Class 6Fractions
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Answer the questions
(1) Solve the following and reduce to the simplest form:
A) ( 11
2 ÷ 2
1
2 ) + 1
1
2 B) ( 2
1
2 ÷ 2
1
2 ) + 1
1
2
C) ( 22
7 ÷ 2
5
7 ) + 3
3
7 D) ( 1
1
2 ÷ 1
1
2 ) + 1
1
2
(2) Simplify the following fractions and reduce them to the simplest form:
A) 716
475 -
14
25 B)
69
40 -
7
8 C)
67
36 -
11
12
D) 229
171 -
4
9 E)
393
272 -
9
16 F)
113
80 -
9
16
(3) Akshiti is reading a book titled 'Creatures of the Deep Sea', and this book has 450 pages. Akshiti
manages to read 2
45 of the book every day. After 2 days, how many pages has she read?
(4) The parking lot of the Shopping Complex has a capacity of 266 cars. On Friday 17
19 of the parking lot
was occupied with cars. How many additional number of cars could be parked there?
(5) Shade the images to show the following fraction addition.
7
12 +
1
12 =
and makes
(6) Shilpa has Rs. 1995 with her. She gives 8
15 of this to her sister. Out of the remaining money, she
gives Rs. 266 to her brother. What fraction of the original amount is left with her?
(7) What will be the result if we divide the sum of 51
5 and 2
2
3 by their difference?
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(8) Sarika is constructing a building. She finishes 1
15 of the construction in 2
1
3 weeks. In how many
days will she finish constructing the building?
(9) Sanjana is baking two different types of bread. She needs 13
4 cup of flour for one type of bread and
41
5 cup of flour for the other type. How many cup of flour will Sanjana need to bake both types of
bread?
Choose correct answer(s) from the given choices
(10) Add:
+
Figure A Figure B
a. 58
40 b.
57
43
c. 40
57 d.
57
40
(11) A cat is walking on the periphery of a regular polygon, as shown below.
If it starts from point s, in the clockwise direction, which side will the cat reach after walking 28
30
distance on the periphery?
a. B b. F
c. A d. E
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(12) What is the mixed fraction that represents the shaded part in the figure below?
a. 511
5 b. 5
8
11
c. 5
11 d. 4
5
11
(13) The fractions 18
53 and
22
53 are :
a. Mixed Fractions b. Unlike Fractions
c. Like Fractions d. Improper Fractions
Fill in the blanks
(14) Fill in the blank to make the two fractions equivalent:
A) 6
13 =
117 B)
5 =
24
40
C) 6
= 30
55 D)
11 =
40
110
(15) Add the following fractions and reduce them to the simplest form:
A) 5
1 +
6
7 = B)
2
6 +
6
5 = C)
7
1 +
6
2 =
D) 8
3 +
2
8 = E)
3
8 +
8
6 = F)
7
7 +
5
4 =
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Answers
(1) A) 21
10
Step 1
( 11
2 ÷ 2
1
2 ) + 1
1
2 can be written as:
( 3
2 ÷
5
2 ) +
3
2 ...[ Converting mixed fractions into improper fractions ]
= ( 3
2 ×
2
5 ) +
3
2 ...[ Dividing by a fraction is same as multiplying with its
reciprocal]
= 3
5 +
3
2
= 6 + 15
10
= 21
10
Step 2
Thus, the simplest form of ( 11
2 ÷ 2
1
2 ) + 1
1
2 is
21
10 .
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B) 5
2
Step 1
( 21
2 ÷ 2
1
2 ) + 1
1
2 can be written as:
( 5
2 ÷
5
2 ) +
3
2 ...[ Converting mixed fractions into improper fractions ]
= ( 5
2 ×
2
5 ) +
3
2 ...[ Dividing by a fraction is same as multiplying with its
reciprocal]
= 5
5 +
3
2
= 10 + 15
10
= 25
10
= 5
2
Step 2
Thus, the simplest form of ( 21
2 ÷ 2
1
2 ) + 1
1
2 is
5
2 .
