Question

use the number selector to find the solution. jayla ran $2\frac{7}{8}$ laps on a treadmill program. each lap was $\frac{3}{4}$ mile long. how many miles did jayla run? $2\frac{7}{8} \times \frac{3}{4} = \frac{\boldsymbol{\square}}{8} \times \frac{3}{4} = \frac{\boldsymbol{\square}}{32} = \boldsymbol{\square}\frac{\boldsymbol{\square}}{32}$

Explanation:

Step1: Convert mixed number to improper fraction

To convert \(2\frac{7}{8}\) to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(2\frac{7}{8}=\frac{2\times8 + 7}{8}=\frac{16 + 7}{8}=\frac{23}{8}\). So the first blank is \(23\).

Step2: Multiply the fractions

Now we multiply \(\frac{23}{8}\times\frac{3}{4}\). When multiplying fractions, we multiply the numerators together and the denominators together. So, \(\frac{23\times3}{8\times4}=\frac{69}{32}\). So the second blank is \(69\).

Step3: Convert improper fraction to mixed number

To convert \(\frac{69}{32}\) to a mixed number, we divide the numerator by the denominator. \(69\div32 = 2\) with a remainder of \(5\) (because \(32\times2 = 64\) and \(69 - 64 = 5\)). So, \(\frac{69}{32}=2\frac{5}{32}\). So the third blank is \(2\) and the fourth blank is \(5\).

Answer:

First blank: \(23\), Second blank: \(69\), Third blank: \(2\), Fourth blank: \(5\) (In the order of the blanks in the problem: \(\frac{23}{8}\times\frac{3}{4}=\frac{69}{32}=2\frac{5}{32}\))