Question

last week, jacob ran 2 miles. this week, he plans to run 1 3/4 times as far as last week. how many miles does jacob plan to run this week? simplify your answer and write it as a fraction or as a whole or mixed number. miles submit

Explanation:

Step1: Convert mixed number to improper fraction

The multiplier is \(1\frac{3}{4}\). To convert this mixed number to an improper fraction, we use the formula \(a\frac{b}{c}=\frac{a\times c + b}{c}\). So, \(1\frac{3}{4}=\frac{1\times4 + 3}{4}=\frac{7}{4}\).

Step2: Multiply by last week's miles

Last week Jacob ran 2 miles. To find this week's distance, we multiply 2 by \(\frac{7}{4}\). So, \(2\times\frac{7}{4}=\frac{2\times7}{4}=\frac{14}{4}\).

Step3: Simplify the fraction

Simplify \(\frac{14}{4}\) by dividing numerator and denominator by their greatest common divisor, which is 2. \(\frac{14\div2}{4\div2}=\frac{7}{2}\), and converting \(\frac{7}{2}\) to a mixed number gives \(3\frac{1}{2}\).

Answer:

\(3\frac{1}{2}\)