Exercise 30 Page p19

The reciprocal of a number is what makes the product of the number and the reciprocal equal to

1 .

For any fraction, we can find the reciprocal by flipping the numerator and denominator.

\frac{a}{b} \cdot \frac{b}{a} = \frac{a \cdot b}{b \cdot a} = 1

To find the reciprocal of

3 \frac{3}{4}

we need to rewrite it as a fraction first.

3 \frac{3}{4}

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Write mixed number as a fraction

$a \frac{b}{c} = \frac{a \cdot c + b}{c}$

\frac{3 \cdot 4 + 3}{4}

\frac{1 2 + 3}{4}

Add terms

\frac{1 5}{4}

For the fraction

\frac{1 5}{4}

its reciprocal has to be

\frac{4}{1 5} .

Let's check that this is true by calculating the product.

\frac{1 5}{4} \cdot \frac{4}{1 5} = ? 1

Multiply fractions

\frac{1 5 \cdot 4}{4 \cdot 1 5} = ? 1

\frac{6 0}{6 0} = ? 1

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

1 = 1

We were able to confirm that the reciprocal of

3 \frac{3}{4}

is

\frac{4}{1 5} .