To express the measurement comparison between 124 inches and 16 feet as a ratio reduced to its lowest terms, follow these steps:
1. Convert all measurements to the same unit:
Since we have measurements in inches and feet, we need to convert feet to inches to have a consistent unit. There are 12 inches in a foot.
Therefore, convert 16 feet to inches:
[tex]\[
16 \text{ feet} \times 12 \text{ inches/foot} = 192 \text{ inches}
\][/tex]
2. Form an initial ratio:
Now that both measurements are in inches, we can form the initial ratio:
[tex]\[
124 \text{ inches} : 192 \text{ inches}
\][/tex]
3. Simplify the ratio to its lowest terms:
To simplify the ratio, find the greatest common divisor (GCD) of the two numbers (124 and 192). The GCD of 124 and 192 is 4.
4. Divide both terms of the ratio by the GCD:
[tex]\[
\frac{124}{4} = 31
\][/tex]
[tex]\[
\frac{192}{4} = 48
\][/tex]
Thus, the ratio 124 inches to 192 inches in simplest form is:
[tex]\[
31 : 48
\][/tex]
So, the comparison of 124 inches to 16 feet, reduced to its lowest terms, is expressed as the ratio:
[tex]\[
31 : 48
\][/tex]
