Maharashtra Board Class 5 Math Solution Chapter 5 – Fractions
Balbharati Maharashtra Board Class 5 Math Solution Chapter 5: Fractions. Marathi or English Medium Students of Class 5 get here Fractions full Exercise Solution.
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Std |
Maharashtra Class 5 |
| Subject |
Math Solution |
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Chapter |
Fractions |
1.) Write the proper number in the box.
(1) 1/2 = 10 /20
When the numerator and denominator of a fraction are multiplied by the same non-zero number, we get a fraction that is equivalent to the given fraction.
We must find the right number for the box.
Here, if we multiply numerator 1 with 2, we get the denominator (1× 2) = 2
So, the half of the denominator 20 will be the numerator (numerator × 2 = denominator)
Dividing 20 by 2, (20 2) = 10.
So the numerator will be 10.
Hence, the fraction 10/20 with numerator 10 is equivalent to ½
(2) ¾ = 15/ 20
We must find the right number for the box.
Here, 5 times the numerator 3 is (3 × 5) = 15.
Hence five times the numerator 4 will be the denominator,
So, 5 × 4 = 20
The denominator will be 20
Hence the fraction 15/20 with denominator 20 is equivalent to ¾.
(3) 9/11 = 18/ 22
Hence 2 times the numerator 9 is 18,
So, the 2 times denominator of 11 is (2 11) = 22
Hence, the fraction 18/22 with denominator 22 is equivalent to 9/11.
(4) 10/40 = ? /8
If the numerator and denominator have a common divisor then the fraction we get on dividing them by that divisor is equivalent to the given fraction.
We must find the number for the box.
40 divided by 5 is 8.
So, we will get the number for the box by dividing 10 by 5. 10 ÷ 5 = 2.
Therefore,
10/40 = 2/8
Thus, the fraction 2/8 is equivalent to the fraction 10/40.
(5) 14/26 = ?/13
26 divided by 2 is 13.
So dividing 14 by 2 will give us the numerator,
(14 ÷ 2) = 7
Therefore, 14/26 = 7/13
(6) ?/3 = 4/6
2 times the denominator 3 is 6.
So, dividing 4 by 2 will give us the numerator,
(4÷2) = 2
Therefore, 2/3 = 4/6.
(7) 1/? = 4/20
4 times the numerator 1 is 4.
So, dividing 20 by 4 will give us the numerator,
(20÷4) = 5
Therefore, 1/5 = 4/20.
(8) ?/5 = 10/25
5 times the denominator 5 is 25.
So, dividing 10 by 5 will give us the numerator,
(10÷5) = 2
Therefore, 2/5 = 10/25
2.) Find an equivalent fraction with denominator 18, for each of the following fractions.
When the numerator and denominator of a fraction are multiplied by the same non-zero number, we get a fraction that is equivalent to the given fraction.
In ½ fraction,
9 times the denominator 2 is 18,
So, the 9 times numerator of 1 is (9× 1) = 9
Therefore ½ =9/18
In fraction 2/3,
6 times the denominator 3 is 18,
So, the 6 times numerator of 2 is (6×2) = 12
Therefore ½ =12/18
In fraction 4/6,
3 times the denominator 6 is 18,
So, the 3 times numerator of 4 is (3×4) = 12
Therefore ½ =12/18
In fraction 2/9,
2 times the denominator 9 is 18,
So, the 2 times numerator of 2 is (2×2) = 4
Therefore ½ =4/18
In fraction 7/9,
7/9 =14/18
In fraction 5/3,
5/3= 30/18
3.) Find an equivalent fraction with denominator 5, for each of the following fractions.
If the numerator and denominator have a common divisor then the fraction we get on dividing them by that divisor is equivalent to the given fraction.
In fraction 6/15,
15 divided by 3 is 5.
So, we will get the numerator of equivalent fraction by dividing 6 by 3. (6 ÷ 3) = 2.
Therefore 6/15= 2/5
In fraction 10/25,
25 divided by 5 is 5.
So, we will get the numerator of equivalent fraction by dividing 10 by 5. (10 ÷ 5) = 2.
Therefore 10/25= 2/5
In fraction 12/30,
30 divided by 6 is 5.
So, we will get the numerator of equivalent fraction by dividing 12 by 6. (12 ÷ 6) = 2.
Therefore 12/30= 2/5
In fraction 6/10, the equivalent fraction is 3/5
In fraction 21/35, the equivalent fraction is 3/5
4.) From the fractions given below, pair off the equivalent fractions.
