# Introduction to Fractions

**Learning Objectives
**

At the end of this lesson, you will be able to:

1. Understand what fractions are and what we use them for in everyday

workplace situations.

2. Understand how the concept of fractions is related to other math skills .

3. Understand how to perform simple mathematical operations with fractions.

4. Apply fractions to everyday workplace situations.

5. Write a fraction for a picture of a part of a whole or group.

6. Understand how to simplify both proper and improper fractions.

7. Understand how to add, subtract , multiply and divide fractions.

This lesson will include exercises on the simple computation of fractions as well as

exercises that will help you to understand what the written forms of fractions actually

represent. This lesson is not meant to teach you difficult computations of fractions but

only introduce you to the concept of fractions and the different expressions of fractions

that you may encounter in the workplace or your every day life.

**Vocabulary and Key Terms**

**common denominator**- A number into which all the denominators of a set of

fractions may be evenly divided.

**denominator**- The quantity below the line indicating the number of units into which a

whole is divided.

**divisor**- The number that you are dividing by.

**equivalent fractions**- Two or more fractions that are of equal value such as 4/8,

2/4, and ½.

**fraction bar**- The line that separates the numerator from the denominator.

**greater than symbol (>)**- This is an arrow between two numbers that looks like a

on its side and pointing toward the smaller number. It is used to express the

fact that one number is larger than the other number.

**greatest common factor (GCF)**- The largest number that will divide evenly into

both the numerator and denominator of a fraction .

**improper fraction**- A fraction with a numerator (top number) equal to or greater

than the denominator (bottom number).

**invert**- To turn upside down.

**least common multiple ( LCM )**- The lowest number that two or more numbers can

be divided into evenly.

**less than symbol (<)**- An arrow between two numbers that is pointing toward the

smaller number. It is used to express the fact that one number is smaller than the

other number.

**lowest common denominator (LCD)**- The lowest/smallest number that all

denominators will divide evenly into.

**mixed number**- A number consisting of a whole number and a fraction such as 1½ or

3 1/8.

**multiplication**- Combining equal groups to get a total. The symbol “×” (times) is

used to indicate multiplication.

**numerator**- This is the top number in a fraction.

**proper fraction**- A fraction where the top number is smaller than the bottom

number.

**reciprocal**- The number turned upside down. The reciprocal of 4/1 is ¼. Likewise,

the reciprocal of 3/5 is 5/3 and the reciprocal of 4/9 is 9/4. This is also known as

inverting.

** Prescription for Understanding **

We use fractions when we want to name a part of something that is less than the
whole

or a group of items. One assumption that we make when we talk about fractions is
that

the whole or group that we are talking about is divided into equal parts. For
example,

we could divide a whole pie into six parts and to use a fraction of one sixth to
refer to

one of the pieces, then we are assuming that pie is divided into six equal
parts. We

may refer to one pencil in a group of ten pencils as being one tenth of the
group of

pencils, even though some of the pencils may be longer than the others. Observe
the

following two examples

**PARTS OF A WHOLE**

The circle above is divided into four equal parts that resemble a pie with four
large

pieces. Each so-called piece of the pie represents one fourth of the total pie.
Each

portion may also be written as 1/4 or sometimes be called a fourth.

PARTS OF A GROUP

Since there are a total of six circles in the group above, the dark shaded
figure above

represents one sixth of the total group of figures. If each of the small circles
represents

balls then we could say that one of the balls is one sixth of the total group of
balls. We

could also express this part of the total group as 1/6 of the total group of
balls.

As health care providers, you will not be required to do any difficult math
operations

with fractions. You may need to understand and use the concept of fractions
while you

are performing your daily work. Since most of your activities do not require a
great deal

of computation, most of our exercises and skill practice will focus on the
understanding

of what fractions are, and how they are used in your work environment.

**Proper Fractions**

When working with proper fractions, it is important to simplify them or, in
other words,

reduce them to their lowest terms. To do this you need to find the Greatest
Common

Factor (GCF) for the numerator and the denominator. This is the greatest number
that

will divide into both the numerator and denominator.

