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. This involves multiplying the corresponding terms of the ratios and simplifying the result to express it in its simplest form.
Answer
27:4
Answer for screen readers
27:4
Steps to Solve
- Write the ratios as fractions
Express 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
Simplify by dividing 15 by 5, which gives 3. $$ \frac{3}{8} \times \frac{18}{1} $$
- Multiply the remaining numbers
Multiply the numerators and denominators: $$ \frac{3 \times 18}{8 \times 1} = \frac{54}{8} $$
- Simplify the resulting fraction
Divide both the numerator and the denominator by their greatest common divisor, which is 2: $$ \frac{54 \div 2}{8 \div 2} = \frac{27}{4} $$
- Express the answer as a ratio
Express the simplified fraction as a ratio: 27:4
27:4
More Information
The compounded ratio of 15:8 and 18:5 is 27:4. This means $27/4$ is the single ratio that represents the combination of the two original ratios.
Tips
A common mistake is failing to simplify the fractions before or after multiplication. For example, you could multiply 15 and 18 to get 270, and 8 and 5 to get 40, then simplify $\frac{270}{40}$ to $\frac{27}{4}$. Simplification before multiplying usually reduces the size of the numbers you are working with and simplifies the arithmetic.
AI-generated content may contain errors. Please verify critical information
