Grade 7Fractions
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Answer the questions
(1) Solve and simplify: ( 32
4 + 2
2
4 ) × ( 3
2
4 - 2
2
4 )
(2) Solve the following and reduce to the simplest form:
A) 4
10 ×
2
3 ÷
2
9 B)
2
8 ×
2
3 ÷
1
6
C) 2
5 ×
3
10 ÷
13
30 D)
1
7 ×
4
5 ÷
5
10
(3) The parking lot of the Shopping Complex has a capacity of 590 cars. On Fridays the ratio of occupiedspots to empty spots in the parking lot was 3:7. How many additional cars could park there?
(4) While doing operations on fractions, in which order should the operations be done among these fouroperations?+ x - ÷
(5) Write the answer in short form (decimal number) :
9000 + 100 + 70 + 6 + 8
10 +
3
1000
(6) Solve the following: 4
5 ×
3
5 - 7
14
.
(7) Ameerah is baking two different types of bread. She needs 31
6 cup of flour for one type of bread and
41
5 cup of flour for the other type. How many cup of flour will Ameerah need to bake both types of
bread?
(8) Solve the following and reduce to the simplest form:
A) 14
5 - 1
4
5 ÷ 2
1
5 B) 1
1
6 - 1
5
6 ÷ 4
5
6
C) 14
6 - 3
4
6 ÷ 1
5
6 D) 2
1
5 - 1
1
5 ÷ 2
3
5
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(9) Aziz covered 32
5 km in the first hour, 3
3
4 km in the second hour, and 4
9
4 km in the third hour.
Find the total distance covered by Aziz in three hours.
(10) Find the value of 3
4 +
( 2
1 -
4
5 ) × 10
1 - 1
2
.
(11) Simplify the following fractions:
A) 17139
195 - 5
13
15 B) 28
59
182 - 2
7
13
C) 17146
255 - 5
12
17 D) 36
99
182 - 7
8
13
(12) There are two containers out of which one can hold 11
3 liters of milk while the other can hold 3
1
2
liters of milk. Suppose there are 9 containers of the first type and 6 containers of the second type. Howmany liters of milk is required to fill them both?
Choose correct answer(s) from the given choices
(13) Add:
+
Figure A Figure B
a. 11
11 b.
11
9
c. 14
9 d.
9
11
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(14) Which figure shows fraction 1
3 ?
a.
♣ ♣ ♣ ♣ ♣ ♣♣ ♣ ♣b.
♦ ♦ ♦♦c.
♥ ♥ ♥ ♥♥ ♥ ♥d.
♠ ♠ ♠ ♠ ♠ ♠♠(15) A bear 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 bear reach after walking 7
25
distance on the periphery?
a. D b. C
c. A d. B
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Answers
(1) 6
Step 1
Let us first convert the given mixed fractions to proper fractions as shown below:
( 32
4 + 2
2
4 ) × ( 3
2
4 - 2
2
4 ) = (
14
4 +
10
4 ) × (
14
4 -
10
4 )
Step 2
Now, the expression involving like fractions, ( 14
4 +
10
4 ) × (
14
4 -
10
4 ), can be simplified as:
( 14
4 +
10
4 ) × (
14
4 -
10
4 )
= ( 14 + 10
4 ) × (
14 - 10
4 )
= ( 24
4 ) × (
4
4 )
= 96
16
Step 3
Let us now find the simplest form of the fraction 96
16 by dividing the numerator 96 and the
denominator 16, by their HCF.The HCF of 96 and 16 = 16.
Thus, the simplest form of the fraction 96
16 =
96/16
16/16 = 6
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(2) A) 6
5
Step 1
First, let us simplify the given fraction: 4
10 ×
2
3 ÷
2
9
To simplify it, let us convert the division into multiplication by reciprocating the thirdfraction, as shown below:
4
10 ×
2
3 ×
9
2
= 72
60
Step 2
Now, to reduce 72
60 to the simplest form, we will divide 72 and 60 by their HCF.
The HCF of 72 and 60 = 12
The simplest form of 72
60 =
72
12
60
12
= 6
5
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B) 1
Step 1
First, let us simplify the given fraction: 2
8 ×
2
3 ÷
1
6
To simplify it, let us convert the division into multiplication by reciprocating the thirdfraction, as shown below:
2
8 ×
2
3 ×
6
1
= 24
24
Step 2
Now, to reduce 24
24 to the simplest form, we will divide 24 and 24 by their HCF.
