5.1Fractions, Mixed Numbers,

and Rational Expressions

Fraction: A number that describes a part of a whole.

Numerator

Denominator

Numerator: The number written in the top position of a fraction

Denominator: The number written in the bottom position of a fraction.

4

3

Rational Number: A number that can be expressed as a ratio of integers.

Name the Fraction Represented by a Shaded Region

Answer:

Explanation: There are 10 equal-sized divisions in the whole region and 3 are shaded.

10

3

Word Question

In a group of 35 people at a conference, 17 are wearing glasses. What fraction of the people at the conference are wearing glasses? What fraction are not wearing glasses?

You Try

Graph fractions on a Number Line

Divide the distance between 0 and 1 into X equal spaces, where X is the number in the denominator position.

Ex.

4

3

More Examples

8

3

6

5

4

1

Simplify Fractions

Simplify: The process of writing an equivalent expression with fewer symbols or smaller numbers

Simplest form: An equivalent expression written with the fewest symbols and the smallest numbers possible

Rules to Keep in Mind

ateindetermin0

0

0n when undefined,0

0n when ,1

001

nn

nn

nn

Write Equivalent Fractions

An equivalent fractions are fractions that name the same number

Ex.

Rule of thumb, You can multiply or divide a fraction by any non-zero number as long as you do it to both the numerator and the denominator.

8

4,

6

3,

4

2,

2

1

Examples

?

5

24

20

16

?

8

3

Use <, >, or = to Write a True Statement

We can easily compare fractions that have the same denominator by looking at their numerator.

What if they do not have the same denominator?

2 35 5<

To Compare Two Fractions:

1. Write equivalent fractions that have a common denominator

2. Compare the numerators of the equivalent fractions

Example

Write equivalent fractions that have a common denominator, then compare numerators. A common multiple for 8 and 7 is 56, so our common denominator is 56.

5 4?

8 7

5 5 358 8 6

77 5

= =gg

a.

47=4 g87 g8

=3256

35 3256 56

>Answer:

You Try

€

3

7 ?

4

9

−2

7 ? −

12

42

Write Improper Fractions as Mixed Numbers

Improper Fraction: A fraction in which the absolute value of the numerator is greater than or equal to the absolute value of the denominator. ie. If the number on top is bigger than or

equal to the number on the bottom.

Mixed Number: An Integer combined with a fraction.

To write an improper fraction as a mixed number:

1. Divide the denominator into the numerator.

2. Write the result in the following form.

€

Quotientremainder

original denominator

Write the improper fraction as a mixed number.

Solution: Divide 20 by 3.

203

a.

3 2018−

2

6

quotient

remainder

original denominator

203 3

62=

Example

€

13

3

32

5

−37

4

Write Mixed Numbers as Improper Fractions

The same but opposite1. Multiply the integer by the denominator.

2. Add the resulting product to the numerator to find the numerator of the improper fraction.

3. Keep the same denominator.

Write the mixed number as an improper fraction.

Solution:

75

8a.

7 8 5 7 40 7 475

8 8 8 8+ += = =g

We multiplied 8 by 5 to get 40 , then added 7 to get 47 for the numerator of the improper fraction. We kept the denominator the same.

You Try

€

62

319

−112

9