2/3 = 18/27
the numerator and denominator of a fraction are multiplied by the same non-zero number, which is 9. (9×2) = 18/(9×3) = 27
5/7 = 10/14
the numerator and denominator of a fraction are multiplied by the same non-zero number, which is 2. (5×2) = 10/(2×7) = 14
5/11 = 15/33
the numerator and denominator of a fraction are multiplied by the same non-zero number, which is 3. (3×5) = 15/(3×11) = 33
7/9 = 14/18
the numerator and denominator of a fraction are multiplied by the same non-zero number, which is 2. (7×2) = 14/(9×2) = 18
5.) Find two equivalent fractions for of the following fractions.
7/9 = 14/18 (multiplying with both numerator and denominator with 2)
= 21/27 (multiplying with both numerator and denominator with 3)
4/5 = 8/10, 12/15
3/11 = 6/22, 18/66
PROBLEM SET 18
Convert the given fractions into like fractions.
Note: Like Fraction means same denominator.
(1) ¾, 5/8
Here, we must find a common multiple for the numbers 4 and 8.
Multiples of 4: 4,8,12,16,20
Multiples of 8 : 8,16, 24,32,40
Here, the number 8 is a multiple of both 4 and 8.So, let us make 8 the denominator of both fractions.
3×2/4×2 = 6/8 5×1/8×1 = 5/8
Thus, 6/8 and 7/8 are like fractions, respectively equivalent to ¾ and 5/8
(2) 3/5 , 3/7
Here, we must find a common multiple for the numbers 5 and 7 .
Multiples of 5 : 5,10,15,20,25,30,35
Multiples of 7 : 7,14,21,28,35
Here, the number 35 is a multiple of both 5 and 7 .So, let us make 35 the denominator of both fractions.
3×7/5×7 = 21/35 3×5/7×5= 15/35
Thus, 21/35 and 15/35 are like fractions, respectively equivalent to 3/5 and 3/7.
(3) 4/5 , 3/10
Here, we must find a common multiple for the numbers 5 and 10 .
Multiples of 5 : 5,10
Multiples of 10 : 10,20
Here, the number 10 is a multiple of both 5 and 10 .So, let us make 10 the denominator of both fractions.
4×2/5×2 = 8/10 3×1/10×1=3/10
Thus, 8/10 and 3/10 are like fractions, respectively equivalent to 4/5 and 3/10
(4) 2/9 , 1/6
The number 18 is a multiple of both 9 and 6 . So, make 18 the common denominator.
2×2/9×2 = 4/18 1×3/6×3 = 3/18
Therefore, 4/18 and 3/18 are required like fractions
(5) ¼,2/3
The number 12 is a multiple of both 4 and 3. So, make 12 the common denominator.
1×3/4×3 = 3/12 2×4/3×4=8/12
Therefore, 3/12 and 8/12 are required like fractions
(6) 5/6 , 4/5
The number 30 is a multiple of both 6 and 5. So, make 30 the common denominator.
5×5/6×5 = 25/30 4×6/5×6=24/30
Therefore, 25/30 and 24/30 are required like fractions
(7) 3/8 = 1/6
The number 24 is a multiple of both 8 and 6. So, make 24 the common denominator.
3×3/8×3 = 9/24 1×4/6×4=4/24
Therefore, 9/24 and 4/24 are required like fractions
(8) 1/6, 4/9
The number 18 is a multiple of both 6 and 9. So, make 18 the common denominator.
1×3/6×3 = 3/18 4×2/9×2=8/18
Therefore, 3/18 and 8/18 are required like fractions
PROBLEM SET 19
(1) 3/7 = 3/7
As both fraction has same numerator and denominator.
(2) 3/8 > 2/8
Both have the same denominator 8.
In like fractions, the fraction with the greater numerator is the greater fraction.
(3) 2/11 < 10/11
Both have the me denominator 11.
In like fractions, the fraction with the greater numerator is the greater fraction.
(4) 5/15 = 10/30
As 30 is twice 15, it is easy to make 30 the common denominator.
5×2/15×2 = 10/30
both fraction has same numerator and denominator.
(5) 5/8 > 5/9
(8×9) = 72 can be divided by both 8 and 9. So, 72 can be the common denominator.
5×9/8×9 = 45/72 5×8/9×8 = 40/72
45/72 > 40/72 so 5/8 >5/9
(6) 4/7 > 4/11
(7×11) = 77 can be divided by both 7 and 11. So, 77 can be the common denominator.
