiply the two fractions: $$ \frac{15}{8} \times \frac{18}{5} $$
- Simplify before multiplying
Divide 15 by 5 to simplify the expression: $$ \frac{3}{8} \times \frac{18}{1} $$
- Multiply the simplified fractions
Multiply the numerators and the denominators: $$ \frac{3 \times 18}{8 \times 1} = \frac{54}{8} $$
- Simplify the resulting fraction
Divide both the numerator and the denominator of $\frac{54}{8}$ by 2: $$ \frac{54 \div 2}{8 \div 2} = \frac{27}{4} $$
- Write the answer as a ratio
Write $\frac{27}{4}$ as a ratio: 27:4
27:4
More Information
The compounded ratio of 15:8 and 18:5 is 27:4.
Tips
A common mistake is not simplifying the fractions before multiplying, which can lead to larger numbers and more difficult simplification at the end. Another common mistake is incorrectly multiplying or simplifying the fractions.
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