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Core Connections: Course 2

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Core Connections: Course 2 View details

2. Section 8.2

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Exercise 37 Page 451

We want to simplify the given expression.

\frac{1 2}{5} \div \frac{7}{1 0}

We can recall that dividing by a fraction is the same as multiplying by its reciprocal. Let's use this information to simplify our expression!

\frac{1 2}{5} \div \frac{7}{1 0}

DivFracByFracSL

$\frac{a}{b} / \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$

\frac{1 2}{5} \cdot \frac{1 0}{7}

Multiply fractions

\frac{1 2 \cdot 1 0}{5 \cdot 7}

Multiply

\frac{1 2 0}{3 5}

$\frac{a}{b} = \frac{a / 5}{b / 5}$

\frac{2 4}{7}

Write fraction as a mixed number

3 \frac{3}{7}

The simplified expression is equal to

3 \frac{3}{7} .

We want to simplify the given expression.

\frac{9}{4} \div (- \frac{1}{3})

We can recall that dividing by a fraction is the same as multiplying by its reciprocal. We also know that the the product of two numbers with different signs is negative. Let's use this information to simplify our expression!

\frac{9}{4} \div (- \frac{1}{3})

DivFracByFracSL

$\frac{a}{b} / \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$

\frac{9}{4} \cdot (- \frac{3}{1})

$a (- b) = - a \cdot b$

- \frac{9}{4} \cdot \frac{3}{1}

Multiply fractions

- \frac{9 \cdot 3}{4 \cdot 1}

Multiply

- \frac{2 7}{4}

Write fraction as a mixed number

- 6 \frac{3}{4}

The simplified expression is equal to

- 6 \frac{3}{4} .

We want to simplify the given expression.

- \frac{3}{5} \div (- \frac{1}{6})

We can recall that dividing by a fraction is the same as multiplying by its reciprocal. We also know that the product of two numbers with the same sign is positive. Let's use this information to simplify our expression!

- \frac{3}{5} \div (- \frac{1}{6})

DivFracByFracSL

$\frac{a}{b} / \frac{c}{d} = \frac{a}{b} \cdot \frac{d}{c}$

- \frac{3}{5} \cdot (- \frac{6}{1})

MultNegNegOnePar

$- a (- b) = a \cdot b$

\frac{3}{5} \cdot \frac{6}{1}

Multiply fractions

\frac{3 \cdot 6}{5 \cdot 1}

Multiply

\frac{1 8}{5}

Write fraction as a mixed number

3 \frac{3}{5}

The simplified expression is equal to

3 \frac{3}{5} .

Subchapter links

8.2.1 Representative Samples p.451-452

8.2.2 Inference from Random Samples p.455-456