EQUIVALENT FRACTIONS If we divide a piece of rectangular paper into 6 equal parts and we shade 5 of the 6 equal parts, then we say that 5/6 of the paper.
The numerator tells the number of parts that have been shaded. The denominator tells the number of equal parts the whole has been. FRACTIONS FROM THE SAME WHOLE Get a strip of paper. The strip of paper is 1 whole. 1. Fold the strip of paper into half
2. Unflod the paper. You will see 2 equal parts. Shade one of the parts. 1 2
1 2
3. Next, fold the paper twice.
4. Unfold the paper. You will see 4 ewual parts. 1 4
1 4
1 4
1 4
Notice that ½ of the paper is the same as 2/4 of the paper.
=
+ =
and are called equivalent fractions. Equivalent fractions come from the same whole. They have different numerators and different denominators but they are equal.
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FINDING EQUIVALENT FRACTIONS Look at these equivalent fractions. 1 3
The whole is divided into 3 equal parts.
Each part is further divided into 2 equal parts, making the whole to have 6 equal parts.
2 6
=
× ×
=
There are many equivalent fractions of
× 3 1 3 = 3 9
3 9
× 3
We can get equivalent fractions by multiplaying the numerator and the denominator of a fraction by the same number.
From the diagram, We can see that 3 parts out of 4 parts is the same as 6 parts out of 8 parts.
1 6 = 2 12
6 1 = 12 2
We can also get equivalent fractions by dividing the numerator and the denominator of fraction by the same number.
Look at the fraction .Its numerator and denominator can both be ivided exactly by 3.
=
Is the equivalent fractio of ,
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The numerator and denominator of the fraction cannot be devided exactly by a common number to get another equivalent fraction. We say that the fraction is in its simplest from. Look at the fraction . Let us change it to its simplest form. 8 4 = 12 6
4 2 = 6 3
is not in its simplest form, as both the numerator and the denominator can be further divided exactly by 2 to give .
COMPARING Whice fraction is greater ,
? 4 7
3 7
When comparing fractions with the same denominator, the greater fraction is the one with the greater numerator.
Whice fraction is greater ,
? We will get a bigger piece if the whole is divided into smaller number of equal pieces.
When comparing fractions whith the same numerator, the greater fraction is the one whith the smaller denominator.
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Here is another way. We can always find the equivalent fractions of 2/3 and 2/5 with the same denominator and make comparison. 2 6 = 5 15
We have another way. 1 2 2/3 is greater than ½
2 3
2/5 is smaller than 1/2
2 5 So 2/3 is greater than 2/5
I can list the equivalent fractions of 2/3 and 5/6 to make comparison.
2 4 = 3 6 5 6
2 4 = 3 6
4/6 is smaller than 5/6 So 2/3 is smaller than 5/6
Mother made a tray of mango pudding. She gave 2/9 of the pudding to Mrs Lee and 1/3 of pudding to Mrs Tan. What fraction of the pudding.
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Equivalent fractions are equal fractions with different numerators and denominators. They come from the same whole. Example : 1 2 2 4
To find equivalent fractions of a given fraction, multiply or divide the numerator and denominator by a common number. Example : 2 4 = 3 6
8 4 = 12 6
When the numerator and denominator of a fraction cannot be divided exactly by a common number to get another equivalent fraction, the fraction is said to be in its simplest form. Example: ½ ; ¾ and 3/5 are fractions in their simplest form. We can draw diagrams to help us compare and order fractions. We can use equivalent fractions to help us compare fractions. Example : Comparing ½ and ¾ is the same as comparing 2/4 and ¾.
Like fractions are fractions with the same denominator You have learnt how to add and subtract like fractions. Let’s recall how to add or subtract like fractions. Take a strip of paper. Fold it into 5 equal parts. Reccal that each part is 1/5 of the paper.
1 5
1 5
1 5
1 5
1 5
If 1/5 of the strip is collourd blue and 2/5 of the strip is coloured yellow, what fraction of the whole strip of paper is coloured? 1/5 1 5
2/5 1 5
1 5
1 5
1 5
3/5 of the whole strip of paper is colloured
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RELATED FRACTIONS Related fractions have 1 denominator that can be divided by the other without a remainder. 1/4 and 3/8 are related fractions because 8 can be devided by 4 without a remainder.
ADDING RELATED FRACTIONS Let us add the 2 related fractions 1/4 and 2/8
2/8 is the equivalent fraction of 1/4
+
The fraction strips below can also show how to add the related fractions. 1
1/4
1/8
1/8
1/4
1/8
1/4
1/8
1/8
1/8
1/4
1/8
1/8
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Subtracting related fractions Let’s subtract 2 related fractions.
Here is 9/10 of a pizza; let’s take away 4/5 of pizza; how much of pizza is left.
We can also subtract related fractions using fraction strips. 1/2
1/2 1/2 – 1/8 = 4/8 – 1/8 = 3/8
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/8
1/2
Word Problem Out of the total population of Singapore, about 1/5 are Malaysia , and about 1/10 are Indians and Eurasians. The rest of the population are Chinese .
a) About what fraction of the total population of Singapore are Malays , Indians and Eurasians ? b) About what fraction of the population of singapore are Chinese ? c) What is the total population of Singapore ?
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