Charlie reads quickly. He reads 1(3)/(7) pages every (2)/(3) minutes. Charlie reads at a constant rate. How many pages does he read per minute? pages per minute

Convert to Improper Fraction: Convert the mixed number to an improper fraction to simplify the calculation. 1(3/7) pages is the same as (7/7 + 3/7) pages, which equals (10/7) pages.Find Pages per Minute: To find out how many pages Charlie reads per minute, divide the number of pages he reads in (2/3) minutes by (2/3). The expression for the number of pages per minute is (10/7) pages ÷ (2/3) minutes.Divide by Reciprocal: To divide by a fraction, multiply by its reciprocal. So, (10/7) pages ÷ (2/3) minutes = (10/7) pages × (3/2) minutes⁻¹.Multiply Numerators and Denominators: Multiply the numerators and the denominators separately. (10 × 3) / (7 × 2) = 30/14 pages per minute.Simplify Fraction: Simplify the fraction. 30/14 can be simplified to 15/7 pages per minute.Convert to Mixed Number: Convert the improper fraction back to a mixed number if necessary. 15/7 pages per minute is the same as 2(1/7) pages per minute.

Home

Math Problems

Grade 7

GCF and LCM: word problems

Full solution

Q. Charlie reads quickly. He reads

1 \frac{3}{7}

pages every

\frac{2}{3}

minutes. Charlie reads at a constant rate.

\newline

How many pages does he read per minute?

\newline

pages per minute

Convert to Improper Fraction: Convert the mixed number to an improper fraction to simplify the calculation. $\newline$ $1\left(\frac{3}{7}\right)$ pages is the same as $\left(\frac{7}{7} + \frac{3}{7}\right)$ pages, which equals $\left(\frac{10}{7}\right)$ pages.
Find Pages per Minute: To find out how many pages Charlie reads per minute, divide the number of pages he reads in $(2/3)$ minutes by $(2/3)$ . $\newline$ The expression for the number of pages per minute is $(10/7)$ pages $\div$ $(2/3)$ minutes.
Divide by Reciprocal: To divide by a fraction, multiply by its reciprocal. $\newline$ So, $(\frac{10}{7})$ pages $\div (\frac{2}{3})$ minutes = $(\frac{10}{7})$ pages $\times (\frac{3}{2})$ minutes $^{-1}$ .
Multiply Numerators and Denominators: Multiply the numerators and the denominators separately. $\newline$ $(10 \times 3) / (7 \times 2) = 30/14$ pages per minute.
Simplify Fraction: Simplify the fraction. $\frac{30}{14}$ can be simplified to $\frac{15}{7}$ pages per minute.
Convert to Mixed Number: Convert the improper fraction back to a mixed number if necessary. $\newline$ $\frac{15}{7}$ pages per minute is the same as $2\left(\frac{1}{7}\right)$ pages per minute.