Answer :
To solve the problem, we need to find out how many pieces of wood, each [tex]\(\frac{3}{4}\)[/tex] of a foot long, can be cut from a beam that is 15 feet long.
Here's a step-by-step solution:
1. Understand the problem: You have a 15-foot-long beam and you want to cut it into smaller pieces, with each piece being [tex]\(\frac{3}{4}\)[/tex] of a foot in length.
2. Set up the division: To determine how many pieces of [tex]\(\frac{3}{4}\)[/tex] foot long can be made from 15 feet, you divide the total length of the beam by the length of each piece:
[tex]\[
\text{Number of pieces} = \frac{\text{Total length of the beam}}{\text{Length of each piece}} = \frac{15}{\frac{3}{4}}
\][/tex]
3. Simplify the division: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of [tex]\(\frac{3}{4}\)[/tex] is [tex]\(\frac{4}{3}\)[/tex]. So:
[tex]\[
\frac{15}{\frac{3}{4}} = 15 \times \frac{4}{3}
\][/tex]
4. Perform the multiplication: Multiply 15 by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[
15 \times \frac{4}{3} = \frac{15 \times 4}{3} = \frac{60}{3}
\][/tex]
5. Simplify the fraction: Simplify [tex]\(\frac{60}{3}\)[/tex] by doing the division:
[tex]\[
\frac{60}{3} = 20
\][/tex]
So, the carpenter can cut 20 pieces of wood, each [tex]\(\frac{3}{4}\)[/tex] of a foot long, from the 15-foot beam. The correct answer is 20.
Here's a step-by-step solution:
1. Understand the problem: You have a 15-foot-long beam and you want to cut it into smaller pieces, with each piece being [tex]\(\frac{3}{4}\)[/tex] of a foot in length.
2. Set up the division: To determine how many pieces of [tex]\(\frac{3}{4}\)[/tex] foot long can be made from 15 feet, you divide the total length of the beam by the length of each piece:
[tex]\[
\text{Number of pieces} = \frac{\text{Total length of the beam}}{\text{Length of each piece}} = \frac{15}{\frac{3}{4}}
\][/tex]
3. Simplify the division: Dividing by a fraction is the same as multiplying by its reciprocal. The reciprocal of [tex]\(\frac{3}{4}\)[/tex] is [tex]\(\frac{4}{3}\)[/tex]. So:
[tex]\[
\frac{15}{\frac{3}{4}} = 15 \times \frac{4}{3}
\][/tex]
4. Perform the multiplication: Multiply 15 by [tex]\(\frac{4}{3}\)[/tex]:
[tex]\[
15 \times \frac{4}{3} = \frac{15 \times 4}{3} = \frac{60}{3}
\][/tex]
5. Simplify the fraction: Simplify [tex]\(\frac{60}{3}\)[/tex] by doing the division:
[tex]\[
\frac{60}{3} = 20
\][/tex]
So, the carpenter can cut 20 pieces of wood, each [tex]\(\frac{3}{4}\)[/tex] of a foot long, from the 15-foot beam. The correct answer is 20.
