NCERT MCQ Solutions for Class 6 Maths Chapter 7 Fractions

Each friend’s share = Total juice ÷ Number of friends
= 3 ÷ 4 = 3/4 glass
Each glass can be divided into four equal parts. Every friend receives one part from each of the three glasses, making three quarters.

Both fractions describe one equal part of the same whole. Dividing the whole into 9 parts gives smaller pieces than dividing it into 5 parts. Therefore, one fifth is larger than one ninth, so 1/5 > 1/9.

The whole is divided into six equal shares.
Each share = 1 ÷ 6 = 1/6
A piece represents one sixth because it has one of the six equal areas. Its shape can differ without changing that fraction.

The denominator 6 identifies the fractional unit as 1/6. The numerator 5 counts how many of these units are taken.
5/6 = 1/6 + 1/6 + 1/6 + 1/6 + 1/6
Thus, five one-sixth parts make the fraction.

Total amount = 5 × 1/4
= 5/4 roti
Four quarter-pieces make one whole roti, and one quarter-piece remains. Therefore, five quarters are more than one whole and can also be written as 1 1/4.

The numerator represents in a fraction is number of equal parts taken.

7/2 = 6/2 + 1/2
= 3 + 1/2
Every two halves make one whole. Six of the seven halves make three complete wholes, while the remaining half is not a complete whole unit.

4/5 = (4 × 2)/(5 × 2)
= 8/10
Each interval is 1/10 of a unit. Moving eight such intervals from 0 reaches 8/10, so 4/5 is at the eighth tick after 0.

Fractions such as 1/2, 1/3, 1/4, 1/5 and so on all lie between 0 and 1. There is no last denominator in this list, so more such fractions can always be formed. Their number is infinite.

47 = 5 × 9 + 2
47/9 = 45/9 + 2/9
= 5 2/9
The quotient 5 is the whole part. The remainder 2 becomes the numerator of the fractional part, while the denominator stays 9.

7 = 21/3
7 2/3 = 21/3 + 2/3
= 23/3
Each whole contains three thirds. Seven wholes contain 21 thirds, and the extra two thirds bring the total to 23 thirds.

The correct fraction for a roti divided equally among 5 children is 1/5.

1/2 = (1 × 3)/(2 × 3)
= 3/6
Therefore, three pieces of length 1/6 unit make 1/2 unit. The lengths add as 1/6 + 1/6 + 1/6 = 3/6 = 1/2.

2/3 = (2 × 2)/(3 × 2)
= 4/6
Both the numerator and denominator are multiplied by the same number. This changes the number and size of the parts together, so the represented quantity remains the same.

The number of friends doubles from 4 to 8. The juice must also double to keep each share unchanged.
Glasses needed = 5 × 2 = 10
Check: 5/4 = 10/8, so the individual shares are equal.

12 kg is 3 times 4 kg, so the number of equal bags must also be 3 times as many.
Number of bags = 3 × 3 = 9
Check: 12/9 = 4/3 kg per bag.

Multiplying the numerator and denominator by the same positive whole number preserves the value.
For example, 2/5 = (2 × 2)/(5 × 2) = 4/10.
The other operations do not preserve a fraction’s value in general.

Which of the following fractions is equivalent to 2/4 is 1/2.

36 and 60 have the common factor 12.
36/60 = (36 ÷ 12)/(60 ÷ 12)
= 3/5
Since 3 and 5 have no common factor other than 1, the fraction cannot be reduced further.

Both 64 and 144 are divisible by 16.
64/144 = (64 ÷ 16)/(144 ÷ 16)
= 4/9
The numbers 4 and 9 have no common factor except 1, so this is the lowest form.

4/5 = 36/45
7/9 = 35/45
Since 36/45 > 35/45, we have 4/5 > 7/9.
The common denominator makes both fractions count the same-sized parts, so their numerators can be compared directly.

7/9 = 49/63
17/21 = 51/63
Since 51 > 49, we have 51/63 > 49/63.

Using denominator 30:
7/10 = 21/30, 11/15 = 22/30, 2/5 = 12/30
Since 12 < 21 < 22, the ascending order is 2/5, 7/10, 11/15. Ascending order runs from the smallest fraction to the largest.

1/3 + 1/6 = (2+1)/6 = 3/6 = 1/2

4/7 + 6/7 = (4 + 6)/7
= 10/7
Both fractions use seventh-parts, so their numerators are added while the denominator stays 7. Ten sevenths contain one whole and three sevenths, so the sum is also 1 3/7.

1/4 = 3/12 and 1/3 = 4/12
1/4 + 1/3 = 3/12 + 4/12
= 7/12
The fractions are first expressed in equal-sized twelfths. Their numerators can then be added without changing the common denominator.

2/3 = 8/12 and 3/4 = 9/12
Total volume = 8/12 + 9/12 = 17/12 litres
= 1 5/12 litres
Twelve twelfths make one litre, leaving five twelfths of a litre.

Total lace = 2/5 + 3/4
= 8/20 + 15/20 = 23/20 m
Lace remaining = 23/20 − 20/20 = 3/20 m
Their combined lace is more than 1 m, so it is enough for the border.

Using the common denominator 60:
3/4 = 45/60, 1/3 = 20/60, 1/5 = 12/60
Sum = (45 + 20 + 12)/60
= 77/60
The three fractions must use the same fractional unit before their numerators are added.

5/8 − 3/8 = (5 − 3)/8
= 2/8
= 1/4
The denominator remains 8 during subtraction because both amounts are measured in eighths. Dividing the numerator and denominator of 2/8 by 2 gives its simplest form.

5/6 = 15/18 and 4/9 = 8/18
5/6 − 4/9 = 15/18 − 8/18
= 7/18
The denominator 18 is common to both fractions. Since 7 and 18 have no common factor except 1, the answer is in lowest terms.

Distance walked = 7/10 − 1/2
= 7/10 − 5/10
= 2/10 = 1/5 km
The distance travelled by auto is subtracted from the total journey because the remaining part is covered on foot.

Jeevika’s time = 10/3 = 40/12 minutes
Namit’s time = 13/4 = 39/12 minutes
Difference = 40/12 − 39/12 = 1/12 minute
Namit takes less time because 39 twelfths is less than 40 twelfths.

1/2 + 1/3 = 3/6 + 2/6 = 5/6
Missing fraction = 1 − 5/6
= 6/6 − 5/6 = 1/6
Thus, three different unit fractions, 1/2, 1/3 and 1/6, add up to one whole.

Egyptian mathematician Al-Hassar introduced the method of writing fractions similar to today’s notation?