Write the ratio 64 : 40 as a fraction in simplest form.
Understand the Problem
The question is asking us to convert the ratio 64:40 into a fraction in its simplest form, meaning we need to simplify the fraction to its lowest terms.
Answer
The simplest form of the ratio \(64 : 40\) is $$ \frac{8}{5} $$
Answer for screen readers
The simplest form of the ratio (64 : 40) as a fraction is
$$ \frac{8}{5} $$
Steps to Solve
- Write the Ratio as a Fraction
To convert the ratio (64 : 40) into a fraction, we can express it as:
$$ \frac{64}{40} $$
- Find the Greatest Common Divisor (GCD)
Next, we need to find the GCD of the numerator (64) and the denominator (40).
The factors of 64 are (1, 2, 4, 8, 16, 32, 64) and the factors of 40 are (1, 2, 4, 5, 8, 10, 20, 40).
The highest common factor is 8.
- Simplify the Fraction
Now, we'll divide both the numerator and the denominator by the GCD, which is 8:
$$ \frac{64 \div 8}{40 \div 8} = \frac{8}{5} $$
The simplest form of the ratio (64 : 40) as a fraction is
$$ \frac{8}{5} $$
More Information
This simplification illustrates how ratios can be represented as fractions. The process of finding the GCD helps in reducing fractions to their simplest form.
Tips
- Not Finding the GCD: A common mistake is to simplify without finding the GCD, which can lead to incorrect results.
- Wrong Division: Make sure to divide correctly; double-check your arithmetic when simplifying fractions.
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