Example: 40/60 will reduce to 2/3 by dividing both the numerator and the
denominator

by 20, which is the greatest common factor (GCF).

To reduce a fraction to its simplest form:

1. Find the GCF of the numerator and denominator

2. Divide both the numerator and denominator by the GCF.

Example: Find the simplest form of 10/15.

1. The GCF of 10 and 15 is 5.

2.

3. 2/3 is the simplest form.

**Improper Fractions
**

When working with an improper fraction, remember to reduce it by making it a mixed

number and then reducing the remainder by the GCF.

1. First change the fraction to a mixed numeral.

2. Then divide the numerator and denominator by the GCF.

Example: Find the simplified form of 6/4.

6/4 is reduced by making it a mixed number and then reducing the remainder by

dividing it by 2, the GCF. The whole number does not change when the fraction

is reduced to lowest terms.

6/4 = 1 2/4 2 ÷ 2 = 1 and 4 ÷ 2 = 2 Therefore 2/4 = ½ so 6/4 = 1½

**Skill Check
**

Reduce each fraction to lowest terms, using the GCF.

1. 4/8 = __________

2. 10/15 = __________

3. 9/3 = __________

Circle the proper fraction in each pair.

4. ½ or 4/3

5. 6/7 or 7/6

6. 3/2 or 5/7

Change each improper fraction to a mixed numeral.

7. 7/3 = __________

8. 16/5 = __________

9. 18/7 = __________

10. 40/9 = __________

** Addition of Fractions **

When adding mixed numbers, find the Least Common Denominator (LCD) of the

fractions as needed. First add the fractions, then add the whole numbers. Reduce
the

fraction sum to lowest terms.

Problem: 1¼ + 2 7/8 = _______________

**
Step 1: **Find the LCD. Since 4 can divide into 8, 8 is the common denominator

(you are looking for the smallest number that both of the denominators, 4 and

8, can divide into evenly, and not have a remainder.)

**Step 2:**Rename (change) the fraction to a fraction using a common denominator:

Example: ¼ = 2/8

**Step 3:**Add the fractions and the whole numbers.

Example

**Step 4:**If required, rename the improper fraction as a mixed number and add.

Example: 3 9/8 = 3 + 1 1/8 = 4 1/8

Problem: 5 ¼ + 3 2/3 = _______________

**Step 1:**Find the LCD.

Example:

¼ + 2/3 = (1/4 × 3/3 ) + (2/3 × 4/4) =

3/12 + 8/12 = 11/12

**Step 2:**Rename (change) the fraction to a fraction using a common denominator:

Example: ¼ = 3/ 12 and 2/3 = 8/12

**Step 3:**Add the fractions and the whole numbers.

Example:

**Step 4:**If required, rename the improper fraction as a mixed number and add.

Not required in this example because 8 11/12 is not an improper fraction.

Problem: 3 2/3 + 7 3/5 + 4 ¼ = _______________

**
Step 1:** Find the LCD.

Example: 2/3 + 3/5 + ¼

**Step 2:**Rename (change) the fractions(s) to a fraction using the common

denominator.

Example: 2/3 = 40/60 and 3/5 = 35/60 and ¼ = 15/60

**Step 3:**Add the fractions and the whole numbers.

Example: 3 40/60 + 7 36/60 + 4 15/60

**Step 4:**If required, rename the improper fraction as a mixed number and add.

Example: 14 91/60 or 14 + 1 31/60 = 15 31/60

**Skill Check**

11. 1 1/3 + 2 3/8 + 3 3/5 = _______________

12. 2 7/8 + 3¼ + 9 5/6 = _______________

13. 2 4/5 + 1 9/8 = _______________

14. 1 7/8 + 3½ + 5 1/9 = _______________

15. 1¾ + 2 1/8 + 1 5/7 = _______________

16. 1 3/5 + 2 1/3 + 3 3/8 = _______________

17. 2 9/8 + 1 4/5 = _______________

18. 1 1/8 + 2¾ + 1 5/7 = _______________

19. 2 5/6 + 3 7/8 + 9¼ = _______________

20. 1 1/9 + 3 7/8 +5½ = _______________

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