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UNIT 4:Equivalent fractions and operations
4.1 Concept of equivalent fractions using models
Practice Activity 4.1
Shade the equivalent fractions below
Shade the equivalent fractions. Explain your steps.
Practice Activity 4.2
Shade two more equivalent fractions in each case.
Shade two more equivalent fractions in each case. Discuss the steps to your
answers.
Activity 4.3
• Draw and shade 2/3
in A. Shade the equivalent fraction in B. Makepaper cutouts and compare their sizes.
• Use circular models like those above to find equivalent fractions.
(i) 3/4
(ii) 4/5Present your findings.
Example 4.3
Using models show equivalent fractions of: (a) 4/7 (b) 2/9
Solution
Practice Activity 4.3
Shade the equivalent fraction of each of the fractions given below.
Shade the equivalent fraction in each case. Explain your answer.
Activity 4.4
Write the shaded fractions. In each case, are they equivalent? Explainyour answer.
Example 4.4
Write the shaded fraction and its equivalent fraction.
Practice Activity 4.4
A. Write the equivalent fractions for the models below.
B. Write the equivalent fractions for the models. Discuss your answer.
Activity 4.5
Identify the shaded parts showing equivalent fractions. Write theequivalent fractions. Discuss and present your findings.
Example 4.5
(i) Which of the shaded parts show equivalent fractions?(ii) Write the equivalent fractions.
Solution
(i) The shaded parts in (a) and (c) are equal.
(ii) The fraction in (a) is 1/2
. The fraction in (c) is 2/4
The equivalent fractions shown are 1/2 = 2/4
Practice Activity 4.5
(i) Which shaded parts show equivalent fractions in each case?(ii) Write the equivalent fractions in each case. Discuss your answer.
4.2 Calculation of equivalent fractions
Activity 4.6
.
What fraction do you get?Use the same size paper cutouts to shade.
Compare 2/3 and 6/9 Are they equivalent or not?
• Repeat the same steps to find equivalent fractions of:
(a) 4/5 (b) 5/6 (c) 3/8
Explain your answer.• Where do we use equivalent fractions in daily life?
Tip:
• To find the equivalent fraction, multiply both denominator and
numerator by a whole number.
• A whole number to use include 2, 3, 4, 5, … If you multiply by 1, you getthe same fraction.
Practice Activity 4.6
Find the equivalent fractions of the given fraction. Then fill in the missingblanks and explain your answer.
Activity 4.7
Find two equivalent fractions for each fraction below. Justify your answer.
(i) 4/5 (ii) 4/7 (iii) 4/9 (iv) 27/81
Example 4.7
Find two equivalent fractions for: (a) 4/11 (b) 5/9
Solution
(a) Multiply 4/11 by 2/2 to find the first one. Multiply 4/11 by 3/3 to find the next
fraction.
• 4/11 × 22= 8/22
• 4 /11 × 3/3= 12/33
Two equivalent fractions of 4/11 are 8/22 and 12/33.
(b) Multiply 5/9 by 2/2 to find the first one. Multiply 5/9 by 3/3 to find next one.
• 5/9× 2/2 = 10/18 • 5/9× 3/3= 15//27
Two equivalent fractions of 5/9 are 10/18 and 15/27.
Practice Activity 4.7
A. Find two equivalent fractions for the following fractions.
1. 5/8
2. 3/7
3. 2/3
4. 6/11
5. 3/10
B. Find two equivalent fractions for the following fractions. Discuss and
present your findings.
1. 7/9
2. 8/12
3. 3/5
4. 6/7
5. 9/13
6. 6/97. 4/6
Activity 4.8
Find three equivalent fractions for each of the following:
(a) 2/3
(b) 3/5
(c) 5/6
(d) 5/9Discuss the steps you have followed to calculate them.
Practice Activity 4.8
A. Find three equivalent fractions for each of the following.
1. 1/5
2. 8/15
3. 5/9
4. 5/12
5. 5/6
B. Write three equivalent fractions for each of the following. Explain your
answer.
1. 3/8
2. 4/5
3. 3/4
C. Find three equivalent fractions for the following. Discuss and present
your findings.
1. 7/16
2. 1/2
3. 5/84. 7/8
Practice Activity 4.9
1. Find the equivalent fraction with the denominator 30 for the following.
(a) 1/3
(b) 1/5
(c) 1/10 (d) 1/15
2. Find the equivalent fraction with the denominator 48 for the fractions
below. Then explain your answer.
(a) 1/2
(b) 1/3
(c) 1/4
(d) 2/96 (e) 1/8.
Change the fractions below so that their denominators are 60. Discuss
and present your findings.
(a) 2/3
(b) 3/4
(c) 4/5
(d) 20/600 (e) 10/120 (f) 7/15
4.3 Addition of fractions with different denominatorsusing equivalent fractions
Practice Activity 4.10
Fill in the missing numbers.
Practice Activity 4.11
Tip:
When finding equivalent fractions to add the fractions:
(i) Identify the different denominators.
(ii) Check if denominators are multiples of each other. Then use the
largest denominator as a common denominator.
(iii) Where denominators are not multiples of each other, find common
multiples for them. For example, 2 and 3 have a common multiple of
6. So common denominator is 6.(iv) Add fractions with a common denominator.
4.4 Addition of fractions with different denominators using LCM
Revision
Least Common Multiple is written as LCM.
