Question

solve each word problem. write your answer as a complete sentence.

1. a strip of fabric measures $1\frac{1}{4}$ yards long. a quilt requires $2\frac{1}{2}$ strips for one row. how long is one row of the quilt?

1. on a trail, a biker travels $3\frac{1}{4}$ miles before stopping for a break. she repeats this ride $1\frac{2}{3}$ times in one day. how many miles does she ride in total?

Explanation:

Problem 1:

Step1: Convert mixed numbers to improper fractions

The length of one fabric strip is \(1\frac{1}{4}\) yards. Converting to an improper fraction: \(1\frac{1}{4}=\frac{1\times4 + 1}{4}=\frac{5}{4}\) yards.
The number of strips needed for one row is \(2\frac{1}{2}\). Converting to an improper fraction: \(2\frac{1}{2}=\frac{2\times2+ 1}{2}=\frac{5}{2}\) strips.

Step2: Multiply the length of one strip by the number of strips

To find the length of one row, we multiply the length of one strip by the number of strips: \(\frac{5}{4}\times\frac{5}{2}\).
Multiplying the numerators and denominators: \(\frac{5\times5}{4\times2}=\frac{25}{8}\).

Step3: Convert back to a mixed number

Converting \(\frac{25}{8}\) to a mixed number: \(25\div8 = 3\) with a remainder of \(1\), so \(\frac{25}{8}=3\frac{1}{8}\) yards.

Step1: Convert mixed numbers to improper fractions

The distance traveled in one ride is \(3\frac{1}{4}\) miles. Converting to an improper fraction: \(3\frac{1}{4}=\frac{3\times4 + 1}{4}=\frac{13}{4}\) miles.
The number of times the ride is repeated is \(1\frac{2}{3}\). Converting to an improper fraction: \(1\frac{2}{3}=\frac{1\times3+ 2}{3}=\frac{5}{3}\) times.

Step2: Multiply the distance per ride by the number of rides

To find the total distance, we multiply the distance per ride by the number of rides: \(\frac{13}{4}\times\frac{5}{3}\).
Multiplying the numerators and denominators: \(\frac{13\times5}{4\times3}=\frac{65}{12}\).

Step3: Convert back to a mixed number

Converting \(\frac{65}{12}\) to a mixed number: \(65\div12 = 5\) with a remainder of \(5\), so \(\frac{65}{12}=5\frac{5}{12}\) miles.

Answer:

One row of the quilt is \(3\frac{1}{8}\) yards long.

Problem 2: