# Equivalent fractions Types of Fractions And Mixed Numbers

**Subject : **

Mathematics

**Term :**

First Term

**Week:**

Week 5

**Class :**

Jss 1

**Previous lesson : **

The pupils have previous knowledge of **Fractions: (a) Meaning of Fraction (b) Types of fractions (Proper & Improper) (c) Mixed numbers**

**Topic : **

I. Equivalent fractions

II. Concept of equivalent fractions in sharing commodities.

III. Problem solving in quantitative aptitude (QR)

Fractions

**Behavioural objectives :**

At the end of the lesson, the pupils should be able to

- Mention ways of converting equivalent fractions to lowest term .
- explain the steps that are involved in using equivalent fractions in sharing commodities

**Instructional Materials :**

- Wall charts
- Pictures
- Related Online Video
- Flash Cards

**Methods of Teaching :**

- Class Discussion
- Group Discussion
- Asking Questions
- Explanation
- Role Modelling
- Role Delegation

**Reference Materials :**

- Scheme of Work
- Online Information
- Textbooks
- Workbooks
- 9 Year Basic Education Curriculum
- Workbooks

**Content :**

**Equivalent Fraction**: Two or more fractions are said to be equivalent if they have the same values. Equivalent fractions can be obtained by multiplying or dividing the numerator and the denominator by the same number.

When the operation performed on the original fraction to get the new fraction is division, it is referred to as simplification .Here their common factor is used in dividing the numerator and the denominator.

i.Multiplication

:. The fraction 3/5, 6/10 and 12/20 are said to be equivalent fractions.

ii. Division

= 150 = 75 = 15

200 100 20

:. The fractions ^{150}/_{200}, ^{75}/_{100} and ^{15}/_{ 20} are said to be equivalent fractions.

iii. Simplification: by dividing both numerator and denominator by a common factor.

44 = 22

70 35

Example 1.

Find the missing numbers

(a) ^{1}/_{3}= ^{3}/_{9} = ^{6}/_{A} = ^{B}/_{24} = ^{50}/_{C} = ^{D}/_{900} = ^{100}/_{E}

(b) ^{1}/_{5} = ^{10}/_{50} = = =

solution

(a) = ^{1}/_{3} =^{3}/_{9} = ^{6}/_{A} =^{B}/_{24} = ^{50}/_{C}= ^{D}/_{900} = ^{100}/_{E}

= ^{1}/_{3} =^{6}/_{A}, ^{1}/_{3} = 1 x 6 =^{ 6}/_{18} A = 18.

= ^{1}/_{3} =^{B}/_{24}, ^{1}/_{3} = 1 x 8 = ^{8}/_{24} B = 8

3 x 8

= ^{1}/_{3} = ^{50}/_{C}, ^{1}/_{3} = 1 x 50 = ^{50}/_{150} , C = 150

= ^{1}/_{3} =^{D}/_{900} , ^{1}/_{3} = 1 x 300 = ^{300}/_{900} , D = 300

3 x 50

= ^{1}/_{3} = ^{100}/_{E}, 1/_{3} = 1 x 100 = ^{100}/_{300} , E = 300

3 x 100.

Thus, the missing numbers calculated will make the fractions equivalent.

= ^{1}/_{3} =^{3}/_{9} = ^{6}/_{18} = ^{8}/_{24} = ^{50}/_{150} = ^{300}/_{900} = ^{100}/_{300}.

(b)

= ^{1}/_{5} = , ^{1}/_{5} x ^{2}/_{2}, missing number = 2

= ^{1}/_{5}= ^{1}/_{5} x ^{4}/_{4} =^{ 4}/_{20} , missing number = 20

= ^{1}/_{5}= ^{1}/_{5} x ^{20}/_{20} = ^{20}/_{100}, missing number = 20

= ^{1}/_{5}= , ^{1}/_{5} x ^{24}/_{24} = ^{24}/_{120},missing number = 120

Example

Find the missing numbers.

(a) =

(b) =

( c ) =

(d) 7 = 14

9

Solution

(a) 2 = ……. think of what will multiply 3 to give 18..

3 18

= 2/3 x 6/6 =2 x 6 = 12/18

3 x 6

:. The missing number is 12.

(b) 5 = 20 think of what will multiply 5 to give 20

6

= 5 x 4 = 20

6 4 24

the missing number is 24

(c ) 3 = ……

5 15 .think of what will multiply 5 to give 15.

= 3 x 3 = 3 x 3 = 9

5 3 5 x 3 15

:.the missing number is 9.

(d) 7 x 2 = 7 x 2 = 14

9 2 9 x 2 18 think of what will multiply 9 to give 18

:. The missing number is 18

**EVALUATION**

1.Find the missing numbers

¾ =^{6}/_{8} = ^{15}/_{A} = ^{24}/_{B} = ^{C}/_{28} =^{ D}/_{100} = ^{E}/_{24}

2. Find the missing numbers

i. 3 =

8 48

ii 5 =

9 36

iii. 5 = 20

6

**READING ASSIGNMENT**

1. Essential Mathematics for JSS1 by AJS Oluwasanmipg 38

2.New General Mathematics for JSS1 by M.F Macrae eta l pg 30-31.

**II.Equivalent Fractions in Sharing Commodities**

Problems involving sharing of commodities can be resolved with the knowledge of fractions. Some examples below will help us to understand this aspect of fraction.

Example1

Some notebooks where shared into 18 equally. If 5 exercise books were given to Ojo, what fraction is left?

Solution

Number of notebooks =18

Ojo’s share = 6

Number left = 18 – 6 = 12

Fraction left =^{12}/_{18 } = ^{12}/_{18} ÷^{ 6}/_{6}

= ^{2}/_{3 }

Example 2

A market woman had 90 yams. She sold^{2}/_{3} of it. How many yam did she sell?

Solution

No of yams = 90

No sold = ^{2}/_{3} of 90

= ^{2}/_{3} x 90 = 2 x 30

= 60 yams

:. 60 yams where sold.

Examples

Some oranges were shared out. Olu got ^{3}/_{8}of them. He gave 5 to his brother and 4 to her sister and had 6 left. How many oranges were there altogether?

Solution

Fraction received by Olu = ^{3}/_{8}

No of oranges he gave out = 5 + 4 = 9

No of oranges left with him = 6 = 9 + 6 = 15.

As equivalent fraction, ^{3}/_{8 } =^{15}/? = 3 x 5 =^{15}_{/40}.

8 x 5

:.40oranges were there altogether.

Example 4

In a shop, the price of a radio is reduced by one third .If the original price of the radio is N24, 000 what is the reduced price?

Solution

Original price = N2400

^{1}/_{3} of this price = ^{1}/_{3} x 2400 =N800

reduced price =2400- 800 = N1600.

Alternatively,

Consider the original price as unit

:. Reduced price = 1 – ^{1}/_{3} = ^{2}/_{3}

^{2}/_{3} of the unit price =^{2}/_{3} x 2400 = N1600

**EVALUATION**

1. In a class of 40 students, ¼ are doing science subjects, ^{1}/_{5}are doing arts and the remaining are doing commercial subjects. How many students are :(a) doing science (b) commercial?

2. In a service. ¼ of the people are men , 1/3 are women and the rest are children. If there are 50 children, how many (a) people are there altogether (b) more women than men are there ?

**READING ASSIGNMENT**

1. Essential Mathematics for JSS1 by AJS Oluwasanmipg 49-51

2. New General Mathematics for JSS1 by MF Macraeetalpg 33 -36.

III. **Problem Solving in Quantitative Aptitude **

Some of the examples under quantitative aptitude(reasoning ) have been seriously dealt with at the early part of this topic. Let us take some more examples .

Example 1

Find the missing numbers

( a) 16 = (B ) 10 =

48 3 168

( c ) 3 =

749

Solution

(a) 16 = think of a number that will divide 48 to give 3

48 3

= 16 ÷ 16 = 1

48 ÷ 16 3

:. The missing number is 1.

(b) 10 =

16 8 ‘ think of a number which will divide 16 to give 8’

= 10 ÷ 2 = 5

16 ÷ 2 8.

The missing number is 5.

( c) 3 = think of a number that will multiply 7 to give 49

7 49

= 3 x 7 = 3 x 7 = 21

7 7 7 x 7 49

:. The missing number is 21.

Example 2

Reduce the following fractions to their lowest terms/

(a) 5 (b) 24 ( c ) 14

100 54 21

Solution

The concept of equivalent fraction using division as the operation can be very helpful.

(a) 5 = 5 ÷ 5 = 1

100 100 ÷5 20

(b) 24 = 24 ÷2 = 12 = 12 ÷ 13 = 4

54 54 ÷2 27 27 ÷ 3 9

(c) 14 = 14 ÷7 = 12

21 21 ÷ 7 3

Example 3

What fraction of

- 6 weeks is 6 days?
- 650m is 1km?
- 4mm is 10cm?
- 500g is 2kg?

Solution

Before reducing fractions, the quantities must be in the same units.

(a) 6 weeks ………..6 days.

= 6 days

6 weeks

= 6 days= 6

6 x 7 days 6 x 7

= 1 the fraction = 1

7 7

(b) 650m ——– 1km

= 650 m = 650m = 65 ÷ 5 = 13

1km 1000m 1000 ÷ 5 20

(c) 4mm ……….10cm

= 4mm = 4mm = 4

10cm 10 x10 100

= 4 ÷ 4 = 1

100 ÷ 4 25

The fraction = 1/25.

(d) 500g ……….2kg

= 500g = 500g = 500 = 5

2kg 2000g 2000 20

= 5÷ 5 = 1

20 ÷ 5 4

the fraction is ¼

**EVALUATION**

1. Find the missing numbers

(a) 55 = 11

305 ?

(b) 9 = ?

11 99

2. Express 13 weeks as a fraction of 1 year.

**READING ASSIGNMENT**

1. Essential Mathematics for JSS 1 by AJS Oluwasanmi ,pg

2. New General Mathematics for JSS1 by Mf Macraeetalpg 37.

**WEEKEND ASSIGNMENT**

1. Which of the following is not equivalent to ½ ?

a. ^{9}/_{18} b. ^{11}/_{22 }c. ^{15}/_{30} d. ^{16}/_{32} e. ^{24}/_{42}

2. To express the fraction 30/48 in its lowest term, divide the numerator and demominator by

A. 2 B. 3 C.5 D. 6 E. 8

3.45 minutes , expressed as a fraction of one hour is

a. 1/60 b. 1/45 c. ¾ d. 4/5 e. 4/3

4. The missing number in the fraction 3 = ?

4 20 is

a. 6 b. 9 c. 12 d. 5 e. 15.

5. A woman bought 2 crates of eggs. ¼ of them are bad. How many of the eggs are good?

a. 3/6 b. 24 c. 48 d.12 e. 32.

**THEORY**

1.Find the missing numbers

1 = ? = ? = ? = 5

4 8 12 16 ?

(b) 2 = ? = ? = 8 = 10

5 10 15 ? ?

2. A drum holds 2 ½ litres of water when itsis ¾ full. How many litres of water can it hold when it is

(a) full, b, two-third (c)empty.

**Presentation**

The topic is presented step by step

Step 1:

The class teacher revises the previous topics

Step 2.

He introduces the new topic

Step 3:

The class teacher allows the pupils to give their own examples and he corrects them when the needs arise

**Conclusion**

The class teacher wraps up or conclude the lesson by giving out short note to summarize the topic that he or she has just taught.

The class teacher also goes round to make sure that the notes are well copied or well written by the pupils.

He or she does the necessary corrections when and where the needs arise.