Find the LCM of the following numbers.1. 3, 9 2. 4, 6 3. 10, 12 4. 3, 9, 6 5. 7, 9
4.5 Addition of more fractions with different denominators
Look at the following.
In these fractions the numerator is smaller than the
denominator. These are called proper fractions.
In these fractions the numerator is bigger than the
denominator. Such fractions are known as improper fractions.
is called a mixed number. It has a whole number and a fraction.
4.6 Addition of mixed numbers with different denominators
4.7 Word problems for addition of fractions
Activity 4.19
Mum wanted to prepare a good meal for lunch. She then bought 1/8
kilogram of beef and 1/2
kilogram of liver. Find the weight of both beef andliver. Discuss the steps to your answer. Present your findings.
Practice Activity 4.19
1. Carene was celebrating her birthday. Her mother bought her a cake.
Carene shared the cake with her mother. Carene ate 4/9
of the cake. Her mother took 1/3 of the same cake. The remaining part of the cake
was eaten by her father. What is the total fraction of the cake eaten by
Carene and her mother? Explain why we should share what we have.
2. In the morning, a cook wanted to make some tea. He mixed 1/4 litre of
milk and 1/8 litre of water. He then boiled them. Find the amount of tea
in litres he made. Discuss your steps.
3. During a sports day, a pupil wanted to carry a bottle of water. The
bottle had 1/3 litre of clean water. He added 1/2
litre more clean water into the bottle. Calculate the amount of clean water he had in the bottle.
Justify your answer. Tell the importance of drinking clean water.
4. A farmer had inherited 4/7 acre of land from his parents in 2014.
In 2016, the farmer bought 7/10 acre of land to expand his investment
activities. Determine the size of land he had altogether in 2016.Explain some importance of farming.
5. In a community work to clean the streets, adults and children
participated. The fraction of men was 1/3 of all people. 1/4 of all people
were women and the rest were children. Find the fraction for both
men and women of all the people. Discuss your steps. What othercommunity work do we do?
4.8 Subtraction of fractions with differentdenominators using equivalent fractions
Practice Activity 4.20
A. Use equivalent fractions to work out the following.
B. Work out the following using equivalent fractions. Discuss your answer.
C. Use equivalent fractions to work out the following questions. In each
case present your findings.
4.9 Subtraction of fractions with different denominators using the LCM
Activity 4.23
Subtract these fractions using Lowest Common Multiple (LCM).
Discuss the steps you followed.
Activity 4.24
Subtract the following using their LCM.
Discuss how you arrived at your answer.
4.10 Subtraction of whole numbers and fractions
4.11 Subtraction of mixed numbers with different
denominators
Activity 4.26Work out the following using the LCM.
4.12 Word problems for subtraction of fractions
Activity 4.27
Use the LCM to solve the following.
(i) A farmer has 7/8 acre of land. A 1/2 acre from the land is planted with
crops. The rest is for the homestead. How much land is used for the
homestead?
(ii) A storage tank weighed 3/4 tonnes when full of water. After five
days, the family had used water from the tank in washing clothes
and cleaning utensils. The weight of the water in the tank became
2/5 tonnes. Calculate the weight of water used by the family in fivedays. Explain your steps.
Example 4.28
A mother had 5/9 litre of milk for her baby. During the day, the baby drank
some of the milk. The milk that remained was 1/3 litre. How much milkdid the baby drank during the day?
Example 4.29
During a lunch in the school, a pupil was served with 1/3 litre of milk for
good health. She drank some of the milk immediately and reserved the
remainder for 4 p.m usage. The amount of milk that remained for 4 p.m
was 1/4 litre. How much milk did she drank during the lunch?
Practice Activity 4.27
1. During an activity on measuring length, Jane and Michael had
different sticks. Jane had a stick that is 7/8 m long. Michael had a
stick that is 5/6 m long. By how many metres is Jane’s stick longer than
Michael’s stick?
2. A teacher had 3/4 metre of a thread. The teacher used 1/2
metre from the thread to mend a cloth. What length of thread remained? Explain
your answer.
3. During a rainy season, a certain school harvested rainwater. The school
tank became full and its weight was 9/12 tonnes. For one week, pupils
used tank water to clean their classes. There was no rain during the
week. The weight of water in the tank finally was 1/2
tonnes. Calculate the weight of water used in cleaning activity. Discuss your steps.
Why should we keep our classes clean?
4. Peggy took a cake whose mass was 1/2 kg to school. During the tea break,
she shared her cake with her friend. The mass of the cake her
friend ate was 2/8 kg. Peggy ate the rest of the cake. Find the mass of
the cake eaten by Peggy during the break. Who ate larger part of the
cake? Discuss your steps. Why should we make friends with others?
5. In a class activity, a pupil found the fraction of boys and girls in his
class. He observed that boys form 3/7 of the class.
(a) What fraction of the class were girls? Justify your answer.
(b) Find the difference of the fraction of girls and boys.
(c) What roles do boys and girls play in our community?
6. A worker wanted to paint the furniture in a hotel. He bought 3/4
litre of white paints. He painted his table using his paints. After completing
his work, the amount of paint that remained was 3/8 litre. Calculate the
amount of paint he used to paint the table. Explain your steps. Tell theimportance of painting.
Word list
Equivalent fractions Models
Denominators Least Common MultipleConcept Determining
Task
Do the following.
(i) Read each word aloud to your friend.
(ii) Write the meaning of each of the words above. Discuss with your friend.(iii) Write sentences using each of the words above. Read with your friend.