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C) 568
133
Step 1
( 22
7 ÷ 2
5
7 ) + 3
3
7 can be written as:
( 16
7 ÷
19
7 ) +
24
7 ...[ Converting mixed fractions into improper fractions ]
= ( 16
7 ×
7
19 ) +
24
7 ...[ Dividing by a fraction is same as multiplying with its
reciprocal]
= 16
19 +
24
7
= 112 + 456
133
= 568
133
Step 2
Thus, the simplest form of ( 22
7 ÷ 2
5
7 ) + 3
3
7 is
568
133 .
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D) 5
2
Step 1
( 11
2 ÷ 1
1
2 ) + 1
1
2 can be written as:
( 3
2 ÷
3
2 ) +
3
2 ...[ Converting mixed fractions into improper fractions ]
= ( 3
2 ×
2
3 ) +
3
2 ...[ Dividing by a fraction is same as multiplying with its
reciprocal]
= 3
3 +
3
2
= 6 + 9
6
= 15
6
= 5
2
Step 2
Thus, the simplest form of ( 11
2 ÷ 1
1
2 ) + 1
1
2 is
5
2 .
(2) A) 18
19
Step 1
We need to subtract the following unlike fractions:
716
475 and
14
25 .
Let us first convert them to like fractions.
Step 2
Let us find the LCM of the denominators 475 and 25.The LCM of 475 and 25 is 475.
Step 3
What should we multiply with the denominator 475 to get the LCM 475?
It is 475
475 = 1.
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So, the first fraction can be written as:
716 × 1
475 =
716
475
Step 4
Similarly, the second fraction can be written as:
14 × 19
475 =
266
475
Step 5
Let us now subtract the like fractions:
716
475 -
266
475
= 716 - 266
475
= 450
475
Step 6
Let us now find the simplest form of the fraction 450
475 , by dividing the numerator 450
and denominator 475, by their HCF.The HCF of 450 and 475 = 25.
Thus, the simplest form of the fraction 450
475 =
450
25
475
25
= 18
19 .
B) 17
20
Step 1
We need to subtract the following unlike fractions:
69
40 and
7
8 .
Let us first convert them to like fractions.
Step 2
Let us find the LCM of the denominators 40 and 8.The LCM of 40 and 8 is 40.
Step 3
What should we multiply with the denominator 40 to get the LCM 40?
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It is 40
40 = 1.
So, the first fraction can be written as:
69 × 1
40 =
69
40
Step 4
Similarly, the second fraction can be written as:
7 × 5
40 =
35
40
Step 5
Let us now subtract the like fractions:
69
40 -
35
40
= 69 - 35
40
= 34
40
Step 6
Let us now find the simplest form of the fraction 34
40 , by dividing the numerator 34
and denominator 40, by their HCF.The HCF of 34 and 40 = 2.
Thus, the simplest form of the fraction 34
40 =
34
2
40
2
= 17
20 .
C) 17
18
Step 1
We need to subtract the following unlike fractions:
67
36 and
11
12 .
Let us first convert them to like fractions.
Step 2
Let us find the LCM of the denominators 36 and 12.The LCM of 36 and 12 is 36.
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Step 3
What should we multiply with the denominator 36 to get the LCM 36?
It is 36
36 = 1.
So, the first fraction can be written as:
67 × 1
36 =
67
36
Step 4
Similarly, the second fraction can be written as:
11 × 3
36 =
33
36
Step 5
Let us now subtract the like fractions:
67
36 -
33
36
= 67 - 33
36
= 34
36
Step 6
Let us now find the simplest form of the fraction 34
36 , by dividing the numerator 34
and denominator 36, by their HCF.The HCF of 34 and 36 = 2.
Thus, the simplest form of the fraction 34
36 =
34
2
36
2
= 17
18 .
D) 17
19
Step 1
We need to subtract the following unlike fractions:
229
171 and
4
9 .
Let us first convert them to like fractions.
Step 2
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Let us find the LCM of the denominators 171 and 9.The LCM of 171 and 9 is 171.