The HCF of 24 and 24 = 24
The simplest form of 24
24 =
24
24
24
24
= 1
1
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C) 18
65
Step 1
First, let us simplify the given fraction: 2
5 ×
3
10 ÷
13
30
To simplify it, let us convert the division into multiplication by reciprocating the thirdfraction, as shown below:
2
5 ×
3
10 ×
30
13
= 180
650
Step 2
Now, to reduce 180
650 to the simplest form, we will divide 180 and 650 by their HCF.
The HCF of 180 and 650 = 10
The simplest form of 180
650 =
180
10
650
10
= 18
65
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D) 8
35
Step 1
First, let us simplify the given fraction: 1
7 ×
4
5 ÷
5
10
To simplify it, let us convert the division into multiplication by reciprocating the thirdfraction, as shown below:
1
7 ×
4
5 ×
10
5
= 40
175
Step 2
Now, to reduce 40
175 to the simplest form, we will divide 40 and 175 by their HCF.
The HCF of 40 and 175 = 5
The simplest form of 40
175 =
40
5
175
5
= 8
35
(3) 413
Step 1
It is given that ratio of occupied spots to empty spots is 3:7, which means if there are 10 ( = 3 + 7)spots, 3 are occupied and 7 are empty
Step 2
But is given that total number of parking spots are 590. Therefore total number of spots are 59times ( = 590/10) of 10
Step 3
Therefore available spots will also be 59 times of 7. Therefore available parking spots,= 7 × 59 = 413
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(4) ÷ x + -
Step 1
We know that division is completed before multiplication, multiplication is completed beforeaddition, and addition is completed before subtraction.
Step 2
Therefore, the order of operations should be:÷ x + -
(5) 9176.803
Step 1
We have the place values of all the digits given in the question. To form a number, we’ll need toadd all of them.
Step 2
First let us convert the given fractions into their decimal forms: 8
10 = 0.8,
0
100 = 0,
3
1000 =
0.003.
Step 3
9000 + 100 + 70 + 6 + 0.8 + 0 + 0.003 = 9176.803.
Step 4
Hence the short form of the above given number is 9176.803.
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(6) 8
15
Step 1
Let us solve the given equation with the help of the following steps:
4
5 ×
3
5 - 7
14
= 4
5 ×
3
(5 × 14) - 7
14
= 4
5 ×
3
70 - 7
14
= 4
5 ×
3
63
14
= 4
5 ×
3 × 14
63
= 4
5 ×
2
3
Step 2
In order to multiply the fractions, we need to multiply the numerators and the denominators, asshown below
= 4 × 2
5 × 3
= 8
15
= 8
15
(7) 711
30 cups
Step 1
In order to find the total amount of flour needed to bake both types of bread, let us add the 31
6
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cup and 41
5 cup.
Step 2
Let us convert the given mixed fractions into improper fractions.
31
6 =
6 × 3 + 1
6 =
19
6
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 6 and 5 = 30
So, 19
6 =
19
6 ×
5
5 =
95
30
and 21
5 =
21
5 ×
6
6 =
126
30
Step 4
Now, let us add the two like fractions.
So, 95
30 +
126
30 =
221
30
Step 5
Converting 221
30 into mixed fraction:
Dividend↴
Divisor→ 30 ) 2 2 1 ( 7 ←Quotient
2 1 0
Remainder← 11
Thus, we have:
221
30 = 7
11
30
Step 6
Thus, Ameerah requires a total of 711
30 cup of flour to bake two different types of bread.
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(8) A) 54
55
Step 1
Let us first convert the given mixed fractions to proper fractions, as shown below:
21
5 =
2 × 5 + 1
5 =
11
5
14
5 =
1 7 × 5 + 4
5 =
9
5
Step 2
Now, in order to solve the like fractions 9
5 -
9
5 ÷
11
5 , we will reciprocate the third
fraction, as shown below:
9
5 -
9
5 ×
5
11
= 9
5 -
9
11 (Since, the multiplication must be solved before the addition and
subtraction)
= (9 × 11) - (9 × 5)
55
= 99 - 45
55
= 54
55
Step 3
Now, to reduce 54
55 to the simplest form, we will divide 54 and 55 by their HCF.
