Practising multiplying fractions questions with solutions is essential to improve children’s skills in fractions. Multiplication of fractions is quite simple; to multiply two fractions, we just have to multiply numerator to numerator and denominator to the denominator. Unlike addition and subtraction of fractions, while multiplying fractions, we do not have to make the denominator the same.
Learn more about fractions.
Video Lesson on Like and Unlike Fractions
Multiplying Fractions Questions with Solutions
Now let us solve questions on the multiplication of fractions.
Question 1:
Solve the following:
(i) ⅔ × ⅗
(ii) 9/7 × ⅜
(iii) ⅘ × ⅚
Solution:
(i) ⅔ × ⅗
= (2 × 3)/(3 × 5)
= 6/15 reducing the fraction to the lowest form
= ⅖.
(ii) 9/7 × ⅜
= (9 × 3)/(7 × 8)
= 27/56.
(iii) ⅘ × ⅚
= 4/6 reducing the fraction to the lowest form
= ⅔.
Question 2:
Simplify the following:
(i) 2½ × 3⅓
(ii) 3¼ × 5 2/9
(iii) 41/7 × 31/8
Solution:
(i) 2½ × 3⅓
Converting the mixed fraction into the improper fraction
= 5/2 × 10/3
= 25/3 = 8⅓.
(ii) 31/4 × 5 2/9
= 13/4 × 47/9
= (13 × 47)/(4 × 9)
= 611/36
(iii) 41/7 × 31/8
= 29/7 × 25/8
= (29 × 25)/(7 × 8)
= 725/56
Also, Refer:
- Mixed to Improper Fractions
- Mixed to Improper Fraction Calculator
- Improper to Mixed Fraction Calculator
Question 3:
Work out the following and express them in the simplest form:
(i) 22/3 ÷ 11/5
(ii) 34/35 ÷ 6/7
(iii) 56/3 ÷ 9/17
Solution:
(i) 22/3 ÷ 11/5
Convert the division into multiplication by taking the reciprocal of the divisor fraction
= 22/3 × 5/11
= ⅔ × 5
= 10/3
= 3⅓.
(ii) 34/35 ÷ 6/7
= 34/35 × 7/6
= 17/5 × ⅓
= 17/15
(iii) 56/3 ÷ 9/17
= 56/3 × 17/9
= 952/27
Question 4:
Work out the following and express them in the simplest form:
(i) 26 × 1/13 ÷ 5/169
(ii) 6.4 × ⅘ ÷ ⅔
(iii) 2.98 ÷ ¾ × ⅖
Solution:
(i) 26 × 1/13 ÷ 5/169
According to the BODMAS rule, we first perform division followed by multiplication.
= 26 × (1/13 ÷ 5/169)
= 26 × (1/13 × 169/5)
= 26 × 13/5
= 338/5
(ii) 6.4 × ⅘ ÷ ⅔
= 64/10 × (⅘ ÷ ⅔)
= 64/10 × (⅘ × 3/2)
= 64/10 × 6/5
= 192/25
(iii) 2.98 ÷ ¾ × ⅖
= (298/100 ÷ 3/4) × ⅖
= (298/100 × 4/3) × ⅖
= 298/(25 × 3) × ⅖
= 298/75 × ⅖
= 596/375.
Question 5:
The length and the width of a rectangular park are 39/4 m and 25/3 m, respectively. Find the area of the park.
Solution:
Length of the park = 39/4
Width of the park = 25/3
Area of the rectangular park = 39/4 × 25/3
= (13 × 25)/4 = 325/4 = 81.25 m2.
Question 6:
A household has an overhead water tank of 1000 litres. Every day 4/5th of the tank is used for household purposes. Find the amount of water needed for a week.
Solution:
The capacity of the tank = 1000 litres
Amount of water used everyday = 4/5th of 1000 litres
= ⅘ × 1000 = 4 × 200 = 800 litres
Amount of water required for a week = 7 × 800 = 5600 litres.
Question 7:
A farmer plants the sapling of a plant at a uniform distance of 5/3 cm. If he plants 27 such saplings in a row, find the total distance between the first and the last sapling.
Solution:
Distance between each sapling = 5/3 cm
Number of saplings in a row = 27
Distance between first and the last sapling = 5/3 × 27 = 5 × 9 = 45 cm.
Question 8:
The area of the triangle is 145/3 cm2. If the base length of the triangle is ⅔ cm, find the height of the triangle.
Solution:
The base of the triangle = ⅔ cm
Area of the triangle = ½ × base × height = 145/3 cm2
⇒ ½ × ⅔ × height = 145/3
⇒ height = 145/3 ÷ ⅓
⇒ height = 145/3 × 3 = 145 cm
Question 9:
Find the following:
(i) 2/5th of a day.
(ii) ¼th of a kilometre.
(iii) 3/4th of a year.
Solution:
(i) 2/5th of a day
Now, 1 day = 24 hours
⅖ × 24 hours = 48/5
= 9.6 hours
= 9 hours 36 minutes.
(ii) ¼th of a kilometre
1 km = 1000 m
¼ × 1000 m
= 250 m.
(iii) 3/4th of a year.
1 year = 12 months
3/4 × 12 = 9 months.
Question 10:
In a class of 60 students, two-thirds are boys. How many girls are there in the class?
Solution:
Number of students = 60
Number of boys = 60 × ⅔ = 40
Number of girls = 60 – 40 = 20.
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Practice Questions on Multiplying Fractions
1. Evaluate the following:
(i) ⅔ × ⅘
(ii) 4/7 × 9/21
(iii) 45/7 × 3½
(iv) 196/7 × 13½
(vi) 34/5 ÷ 6/7
(vii) 2 ÷ ⅘
(viii) ⅞ ÷ 13
(ix) ⅚ ÷ 96/5
(x) 12 × ¾ ÷ 1/2
2. Find the base of the triangle whose height is 4⅗ cm and the area is 28/35 cm2.
3. Three times more flour is needed to make a large cake than a small one. If 3⅕ kg flour is needed to make a large size cake, how much flour is needed to make a small size cake?
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