4×11/7×11 = 44/77 4×7/11×7 = 28/77
44/77 > 28/77 so 4/7> 4/11
(7) 10/11 > 10/13
(11×13) = 143.can be divided by both 11and 13. So, 143 can be the common denominator.
10×13/11×13 = 130/143 10×11/13×11 = 110/143
130/143 > 110/143 so 10/11 > 10/13
(8) 1/5 > 1/9 (common denominator 5×9 = 45)
(9) 5/6 > 1/8 (common denominator 6×8 = 48)
(10) 5/12 > 1/6 (common denominator 6×2 = 12)
(11) 7/8 = 14/16 (common numerator and denominator)
(12) 4/9 = 4/9 (common numerator and denominator)
(13) 5/18 > 1/9 (common denominator 9×2 = 18)
(14) 2/3 > 4/7 (common denominator 3×7 = 21)
(15) 3/7 < 5/9 (common denominator 7×9 = 63)
(16) 4/11 < 1/5 (common denominator 5×11 = 55)
PROBLEM SET 20
1.) ADD
(1) 1/5+3/5
When adding like fractions, we add the numerators of the two fractions and write the denominator as it is.
So, 1/5+3/5 = 1+3/5 = 4/5
(2) 2/7+4/7
When adding like fractions, we add the numerators of the two fractions and write the denominator as it is.
So, 2/7+4/7 = 2+4/7 = 6/7
(3) 7/12+2/12
When adding like fractions, we add the numerators of the two fractions and write the denominator as it is.
So, 7/12+2/12 = 7+2/12 = 9/12
They have a common divisor, which is 3.
So we can also write it as, 9÷3/12÷3 = ¾
(4) 2/9+7/9
When adding like fractions, we add the numerators of the two fractions and write the denominator as it is.
So, 2/9+7/9 = 2+7/9 =9/9
If the numerator and denominator of a fraction are equal, the fraction is equal to one.
Therefore, 9/9 = 1
(5) 3/15+4/15 = 3+4/15 = 7/15
(6) 2/7+1/7+3/7 = 2+1+3/7 = 6/7
(7) 2/10+4/10+3/10 = 2+4+3/10 =9/10
(8) 4/9+1/9 = 4+1/9 = 5/9
(9) 5/8+3/8 = 5+3/8 = 8/8
If the numerator and denominator of a fraction are equal, the fraction is equal to one.
Therefore, 8/8 = 1
2.) Mother gave 3/8 of one guava to Meena and 2/8 of the guava to Geeta. What part of the guava did she give them altogether ?
Mother gave Meena 3/8 of one guava
Mother gave Geeta got 2/8 of one guava
So total part she gave them = 3/8+2/8 = 3+2/8 = 5/8
Answer = 5/8 part of the guava she gave them altogether.
3.) The girls of Std V cleaned 3/4 of a field while the boys cleaned 1/4 . What part of the field was cleaned altogether ?
Girls cleaned ¾ parts of field
Boys cleaned ¼ parts of field
Total part of field was cleaned = ¾ + ¼ = 3+1/4 = 4/4
the numerator and denominator of a fraction are equal, the fraction is equal to one.
Therefore, 4/4 = 1
Answer = total field was cleaned.
PROBLEM SET 21
1.) Subtract :
(1) 5/7 – 1/7
These two fractions have a common denominator. So, we shall subtract the second numerator from the first and write the denominator as it is.
5/7 – 1/7 = 5 – 1/7 = 4/7
(2) 5/8 – 3/8
These two fractions have a common denominator. So, we shall subtract the second numerator from the first and write the denominator as it is.
5/8 – 3/8 = 5 – 3/8 = 2/8
(3) 7/9 – 2/9
These two fractions have a common denominator. So, we shall subtract the second numerator from the first and write the denominator as it is.
7/9 – 2/9 = 7 – 2/9 = 5/9
(4) 8/11 – 5/11
These two fractions have a common denominator. So, we shall subtract the second numerator from the first and write the denominator as it is.
8/11 – 5/11 = 8 – 5/11 = 3/11
(5) 9/13 – 4/13 = 9 – 4/13 = 5/13
(6) 7/10 – 3/10 = 7 – 3/10 = 4/10
(7) 9/12 – 2/12 = 9 – 2/12 = 7/12
(8) 10/15 – 3/15 = 10 – 3/15 = 7/15
2.) 7/10 of a wall is to be painted. Ramu has painted 4/10 of it.How much more needs to be painted ?