Step 3
What should we multiply with the denominator 171 to get the LCM 171?
It is 171
171 = 1.
So, the first fraction can be written as:
229 × 1
171 =
229
171
Step 4
Similarly, the second fraction can be written as:
4 × 19
171 =
76
171
Step 5
Let us now subtract the like fractions:
229
171 -
76
171
= 229 - 76
171
= 153
171
Step 6
Let us now find the simplest form of the fraction 153
171 , by dividing the numerator 153
and denominator 171, by their HCF.The HCF of 153 and 171 = 9.
Thus, the simplest form of the fraction 153
171 =
153
9
171
9
= 17
19 .
E) 15
17
Step 1
We need to subtract the following unlike fractions:
393
272 and
9
16 .
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Let us first convert them to like fractions.
Step 2
Let us find the LCM of the denominators 272 and 16.The LCM of 272 and 16 is 272.
Step 3
What should we multiply with the denominator 272 to get the LCM 272?
It is 272
272 = 1.
So, the first fraction can be written as:
393 × 1
272 =
393
272
Step 4
Similarly, the second fraction can be written as:
9 × 17
272 =
153
272
Step 5
Let us now subtract the like fractions:
393
272 -
153
272
= 393 - 153
272
= 240
272
Step 6
Let us now find the simplest form of the fraction 240
272 , by dividing the numerator 240
and denominator 272, by their HCF.The HCF of 240 and 272 = 16.
Thus, the simplest form of the fraction 240
272 =
240
16
272
16
= 15
17 .
F) 17
20
Step 1
We need to subtract the following unlike fractions:
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113
80 and
9
16 .
Let us first convert them to like fractions.
Step 2
Let us find the LCM of the denominators 80 and 16.The LCM of 80 and 16 is 80.
Step 3
What should we multiply with the denominator 80 to get the LCM 80?
It is 80
80 = 1.
So, the first fraction can be written as:
113 × 1
80 =
113
80
Step 4
Similarly, the second fraction can be written as:
9 × 5
80 =
45
80
Step 5
Let us now subtract the like fractions:
113
80 -
45
80
= 113 - 45
80
= 68
80
Step 6
Let us now find the simplest form of the fraction 68
80 , by dividing the numerator 68
and denominator 80, by their HCF.The HCF of 68 and 80 = 4.
Thus, the simplest form of the fraction 68
80 =
68
4
80
4
= 17
20 .
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(3) 40
Step 1
Number of pages in the book Akshiti is reading = 450
Step 2
Number of pages read by Akshiti in one day = 2
45 of the book
= 2
45 × 450
= 900
45
= 20
Step 3
Number of pages read by Akshiti in 2 days = 20 × 2 = 40
Step 4
Therefore, after the 2 days, she reads 40 pages.
(4) 28
Step 1
Total number of cars that can be parked = 266
Step 2
Number of cars already parked = 17
19 × 266
= 238
Step 3
Number of cars that can be parked in vacant space = Total - Occupied= 266 - 238= 28
(5) 7
12 +
1
12 =
+ =
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(6) 1
3
Step 1
The initial amount of money Shilpa had = Rs. 1995
Step 2
The amount of money Shilpa gives to her sister = 8
15 of the initial money she had
= 8
15 of Rs. 1995
= 8
15 × 1995
= 8 × 133 ... (Dividing 1995 by 15)= Rs. 1064
Step 3
The amount remaining with her after giving money to her sister = Amount Shilpa initially had -Amount she gave to her sister= Rs. 1995 - Rs. 1064= Rs. 931
Step 4
The amount Shilpa gives to her brother = Rs. 266
Step 5
The remaining amount after giving money to her brother = Rs. 931 - Rs. 266 = Rs. 665
Step 6
Now, we know that the final amount of money left with Shilpa is Rs. 665. We need to find whatfraction of Rs. 1995 is Rs. 665. This fraction will be the one with the remaining amount as
numerator and the initial amount as denominator, that is, 665
1995 .
