Exercise 46 Page p19

To determine how many boards we can cut, we must determine the number of times

2

feet

8

inches goes into

16

feet. To begin, we should express

2

feet

8

inches in feet. Since there are

12

inches in one foot, we can rewrite

8

inches as follows.

\frac{8 inches}{1 2 inches} \Rightarrow \frac{8}{1 2} = \frac{3}{4}

Thus,

2

feet

8

inches can be expressed as

2 \frac{3}{4}

feet. Next, let's write this mixed number as an improper fraction.

2 \frac{8}{1 2} = \frac{1 2 \cdot 2 + 8}{1 2} = \frac{3 2}{1 2}

Now, we can divide

16

feet by

\frac{3 2}{1 2}

feet to determine the number of boards we can cut. If we write

16

as a fraction, we can then divide the fractions.

16 \div \frac{3 2}{1 2}

$\frac{a}{1} = a$

\frac{1 6}{1} \div \frac{3 2}{1 2}

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

\frac{1 6}{1} \cdot \frac{1 2}{3 2}

Multiply fractions

\frac{1 6 \cdot 1 2}{1 \cdot 3 2}

$\frac{a}{b} = \frac{a / 1 6}{b / 1 6}$

\frac{1 \cdot 1 2}{1 \cdot 2}

$\frac{a}{b} = \frac{a / 2}{b / 2}$

\frac{1 \cdot 6}{1 \cdot 1}

\frac{6}{1}

Calculate quotient

6

From one

16

feet long board, we can cut

6

smaller boards measuring

2

feet

8

inches.