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Section 17.2 Worksheets

PDF Version of these Worksheets

Worksheet Worksheet 1
A4US

1.

Convert \(\frac{15}{4}\) from an improper fraction to a mixed number using a diagram.

2.

Convert \(\frac{17}{3}\) from an improper fraction to a mixed number using a diagram.

3.

Convert \(3 \frac{1}{5}\) from a mixed number to an improper fraction using a diagram.

4.

Convert \(2 \frac{3}{7}\) from a mixed number to an improper fraction using a diagram.

5.

Represent \(2 \frac{3}{4}\) on a number line.

Worksheet Worksheet 2
A4US

1.

Convert \(\frac{12}{7}\) from an improper fraction to a mixed number using a diagram.

2.

Suppose you are given the fraction \(\frac{a}{b}\) where \(a\) and \(b\) are both integers and \(b \neq 0\text{.}\) Describe a calculation that would give you the corresponding mixed number without drawing out a diagram.

3.

Determine the values corresponding to the positions indicated in the diagram below.

4.

Completely reduce the fractions \(\frac{21}{28}\) and \(\frac{18}{48}\text{.}\)

5.

Completely reduce the fractions \(\frac{8x^2}{6x^4}\) and \(\frac{15x^5}{35x^2}\text{.}\)

Worksheet Worksheet 3
A4US

1.

Convert \(2 \frac{3}{8}\) from a mixed number to an improper fraction using a diagram.

2.

Suppose you are given the mixed number \(a \frac{b}{c}\) where \(a\text{,}\) \(b\) and \(c\) are all integers and \(c \neq 0\text{.}\) Describe a calculation that would give you the corresponding improper fraction without drawing out a diagram.

3.

Determine the values corresponding to the positions indicated in the diagram below.

4.

Completely reduce the fractions \(\frac{25}{40}\) and \(\frac{12}{27}\text{.}\)

5.

Completely reduce the fractions \(\frac{10x^3y^2}{25xy^5}\) and \(\frac{21a^3 b^3}{49a^3b^2}\text{.}\)

Worksheet Worksheet 4
A4US

1.

Convert \(\frac{23}{5}\) and \(\frac{25}{7}\) from improper fractions to mixed numbers without drawing a diagram.

2.

Convert \(3 \frac{2}{9}\) and \(4 \frac{4}{5}\) from mixed numbers to improper fractions without drawing a diagram.

3.

Completely reduce the fractions \(\frac{35}{60}\) and \(\frac{28m^2 n^3}{36m n^8}\text{.}\)

4.

Check the presentation for errors. If you find one, circle it and describe the mistake in words.

\begin{equation*} \frac{4xy}{12x^2 y^3} = \frac{4xy}{3xy^2 \cdot 4xy} = \frac{\cancel{4xy}}{3xy^2 \cdot \cancel{4xy}} = 3xy^2 \end{equation*}

5.

Check the presentation for errors. If you find one, circle it and describe the mistake in words.

\begin{equation*} \frac{20x^2}{5x^5} = \frac{4 \cdot 5x^2}{x^3 \cdot 5x^2} = \frac{4 \cdot \cancel{5x^2}}{x^3 \cdot \cancel{5x^2}} = 4x^3 \end{equation*}

Worksheet Worksheet 5
A4US

1.

Completely reduce the fractions \(\frac{4x^2}{6x^4}\) and \(\frac{4(x+2)^2}{6(x+2)^4}\)

2.

Completely reduce the fractions \(\frac{12x y^4}{18x^4 y^2}\) and \(\frac{12 (x+2)(x-3)^4}{18(x+2)^4 (x-3)^2}\text{.}\)

3.

Completely reduce the fractions and \(\frac{9 \sin(x) \cos^3(x)}{12 \sin^2(x) \cos(x)}\text{.}\)

4.

Completely reduce the fraction \(\frac{x^2 + 5x + 6}{x^2 - 3x - 10}\text{.}\)