WRP Basic Math Skills

Work Readiness Program

WRMA – N 1100

Business Math

Unit 2

Fractions

14

14

34

WRP Basic Math Skills

Section 2.1 What is a Fraction?

A fraction is a part of a whole.

Cut a circle into two equal parts. Each part is called one half of a circle.

We write this as .

Now cut a circle into 4 equal parts (fractions). Each piece is called one fourth or one quarter of a circle.

We write this as

If we take away one fourth we have got three fourths or three quarters.

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Example 1

A chocolate bar is divided into 8 equal parts. If Wassim eats 5 parts, we can say that he ate ‘five eighths’ of the chocolate bar.

is a fraction where:

5 represents the number of parts Wassim ate and it is called the numerator of the fraction (the number above the fraction bar).

8 represents the total number of equal parts in the chocolate bar and it is called the denominator (the number below the fraction bar)

DenominatorNumeratorFraction

73

Exercise 1

Fill in the blanks with the numerator and denominator:

DenominatorNumeratorFraction

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Section 2:1.1 Fractions Representing Shaded Parts

Example 1

Write a fraction showing the shaded part of the figure.

The numerator 2 shows the number of shaded parts.The denominator 6 shows the total number of equal parts in the figure.

Exercise 1

Write a fraction showing the shaded part of the figure.

a)

b)

c)      

d)  

   

e)

f)

Exercise 2

         

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Write a fraction showing the shaded part of each figure.

Section 2.2 Equivalent Fractions

(a) ______________

(d) ______________

(c) ______________

(b) _____________

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Fractions with the same value are called equivalent fractions.

These are fractions that represent the same amount.

From the shaded parts in the table you can see that =

We can say that is equivalent to

or

We can say that is the same as

Example 1

Galaxy decided to change the shape of their chocolate bar.

Old New

They only changed the number of pieces in the new chocolate bar.

12

12

13

13

13

14

14

15

16

16

16

1718

18

18

18

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One piece in the old bar makes two pieces in the new one.So =

We say the two fractions are equivalent because they represent the same value.

2:2.1 Identifying Equivalent Fractions

There are different methods to find if two fractions are equivalent.

1. We can cross-multiply the numerators with the denominators. If the products are equal, then fractions are equivalent.

Then =

2 × 15

30?=

3 × 10

30

2. If the quotient of the division of the numerators is equal to the quotient of the division of the denominators, the two fractions are equivalent.

Then = 15 ÷ 3 5

?=

10 ÷ 2 5

3. If the quotients of the numerators by the denominators are equal,

the fractions are equivalent.

?

2 ÷ 3 = 0.666

10 ÷ 15 = 0.666

Then =

Exercise 1

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Fill in the blanks with = or ≠

a) d)

b) e)

c) f)

2:2.2 Finding Equivalent Fractions

To find an equivalent fraction to a given one, we can either multiply or divide both numerator and denominator by the same number.

× 4

=

× 4

× 10

=

× 10

÷ 5

=

÷ 5

When we use multiplication we can find an infinite number of equivalent fractions to the original one.

We can only divide by a common factor of the numerator and the denominator.

Note here that when we multiplied by 4 or by 10 we could have multiplied by any other whole number, but in the case of the division we were only able to divide by 5.

Example 1

Find the missing value: =

Since 21 ÷ 7 = 3, then we can divide 27 by 3.

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27 ÷ 3 = 9 =

Exercise 1

Find the missing value:

a) = d) =

b) = e) =

c) =

Example 2Find two equivalent fractions.

= =

= =

Exercise 2

Find two equivalent fractions. Multiply by any number you choose.

a) = =

b) = =

c) = =

d) = =

e) =

Section 2.3 Simplifying Fractions

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When we divide the numerator and denominator of a fraction by a number

we are simplifying the fraction. The new fraction is equivalent to the first.

Can be simplified by dividing both numerator and denominator by 2. = We say that a fraction is in its simplest form when we cannot simplify it any more. = =

Exercise 1

Find equivalent fractions by dividing. Show your work.

a) 818 =

b) 1015 =

c) 2030 =

d) 1421 =

e) =

f) =

2:3.1 Simplifying Fractions Using a Calculator

To write in its simplest form using a calculator we follow the steps below:

You can use the on your scientific calculator to help simplify fractions.

It’s quicker!

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Enter the numerator 30Press on aEnter the denominator 45Press on =The screen will read 2 ⌟ 3This means that: =

Exercise 2

Use your calculator to write these fractions in their simplest form.a) b) c) d)

Section 2.4 Proper Fractions, Improper Fractions and Mixed Numbers

Proper fractions are fractions with numerators smaller than their

denominators. For example:

Proper fractions represent a part less than a whole and therefore are smaller than 1.

