Page 75 - ArithBook5thEd ~ BCC

8. Write five fractions which are equal to 1.

9. Write five fractions which are equal to 0.

10. Write 15 as a fraction.

3.3 Mixed Numbers

We have seen that a positive improper fraction represents either awhole number or a whole number
plus a proper fraction. In the latter form, it is called a mixed number.Even though it is a sum, the +
sign is omitted. Thus
1
3
2
1
represents 3 “wholes” plus an extra .
2

3.3.1 Converting an improper fraction into a mixed or whole number

Suppose we have an improper fraction
numerator
.
denominator
To convert this to a mixed number, we simply perform the division

numerator ÷ denominator,

obtaining a quotient and a remainder. Then we use these to build the mixed number as follows: the
quotient is the whole number part; the remainder over the divisor is the fractional part. Note that the
fractional part obtained in this way is always proper, because the remainder is always smaller than the
divisor. Summarizing:

numerator remainder
=quotient
denominator divisor

Example 78. Write the improper fraction 13/3 as a mixed number.

Solution. Dividing 13 by 3 yields a quotient of 4 and a remainder of 1. The corresponding mixed number
has whole number part 4 and fractional part 1/3. Thus

13 1
=4 .
3 3

If the remainder is 0, the mixed number is actually just a whole number.
Example 79. Write the improper fraction 84/7 as a mixed number.

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