Step 7
Let us now reduce 665
1995 to the simplest form by dividing both the denominator and the
numerator by 665, the HCF of 665 and 1995:
665
1995 =
665 ÷ 665
1995 ÷ 665
= 1
3
Step 8
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Hence, the fraction of the original amount that is left with Shilpa is 1
3 .
(7) 59
19
Step 1
We have to divide the sum of 51
5 and 2
2
3 by the difference of 5
1
5 and 2
2
3 .
Step 2
The sum of 51
5 and 2
2
3 = 5
1
5 + 2
2
3
= 26
5 +
8
3
= 26 × 3 + 8 × 5
15
= 78 + 40
15
= 118
15
Step 3
The difference of 51
5 and 2
2
3 = 5
1
5 - 2
2
3
= 26
5 -
8
3
= 26 × 3 - 8 × 5
15
= 78 - 40
15
= 38
15
Step 4
Now, let us divide the sum of 51
5 and 2
2
3 by their difference. We get:
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=
118
15
38
15
= 118
15 ×
15
38
= 59
19
Step 5
Hence, we get 59
19 as the result on dividing the sum of 5
1
5 and 2
2
3 by their difference.
(8) 245
Step 1
We know, 1 week = 7 days
Therefore, the number of days in 21
3 weeks = 2
1
3 × 7 days
= 7
3 × 7 days
= 49
3 days
Step 2
1
15 of the construction is finished in
49
3 days.
Therefore, the whole construction will be finished in =
49
3
1
15
days
= 49
3 ×
15
1 days
= 245 days.
(9) 519
20 cups
Step 1
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In order to find the total amount of flour needed to bake both types of bread, let us add the 13
4
cup and 41
5 cup.
Step 2
Let us convert the given mixed fractions into improper fractions.
13
4 =
4 × 1 + 3
4 =
7
4
41
5 =
5 × 4 + 1
5 =
21
5
Step 3
We find that the two fractions are unlike fractions.
Let us now take the L.C.M of the denominators to convert them into like fractions.
L.C.M of 4 and 5 = 20
So, 7
4 =
7
4 ×
5
5 =
35
20
and 21
5 =
21
5 ×
4
4 =
84
20
Step 4
Now, let us add the two like fractions.
So, 35
20 +
84
20 =
119
20
Step 5
Converting 119
20 into mixed fraction:
Dividend↴
Divisor→ 20 ) 1 1 9 ( 5 ←Quotient
1 0 0
Remainder← 19
Thus, we have:
119
20 = 5
19
20
Step 6
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Thus, Sanjana requires a total of 519
20 cup of flour to bake two different types of bread.
(10) d. 57
40
Step 1
We see that the 5 out of 8 parts of figure A are shaded.
So, the fraction of shaded part of figure A = 5
8
Also, 4 out of 5 parts of figure B are shaded.
So, the fraction of shaded part of figure B = 4
5
Step 2
In order to add the unlike fractions, let us first convert them into like fractions.
L.C.M of 8 and 5 = 40
So, 5
8 =
5
8 ×
5
5 =
25
40
and 4
5 =
4
5 ×
8
8 =
32
40
Step 3
Adding:
5
8 +
4
5 =
25
40 +
32
40 =
57
40
Step 4
Hence, + = 57
40
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(11) b. F
Step 1
If we look at the regular polygon carefully, we notice that there are 6 sides of a regular polygon.
Therefore, the length of a side of the regular polygon = 1
6
Step 2
Since, the distance walked by the cat on the periphery, in the clockwise direction = 28
30
Therefore, the number of sides walked by the cat on the regular polygon =
Distance walked by the cat
Length of a side of the polygon
=
28
30
1
6
= 28
30 ×
6
1
= 28
5
= 5.6
It means that the cat walked on 5 sides of the regular polygon and the cat is walking on the 6th
side of the regular polygon, in the clockwise direction.
Step 3
Since, it started from point s, the cat will be on the side F, after walking 28
30 distance on the
periphery in the clockwise direction.
Step 4
Hence, option b is the correct answer.