Total part of wall to be painted = 7/10
Ramu painted = 4/10
To find the part is to be painted, we must subtract
7/10 – 4/10 = 7 – 4/10 = 3/10
Answer = 3/10 part is to be painted.
PROBLEM SET 22
1.) Add
(1) 1/8+3/4
Here, 8 is twice 4. So, we shall change. So, the denominator of both fractions to 4.
1×1/8×1 + 3×2/4×2 = 1/8 + 6/8 = 1+6/8 = 7/8
(2) 2/21+3/7
Here, 21 is 3 times of 7, (7×3) = 21
So we shall change the denominator of first fraction to 21 to make them equivalent fraction,
2×1/21×1 + 3×3/7×3 = 2/21+9/21 = 2+9/21 = 11/21
(3) 2/5+1/3
Here, the smallest common multiple of the two denominators is 15. So, we shall change the denominator of both fraction to 15.
2×3/5×3 +1×5/3×5 = 6/15+5/15 = 6+5/15 =11/15
(4) 2/7+1/2 = 2×2/7×2 + 1×7/2×7 = 4/14 + 7/14 = 11/14
(5) 3/9+3/5 = 3×5/9×5 + 3×9/5×9 =15/45 + 27/45 = 15+27/45 = 42/45
2.) Subtract
(1) 3/10 – 1/20
Here, 20 is twice 10. So, we shall change. So, the denominator of both fractions to 20.
3×2/10×2 – 1/20 = 6/20 – 1/20 = 6 – 1/20 = 5/20
(2) ¾ – ½
Here, 4 is twice 2. So, we shall change. So, the denominator of both fractions to 4.
¾ – 1×2/2×2 = ¾ – 2/4 = 3 – 2/4 = ¼
(3) 6/14 – 2/7
Here, 14 is twice 7. So, we shall change. So, the denominator of both fractions to 14.
6/14 – 2×2/7×2 = 6/14 – 4/14 = 2/14
(4) 4/6 – 3/5
4×5/6×5 – 3×6/5×6 = 20/30 – 18/30 = 20 – 18/30 = 2/30
(5) 2/7 – ¼
2×4/7×4 – 1×7/4×7 = 8/28 – 7/28 = 8 – 7/28 = 1/28
PROBLEM SET 23
1.) What is 1/3 of each of the collections given below?
(1) 1/3 times 15 pencil is = 1/3×15 = 5 pencil
First we divide the 15 with the denominator 3,(15÷3) = 5
Then we multiply the quotient 5 with numerator 1, (5×1) = 5
(2) 1/3 times of 21 balloon is = 1/3 ×21 = 7
First we divide 21 with the denominator 3, (21÷3) = 7
Then we multiply the quotient 7 with numerator 1, (7×1) = 7
(3) 1/3 times of 9 children is = 1/3×9 = 3 children.
(4) 1/3 times of 18 books is = 1/3×18 = 6 books.
- What is 1/5 of each of the following?
(1) 1/5 times of 20 rupees is = 1/5×20 = 4
First we divide the 20 with the denominator 5,(20÷5) = 4
Then we multiply the quotient 4with numerator 1, (4×1) = 4
(2) 1/5 times of 30 km is = 1/5×30 = 6 km
First we divide the 30 with the denominator 5,(30÷5) = 6
Then we multiply the quotient 6 with numerator 1, (6×1) = 6
(3) 1/5 times of 15 litres is = 1/5×15 = 3 litres
(4) 1/5 times of 25 cm is = 1/5×25 = 5 cm
- Find the part of each of the following numbers equal to the given fraction.
(1) 2/3 of 30 is = 2/3×30 = 20
First we divide the 30 with the denominator 3,(30÷3) = 10
Then we multiply the quotient 10 with numerator 2, (10×2) = 20
(2) 7/11 of 22 is = 7/11×22 = 14
First we divide the 22 with the denominator 11,(22÷11) = 2
Then we multiply the quotient 2 with numerator 7, (7×2) = 14
(3) 3/8 of 64 is = 3/8×64 = 24
First we divide the 64 with the denominator 8,(64÷8) = 8
Then we multiply the quotient 8 with numerator 3, (8×3) = 24
(4) 5/13 of 65 is = 25
For More Solutions, Click Below:
Part One:
- Chapter 1 Roman Numerals
- Chapter 2 Number Work
- Chapter 3 Addition and Subtraction
- Chapter 4 Multiplication and Division
- Chapter 6 Angles
- Chapter 7 Circles
Part Two:
