Writ the ratio as a fraction in simplest form, 24 inches : 16 inches
The Correct Answer and Explanation is:
To write the ratio 24 inches : 16 inches as a fraction in its simplest form, we begin by expressing it as a fraction:2416\frac{24}{16}1624
Step 1: Simplify the Fraction
The first step is to simplify the fraction. To do this, we find the greatest common divisor (GCD) of 24 and 16. The GCD is the largest number that can divide both 24 and 16 without leaving a remainder.
- List the factors of 24:
- 1, 2, 3, 4, 6, 8, 12, 24
- List the factors of 16:
- 1, 2, 4, 8, 16
The greatest common divisor of 24 and 16 is 8.
Step 2: Divide Both the Numerator and Denominator by the GCD
Now, we divide both the numerator (24) and the denominator (16) by the GCD, which is 8:2416=24÷816÷8=32\frac{24}{16} = \frac{24 \div 8}{16 \div 8} = \frac{3}{2}1624=16÷824÷8=23
Step 3: Write the Ratio in Simplest Form
Thus, the ratio 24 inches : 16 inches simplifies to:32\frac{3}{2}23
This means the ratio of 24 inches to 16 inches is equivalent to 3:2.
Explanation
Ratios are used to compare quantities, and they can be written as fractions. To simplify a ratio, you need to reduce the fraction to its simplest form by dividing both the numerator and the denominator by their GCD. In this case, simplifying the ratio 24:16 required us to find the GCD, which was 8, and divide both 24 and 16 by 8 to obtain the simplest form of 3:2. This fraction means that for every 3 parts of 24 inches, there are 2 parts of 16 inches. The process of simplifying ratios helps in understanding the proportional relationship between quantities in their simplest terms.