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(12) d. 45
11
Step 1
A fraction represents a particular part of a whole entity.
Step 2
In the given figures we can see that the circles are divided into 11 parts each. The first 4 circles isfully shaded, and in the last circle 5 out of 11 parts are shaded.
Step 3
This means that the first 4 circles will be represented by 4, and the last circle will be represented
by 5
11 .
Step 4
So the mixed fraction that represents the shaded part in the figure is 45
11 .
(13) c. Like Fractions
We find that the fractions 18
53 and
22
53 have the same denominator.
Therefore, the fractions 18
53 and
22
53 are Like Fractions.
(14) A) 54
Step 1
We know that Equivalent fractions are obtained by multiplying or dividing thenumerator and denominator of a fraction by the same number.
Step 2
We can see that we have multiplied the denominator 13 with 9 to get the denominatorof another fraction as 117.
Step 3
Since both the fractions are equivalent, the numerator of the first fraction have to bemultiplied with the same number to get the numerator of the second fraction.
Step 4
This means the new numerator will be equal to 6 × 9 = 54.
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B) 3
Step 1
We know that Equivalent fractions are obtained by multiplying or dividing thenumerator and denominator of a fraction by the same number.
Step 2
We can see that we have divided the denominator 40 by 8 to get the denominator ofanother fraction as 5.
Step 3
Since both the fractions are equivalent, the numerator of the second fraction have tobe divided by the same number to get the numerator of the first fraction.
Step 4
This means the new numerator will be equal to 24
8 = 3.
C) 11
Step 1
We know that Equivalent fractions are obtained by multiplying or dividing thenumerator and denominator of a fraction by the same number.
Step 2
We can see that we have divided the numerator 30 by 5 to get the numerator ofanother fraction as 6.
Step 3
Since both the fractions are equivalent, the denominator of the second fraction have tobe divided by the same number to get the denominator of the first fraction.
Step 4
This means the new denominator will be equal to 55
5 = 11.
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D) 4
Step 1
We know that Equivalent fractions are obtained by multiplying or dividing thenumerator and denominator of a fraction by the same number.
Step 2
We can see that we have divided the denominator 110 by 10 to get the denominator ofanother fraction as 11.
Step 3
Since both the fractions are equivalent, the numerator of the second fraction have tobe divided by the same number to get the numerator of the first fraction.
Step 4
This means the new numerator will be equal to 40
10 = 4.
(15) A) 5
1 +
6
7 =
41
7
Step 1
The fractions 5
1 and
6
7 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 7 and 1. The LCM is 7.
Step 3
To write 5
1 as an equivalent fraction which has 7 as denominator, we need to
multiply both the numerator and denominator by 7
1 = 7. So, the equivalent fraction is:
5 × 7
1 × 7 =
35
7
Step 4
Similarly, to write 6
7 as an equivalent fraction which has 7 as denominator, we need
to multiply both the numerator and denominator by 7
7 = 1. So, the equivalent fraction
is:
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6 × 1
7 × 1 =
6
7
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
35
7 +
6
7 =
35 + 6
7 =
41
7
Step 6
In order to convert the fraction 41
7 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 41 and 7 is 1.
Step 8
Hence, the simplest/lowest form of 41
7 is
41
1
7
1
= 41
7
B) 2
6 +
6
5 =
23
15
Step 1
The fractions 2
6 and
6
5 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 5 and 6. The LCM is 30.
Step 3
To write 2
6 as an equivalent fraction which has 30 as denominator, we need to
multiply both the numerator and denominator by 30
6 = 5. So, the equivalent fraction
is:
2 × 5
6 × 5 =
10
30
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Step 4
Similarly, to write 6
5 as an equivalent fraction which has 30 as denominator, we need
to multiply both the numerator and denominator by 30
5 = 6. So, the equivalent
fraction is:
6 × 6
5 × 6 =
36
30
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
10
30 +
36
30 =
10 + 36
30 =
46
30
Step 6
In order to convert the fraction 46
30 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 46 and 30 is 2.
