Problem Solving - Fractions worksheet - Free Printable

Let's solve each problem step by step:

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Problem 1:

Mark ran \(\frac{3}{4}\) of a mile. Tony ran \(\frac{5}{8}\) of a mile. Who ran further?

#### Solution:
To compare the distances, we need to find a common denominator for the fractions \(\frac{3}{4}\) and \(\frac{5}{8}\).

- The denominators are 4 and 8.
- The least common denominator (LCD) is 8.

Convert \(\frac{3}{4}\) to a fraction with a denominator of 8:
\[
\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}
\]

Now compare \(\frac{6}{8}\) and \(\frac{5}{8}\):
- \(\frac{6}{8} > \frac{5}{8}\)

Thus, Mark ran further.

Answer: Mark

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Problem 2:

A pizza is cut into eight equal slices. Jessica is told to take one-fourth of the pizza. How many slices should she take?

#### Solution:
The pizza is divided into 8 slices, and Jessica needs to take \(\frac{1}{4}\) of the pizza.

Calculate \(\frac{1}{4}\) of 8 slices:
\[
\frac{1}{4} \times 8 = \frac{8}{4} = 2
\]

Jessica should take 2 slices.

Answer: 2

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Problem 3:

Shawn read \(\frac{5}{6}\) of a book. Terrance read \(\frac{6}{8}\) of the same book. Who read most of the book?

#### Solution:
To compare the fractions \(\frac{5}{6}\) and \(\frac{6}{8}\), we need a common denominator.

- The denominators are 6 and 8.
- The least common denominator (LCD) is 24.

Convert \(\frac{5}{6}\) to a fraction with a denominator of 24:
\[
\frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24}
\]

Convert \(\frac{6}{8}\) to a fraction with a denominator of 24:
\[
\frac{6}{8} = \frac{6 \times 3}{8 \times 3} = \frac{18}{24}
\]

Now compare \(\frac{20}{24}\) and \(\frac{18}{24}\):
- \(\frac{20}{24} > \frac{18}{24}\)

Thus, Shawn read more of the book.

Answer: Shawn

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Problem 4:

Fred’s teacher told him to simplify the fraction \(\frac{6}{9}\). What should be Fred’s answer?

#### Solution:
To simplify \(\frac{6}{9}\), we need to find the greatest common divisor (GCD) of 6 and 9.

- The factors of 6 are: 1, 2, 3, 6
- The factors of 9 are: 1, 3, 9
- The GCD is 3.

Divide both the numerator and the denominator by 3:
\[
\frac{6 \div 3}{9 \div 3} = \frac{2}{3}
\]

The simplified fraction is \(\frac{2}{3}\).

Answer: \(\frac{2}{3}\)

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Problem 5:

Ray bought a large pizza cut into 12 slices. He ate 3 of the slices. Write the fraction of the pizza eaten in its simplest form.

#### Solution:
Ray ate 3 out of 12 slices. The fraction of the pizza eaten is:
\[
\frac{3}{12}
\]

Simplify \(\frac{3}{12}\) by finding the GCD of 3 and 12.

- The factors of 3 are: 1, 3
- The factors of 12 are: 1, 2, 3, 4, 6, 12
- The GCD is 3.

Divide both the numerator and the denominator by 3:
\[
\frac{3 \div 3}{12 \div 3} = \frac{1}{4}
\]

The simplified fraction is \(\frac{1}{4}\).

Answer: \(\frac{1}{4}\)

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Final Answers:

1. Mark
2. 2
3. Shawn
4. \(\frac{2}{3}\)
5. \(\frac{1}{4}\)

\boxed{Mark, 2, Shawn, \frac{2}{3}, \frac{1}{4}}