Solve the problems. Show your
complete solution.
1. A rope is 6 3/4 meters long. If it is cut
into ¾4-meter pieces, and then ½ of all
those pieces are used for a project,
how many meters of rope were used?

The answer is 3.375 meters.1. Convert the mixed number to an improper fraction.The length of the rope is [tex]$$6 \dfrac{3}{4}$$[/tex] meters. To convert this to an improper fraction:[tex]$$6 \dfrac{3}{4} = \frac{6 \times 4 + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4}$$[/tex] meters.2. Determine the number of [tex]$$\dfrac{3}{4}$$[/tex]-meter pieces.To find how many pieces of [tex]$$\dfrac{3}{4}$$[/tex] meters can be cut from [tex]$$\dfrac{27}{4}$$[/tex] meters, divide:[tex]$$\dfrac{27}{4} \div \frac{3}{4} = \frac{27}{4} \times \frac{4}{3} = \frac{27 \times 4}{4 \times 3} = \frac{27}{3} = 9$$[/tex] pieces.3. Calculate half of the total pieces.Half of the 9 pieces is:[tex]$$\dfrac{9}{2} = 4.5$$[/tex] pieces.4. Calculate the total length of rope used.Each piece is [tex]$$\dfrac{3}{4}$$[/tex] meters long, so the total length used is:[tex]$$4.5 \times \dfrac{3}{4} = \frac{4.5 \times 3}{4} = \frac{13.5}{4} = 3.375$$[/tex] meters.

Answered by Storystork | 2025-07-31