HCF (54 and 55) = 1
Since, the HCF is 1, this fraction cannot be simplified further and the answer is 54
55
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B) 137
174
Step 1
Let us first convert the given mixed fractions to proper fractions, as shown below:
45
6 =
4 × 6 + 5
6 =
29
6
11
6 =
1 7 × 6 + 1
6 =
7
6
15
6 =
1 × 6 + 5
6 =
11
6
Step 2
Now, in order to solve the like fractions 7
6 -
11
6 ÷
29
6 , we will reciprocate the
third fraction, as shown below:
7
6 -
11
6 ×
6
29
= 7
6 -
11
29 (Since, the multiplication must be solved before the addition and
subtraction)
= (7 × 29) - (11 × 6)
174
= 203 - 66
174
= 137
174
Step 3
Now, to reduce 137
174 to the simplest form, we will divide 137 and 174 by their HCF.
HCF (137 and 174) = 1
Since, the HCF is 1, this fraction cannot be simplified further and the answer is 137
174
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C) -1
3
Step 1
Let us first convert the given mixed fractions to proper fractions, as shown below:
15
6 =
1 × 6 + 5
6 =
11
6
14
6 =
1 7 × 6 + 4
6 =
10
6
34
6 =
3 × 6 + 4
6 =
22
6
Step 2
Now, in order to solve the like fractions 10
6 -
22
6 ÷
11
6 , we will reciprocate the
third fraction, as shown below:
10
6 -
22
6 ×
6
11
= 10
6 -
2
1 (Since, the multiplication must be solved before the addition and
subtraction)
= (10 × 1) - (2 × 6)
6
= 10 - 12
6
= -2
6
Step 3
Now, to reduce -2
6 to the simplest form, let us find the HCF of -2 6.
HCF(-2 ,6) = 2
The simplest form of -2
6 =
-2
2
6
2
= -1
3
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D) 113
65
Step 1
Let us first convert the given mixed fractions to proper fractions, as shown below:
23
5 =
2 × 5 + 3
5 =
13
5
21
5 =
2 7 × 5 + 1
5 =
11
5
11
5 =
1 × 5 + 1
5 =
6
5
Step 2
Now, in order to solve the like fractions 11
5 -
6
5 ÷
13
5 , we will reciprocate the
third fraction, as shown below:
11
5 -
6
5 ×
5
13
= 11
5 -
6
13 (Since, the multiplication must be solved before the addition and
subtraction)
= (11 × 13) - (6 × 5)
65
= 143 - 30
65
= 113
65
Step 3
Now, to reduce 113
65 to the simplest form, we will divide 113 and 65 by their HCF.
HCF (113 and 65) = 1
Since, the HCF is 1, this fraction cannot be simplified further and the answer is 113
65
(9) 132
5 km
Step 1
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In order to find the total distance covered by Aziz, we need to add the three distances.
Let us convert the given mixed fractions into improper fractions.
32
5 =
5 × 3 + 2
5 =
17
5
33
4 =
4 × 3 + 3
4 =
15
4
49
4 =
4 × 4 + 9
4 =
25
4
Step 2
We find that all the three 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 5 and 4 = 20
So, 17
5 =
17
5 ×
4
4 =
68
20
15
4 =
15
4 ×
5
5 =
75
20
25
4 =
25
4 ×
5
5 =
125
20
Step 3
Now, let us add the three like fractions.
So, 68
20 +
75
20 +
125
20 =
268
20 =
67
5
Step 4
Converting 67
5 into mixed fraction:
Dividend↴
Divisor→ 5 ) 6 7 ( 13 ←Quotient
5
1 7
1 5
Remainder← 2
We have:
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67
5 = 13
2
5
Step 5
Thus, Aziz traveled a total of 132
5 km in three hours.
(10) 99
4
Step 1
Let us first simplify the numerator of the second term:
( 2
1 -
4
5 ) × 10
= (2 × 5) - (4 × 1)
5 × 10
= 6
5 × 10
= 12
Step 2
Similarly, simplify the denominator of the second term:
1 - 1
2
= 1
2
Step 3
Now,
3
4 +
( 2
1 -
4
5 ) × 10
1 - 1
2
= 3
4 +
12
1
2
= 3
4 +
12 × 2
1
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= 3
4 +
24
1
= (3 × 1) + (24 × 4)
4
= 3 + 96
4
= 99
4
(11) A) 1111
13
Step 1
Let us first convert the given mixed fractions into improper fractions.
