Exercise 7 Page 330

We are asked to complete the steps in the following guide to dividing mixed numbers.

First, let's think about how we divide a mixed number by a mixed number. Here is an example. 3 14 ÷ 1 25 We will explain step by step how we divide mixed numbers using this quotient.

1. First, write the mixed numbers as improper fractions. An improper fraction is a fraction where the numerator is larger than the denominator. 3 14 ÷ 1 25 = 13/4 ÷ 7/5
2. Next, multiply by the reciprocal of the divisor. To write the reciprocal of the divisor, we swap its numerator with its denominator.13/4 ÷ 7/5 = 13/4 * 5/7
3. Last, multiply the fractions as we would normally do, then simplify the expression.

Now let's think about what we would do if one of the numbers was a whole number. We would follow slightly different steps. 5 ÷ 1 25

1. First, rewrite the whole number as a fraction. Remember that we can always write a whole number as itself over 1. 5 ÷ 1 25 = 5/1 ÷ 1 25
2. Rewrite the mixed number as an improper fraction. 5/1 ÷ 1 25 = 5/1 ÷ 7/5
3. Next, write the reciprocal of the divisor. 5/1 ÷ 7/5 = 5/1 * 5/7
4. Finally, multiply the fractions.

Notice that the last three steps are the same steps as when we divide two mixed numbers. Let's then fill in the blanks with what we found.