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# 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 = __________

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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