< 1

We see here that the numerator and denominator are equal. The fraction represents one whole.

= 1

   

   

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Fractions with numerators larger than denominators are called improper fractions. The fraction represents more than a whole.

> 1

The fractions 65

32

128 are all improper fractions and they are

larger than 1.

Improper fractions can also be written as mixed numbers.

A mixed number consists of a whole number and a fraction.

2 1

3 is a mixed number. We read this as ‘two and one third’.

Example 1

Identify each number as a proper fraction, improper fraction or mixed

number. Then write the number in words.

Whole number

Fraction

   

   

       

       

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(a) 5 1

3 proper fraction improper fraction mixed number

Five and one third

(b)127 Proper fraction improper fraction mixed number

Twelve sevenths

(c)35 proper fraction improper fraction mixed number

three fifths

Exercise 1

Write each of these as a proper fraction, improper fraction, or mixed number. Then write the fraction in words.

(a) proper fraction improper fraction mixed number

__________________________________________

(b) proper fraction improper fraction mixed number

________________________________________

(c) proper fraction improper fraction mixed number __________________________________________

(d) proper fraction improper fraction mixed number

___________________________________________

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(e) proper fraction improper fraction mixed number

____________________________________

2:4.1 Changing Improper Fractions into Mixed Numbers

We can write an improper fraction as a mixed number either manually or using a calculator.

Manually, to write as a mixed number we divide 7 by 2.7 ÷ 2 = 3 remainder 1Then = 3

So the quotient of the division is the whole number, the remainder of the division is the numerator of the fraction and the denominator stays as it is.

Using a calculator we follow the same steps we used to simplify a fraction:

Enter the numerator 7

Press on a

Enter the denominator 2Press on =

The screen will read 3 ⌟ 1 ⌟ 2This means that: = 3

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Exercise 1

Write these improper fractions as a mixed number or a whole number.

(a) (b) (c)334

(d) (e) (f)653

2:4.2 Changing Mixed Numbers into Improper Fractions

Example 5

Using a calculator we follow the steps below:

Enter the number 2Press on a

Enter the number 1Press on a

Enter the number 4Press on shift

Press ona

The screen will read 9 ⌟ 4

This means that: 2 =

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Exercise 2

Write as an improper fraction

a) 3 = d) 10 =

b) 5 = e) 15 =

c) 8 = f) 3=

2.5 Comparing Fractions

?

When both fractions have the same denominator, we only need to compare the numerators.Here 1 < 3 therefore <

?

When the denominators are not equal, we need to find equivalent fractions to the ones we have with a common denominator.In this case the common denominator is 15.

= and = Since 10 > 9 then > which means that >

We also can use the cross-multiplication method:

2× 5 = 10 3 ×3 =9 10 > 9 which means that >

If the numerators of the fractions are equal, the fraction with the larger denominator is smaller. <

WRP Basic Math Skills

Exercise 1

Compare using >, <, or =

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

m)

n) 3 2

Section 2.6 Word Problems

1) A branch office of a company consists of 16 employees. Five

employees work in the morning and the rest are full-time

employees.

a) What is the number of full-time employees?b) What fraction of the employees work in the morning?c) What fraction are the full-time employees?

2) Ahmed spends his day as follows:

of the day sleepingof the day at workof the remaining time with his family

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a) How many hours does Ahmed spend?

Sleeping?

At work?

With his family?

3) Salem’s family consists of his wife Karima, his son Wahid and his

daughter Sahar.

Find the age of his family members, knowing that:

Salem is 30 years old.Sahar’s age is her father’s age.Wahid’s age is his sister’s age.

Karima’s age is the sum of two fifths Wahid’s age and five sixths Salem’s age.

Unit 2 Review

1. Write these fractions in simplest form.

(a) (b)

2. Use your calculator to write these as a mixed number or a whole number.

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(a) 185 (b)

7010

(c) 6410 (d)

12814

3. Write the following mixed numbers as improper fractions.

(a) 5 3

4 (b) 2 4

5

(c) 1 4

11 (d) 5 2

7

4. On an exam, Kassim gets 26 questions correct out of 40

questions.

(i) What fraction of the questions are correct?

(ii) What fraction of the total does he get wrong?

6.

7.

There are 243 boys in a school and 123 girls. What fraction of the total is girls?

The total number of employees in a private company is

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85. 15 are American, 23 British, 7 Emirati, and the rest are employees of other nationalities.

a) What fraction represents the Emirati employees?

b) What fraction represents the employees of other nationalities?