Basic Mathematics for College Students

We can obtain the same result with far less work. To change to an improper
fraction, we simply multiply 5 by 2 and add 1 to get the numerator, and keep the
denominator of 5.

This example illustrates the following procedure.

Writing a Mixed Number as an Improper Fraction

To write a mixed number as an improper fraction:

1. Multiply the denominator of the fraction by the whole-number part.


2. Add the numerator of the fraction to the result from Step 1.


3. Write the sum from Step 2 over the original denominator.

2

1

5



5  2  1

5



10  1

5



11

5

2 15

3.5 Multiplying and Dividing Mixed Numbers 259

EXAMPLE 2

Write the mixed number as an improper fraction.

Strategy We will use the 3-step procedure to find the improper fraction.

WHY It’s faster than writing as , building to get an LCD, and adding.

Solution
To find the numerator of the improper fraction, multiply 6 by 7, and add 5 to that
result. The denominator of the improper fraction is the same as the denominator of
the fractional part of the mixed number.

Step 2: add

Step 1: multiply Step 3: Use the same denominator

 

By the order of operations rule,

multiply first, and then add in

the numerator.

7

5

6



6  7  5

6



42  5

6



47

6



7 56 7 ^56

7

5

6

To write a negative mixed numberin fractional form, ignore the sign and use the
method shown in Example 2 on the positive mixed number. Once that procedure is
completed, write a sign in front of the result. For example,

Write improper fractions as mixed numbers.

To write an improper fraction as a mixed number, we must find two things: the whole-
number partand the fractional partof the mixed number. To develop a procedure to
do this, let’s consider the improper fraction. To find the number of groups of 3 in 7,
we can divide 7 by 3. This will find the whole-number part of the mixed number. The
remainder is the numerator of the fractional part of the mixed number.

Whole-number part

T d

—

The remainder is the

numerator of the

fractional part.

The divisor is the

denominator of the

fractional part.

2

1

3

2

(^3)  7
 6
1
7
3
3

 12

3

8



99

8

 1

9

10



19

10

 6

1

4



25

4

Self Check 2

Write the mixed number as an

improper fraction.

Now TryProblems 23 and 27

(^3 38)