Step 8
Hence, the simplest/lowest form of 46
30 is
46
2
30
2
= 23
15
C) 7
1 +
6
2 =
10
1
Step 1
The fractions 7
1 and
6
2 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 2 and 1. The LCM is 2.
Step 3
To write 7
1 as an equivalent fraction which has 2 as denominator, we need to
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multiply both the numerator and denominator by 2
1 = 2. So, the equivalent fraction is:
7 × 2
1 × 2 =
14
2
Step 4
Similarly, to write 6
2 as an equivalent fraction which has 2 as denominator, we need
to multiply both the numerator and denominator by 2
2 = 1. So, the equivalent fraction
is:
6 × 1
2 × 1 =
6
2
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
14
2 +
6
2 =
14 + 6
2 =
20
2
Step 6
In order to convert the fraction 20
2 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 20 and 2 is 2.
Step 8
Hence, the simplest/lowest form of 20
2 is
20
2
2
2
= 10
1
D) 8
3 +
2
8 =
35
12
Step 1
The fractions 8
3 and
2
8 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
ID : in-6-Fractions [26]
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Step 2
Let us first find the LCM of the denominators 8 and 3. The LCM is 24.
Step 3
To write 8
3 as an equivalent fraction which has 24 as denominator, we need to
multiply both the numerator and denominator by 24
3 = 8. So, the equivalent fraction
is:
8 × 8
3 × 8 =
64
24
Step 4
Similarly, to write 2
8 as an equivalent fraction which has 24 as denominator, we need
to multiply both the numerator and denominator by 24
8 = 3. So, the equivalent
fraction is:
2 × 3
8 × 3 =
6
24
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
64
24 +
6
24 =
64 + 6
24 =
70
24
Step 6
In order to convert the fraction 70
24 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 70 and 24 is 2.
Step 8
Hence, the simplest/lowest form of 70
24 is
70
2
24
2
= 35
12
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E) 3
8 +
8
6 =
41
24
Step 1
The fractions 3
8 and
8
6 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 6 and 8. The LCM is 24.
Step 3
To write 3
8 as an equivalent fraction which has 24 as denominator, we need to
multiply both the numerator and denominator by 24
8 = 3. So, the equivalent fraction
is:
3 × 3
8 × 3 =
9
24
Step 4
Similarly, to write 8
6 as an equivalent fraction which has 24 as denominator, we need
to multiply both the numerator and denominator by 24
6 = 4. So, the equivalent
fraction is:
8 × 4
6 × 4 =
32
24
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
9
24 +
32
24 =
9 + 32
24 =
41
24
Step 6
In order to convert the fraction 41
24 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 41 and 24 is 1.
Step 8
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Hence, the simplest/lowest form of 41
24 is
41
1
24
1
= 41
24
F) 7
7 +
5
4 =
9
4
Step 1
The fractions 7
7 and
5
4 are unlike fractions as their denominators are different. We
will first convert the given fractions into equivalent like fractions.
Step 2
Let us first find the LCM of the denominators 4 and 7. The LCM is 28.
Step 3
To write 7
7 as an equivalent fraction which has 28 as denominator, we need to
multiply both the numerator and denominator by 28
7 = 4. So, the equivalent fraction
is:
7 × 4
7 × 4 =
28
28
Step 4
Similarly, to write 5
4 as an equivalent fraction which has 28 as denominator, we need
to multiply both the numerator and denominator by 28
4 = 7. So, the equivalent
fraction is:
5 × 7
4 × 7 =
35
28
Step 5
Now, we can add the equivalent like fractions by adding the numerators together andkeeping the denominator same:
28
28 +
35
28 =
28 + 35
28 =
63
28
Step 6
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In order to convert the fraction 63
28 in the simplest/lowest form, let us divide both the
numerator and denominator by their HCF.
Step 7
The HCF of 63 and 28 is 7.
Step 8
Hence, the simplest/lowest form of 63
28 is
63
7
28
7
= 9
4
ID : in-6-Fractions [30]
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