In order to convert the mixed fraction 17139
195 into an improper fraction, we need to
multiply the denominator 195 by 17 and add the numerator 139 to the result.The resulting number is the numerator of the improper fraction and the denominatorremains the same:
17139
195 =
17 × 195 + 139
195 =
3454
195
Similarly, the mixed fraction 513
15 can be converted into an improper fraction as:
513
15 =
5 × 15 + 13
15 =
88
15
Step 2
Now, we need to subtract the following Unlike fractions: 3454
195 and
88
15 .
Before we subtract, let us first convert them to Like fractions.
Step 3
Let us find the LCM of the denominators 195 and 15.The LCM of 195 and 15 is 195.
Step 4
What should we multiply with the denominator 195 to get the LCM 195?
It is 195
195 = 1.
So, the first fraction can be written as:
3454 × 1
195 × 1 =
3454
195
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Step 5
Similarly, the second fraction can be written as:
88 × 13
15 × 13 =
1144
195
Step 6
Let us now subtract the two Like fractions:
3454
195 -
1144
195
= 3454 - 1144
195
= 2310
195
= 2310 ÷ 15
195 ÷ 15 ...( Dividing both the numerator and denominator by their HCF )
= 154
13
= 1111
13
Step 7
Hence, the simplified value of the given fractions is 1111
13 .
B) 2511
14
Step 1
Let us first convert the given mixed fractions into improper fractions.
In order to convert the mixed fraction 2859
182 into an improper fraction, we need to
multiply the denominator 182 by 28 and add the numerator 59 to the result.The resulting number is the numerator of the improper fraction and the denominatorremains the same:
2859
182 =
28 × 182 + 59
182 =
5155
182
Similarly, the mixed fraction 27
13 can be converted into an improper fraction as:
27
13 =
2 × 13 + 7
13 =
33
13
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Step 2
Now, we need to subtract the following Unlike fractions: 5155
182 and
33
13 .
Before we subtract, let us first convert them to Like fractions.
Step 3
Let us find the LCM of the denominators 182 and 13.The LCM of 182 and 13 is 182.
Step 4
What should we multiply with the denominator 182 to get the LCM 182?
It is 182
182 = 1.
So, the first fraction can be written as:
5155 × 1
182 × 1 =
5155
182
Step 5
Similarly, the second fraction can be written as:
33 × 14
13 × 14 =
462
182
Step 6
Let us now subtract the two Like fractions:
5155
182 -
462
182
= 5155 - 462
182
= 4693
182
= 4693 ÷ 13
182 ÷ 13 ...( Dividing both the numerator and denominator by their HCF )
= 361
14
= 2511
14
Step 7
Hence, the simplified value of the given fractions is 2511
14 .
C) 1113
15
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Step 1
Let us first convert the given mixed fractions into improper fractions.
In order to convert the mixed fraction 17146
255 into an improper fraction, we need to
multiply the denominator 255 by 17 and add the numerator 146 to the result.The resulting number is the numerator of the improper fraction and the denominatorremains the same:
17146
255 =
17 × 255 + 146
255 =
4481
255
Similarly, the mixed fraction 512
17 can be converted into an improper fraction as:
512
17 =
5 × 17 + 12
17 =
97
17
Step 2
Now, we need to subtract the following Unlike fractions: 4481
255 and
97
17 .
Before we subtract, let us first convert them to Like fractions.
Step 3
Let us find the LCM of the denominators 255 and 17.The LCM of 255 and 17 is 255.
Step 4
What should we multiply with the denominator 255 to get the LCM 255?
It is 255
255 = 1.
So, the first fraction can be written as:
4481 × 1
255 × 1 =
4481
255
Step 5
Similarly, the second fraction can be written as:
97 × 15
17 × 15 =
1455
255
Step 6
Let us now subtract the two Like fractions:
4481
255 -
1455
255
= 4481 - 1455
255
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= 3026
255
= 3026 ÷ 17
255 ÷ 17 ...( Dividing both the numerator and denominator by their HCF )
= 178
15
= 1113
15
Step 7
Hence, the simplified value of the given fractions is 1113
15 .
D) 2813
14
Step 1
Let us first convert the given mixed fractions into improper fractions.
In order to convert the mixed fraction 3699
182 into an improper fraction, we need to
multiply the denominator 182 by 36 and add the numerator 99 to the result.The resulting number is the numerator of the improper fraction and the denominatorremains the same:
3699
182 =
36 × 182 + 99
182 =
6651
182
Similarly, the mixed fraction 78
13 can be converted into an improper fraction as:
78
13 =
7 × 13 + 8
13 =
99
13
Step 2
Now, we need to subtract the following Unlike fractions: 6651
182 and
99
13 .
Before we subtract, let us first convert them to Like fractions.
Step 3
Let us find the LCM of the denominators 182 and 13.The LCM of 182 and 13 is 182.
Step 4
What should we multiply with the denominator 182 to get the LCM 182?
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It is 182
182 = 1.
So, the first fraction can be written as:
6651 × 1
182 × 1 =
6651
182
Step 5
Similarly, the second fraction can be written as:
99 × 14
13 × 14 =
1386
182
Step 6
Let us now subtract the two Like fractions:
6651
182 -
1386
182
= 6651 - 1386
182
= 5265
182
= 5265 ÷ 13
182 ÷ 13 ...( Dividing both the numerator and denominator by their HCF )
= 405
14
= 2813
14
Step 7
Hence, the simplified value of the given fractions is 2813
14 .
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(12) 33 liters
Step 1
We have been told that the volume of milk the first type of container can hold = 11
3 liters =
4
3
liters
Step 2
Since, there are 9 containers of the first type, the volume of milk they can hold = 4
3 × 9
= 4 × 3= 12 liters.
Step 3
Now, the volume of milk the second type of container can hold = 31
2 liters =
7
2 liters
Step 4
Since, there are 6 containers of the second type, the volume of milk 6 containers of the second
type can hold = 7
2 × 6
= 7 × 3= 21 liters.
Step 5
The volume of milk required to fill both the containers = 12 + 21 = 33 liters.
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(13) b. 11
9
Step 1
We see that the 5 out of 9 parts of figure A are shaded.
So, the fraction of shaded part of figure A = 5
9
Also, 2 out of 3 parts of figure B are shaded.
So, the fraction of shaded part of figure B = 2
3
Step 2
In order to add the unlike fractions, let us first convert them into like fractions.
L.C.M of 9 and 3 = 9
So, 5
9 =
5
9 ×
1
1 =
5
9
and 2
3 =
2
3 ×
3
3 =
6
9
Step 3
Adding:
5
9 +
2
3 =
5
9 +
6
9 =
11
9
Step 4
Hence, + = 11
9
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(14) a.
♣ ♣ ♣ ♣ ♣ ♣♣ ♣ ♣
Step 1
Look at the all of the figures carefully and notice that in figure
♣ ♣ ♣ ♣ ♣ ♣♣ ♣ ♣The number of ♣ in selected box = 3and the total number of ♣ = 9
Step 2
Now the fraction of the number of ♣ in the selected box to the total number of ♣ in given figure =
3
9 =
1
3
Step 3
Therefore the figure
♣ ♣ ♣ ♣ ♣ ♣♣ ♣ ♣shows fraction
1
3 .
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(15) d. B
Step 1
If we look at the regular polygon carefully, we notice that there are 5 sides of a regular polygon.
Therefore, the length of a side of the regular polygon = 1
5
Step 2
Since, the distance walked by the bear on the periphery, in the clockwise direction = 7
25
Therefore, the number of sides walked by the bear on the regular polygon =
Distance walked by the bear
Length of a side of the polygon
=
7
25
1
5
= 7
25 ×
5
1
= 7
5
= 1.4
It means that the bear walked on 1 side of the regular polygon and the bear is walking on the 2nd
side of the regular polygon, in the clockwise direction.
Step 3
Since, it started from point s, the bear will be on the side B, after walking 7
25 distance on the
periphery in the clockwise direction.
Step 4
Hence, option d is the correct answer.
ID : ae-7-Fractions [27]
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