Multiplication and Division of Fractions - Class 5 - Mathematics
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Exercise 33 - Multiplication and Division of Fractions | R.S. Aggarwal | Mathematics | Class 5
$\frac{1}{2} \times 5$
To solve the expression $\frac{1}{2} \times 5$, you multiply the fraction by the number:
$$ \frac{1}{2} \times 5 = \frac{5}{2} = 2.5 $$
So, $\frac{1}{2} \times 5 = 2.5$.
$\frac{1}{3} \times 8$
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Sign up now$\frac{2}{3} \times 7$
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Sign up now$\frac{3}{5} \times 6$
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Sign up now$\frac{5}{6} \times 8$
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Sign up now$\frac{7}{8} \times 12$
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Sign up now$\frac{13}{21} \times 9$
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Sign up now$\frac{17}{18} \times 14$
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Sign up now$\frac{21}{25} \times 10$
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Sign up now$2 \frac{1}{2} \times 6$
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Sign up now$3 \frac{2}{3} \times 8$
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Sign up now$4 \frac{1}{6} \times 21$
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Sign up now$5 \frac{3}{8} \times 20$
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Sign up now$3 \frac{7}{15} \times 25$
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Sign up now$10 \frac{7}{13} \times 26$
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Sign up now$2 \frac{10}{21} \times 28$
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Sign up nowExercise 34 - Multiplication and Division of Fractions | R.S. Aggarwal | Mathematics | Class 5
$\frac{3}{4} \times \frac{5}{7}$
The product of $\frac{3}{4}$ and $\frac{5}{7}$ is:
$$ \frac{15}{28} $$
Here's a visual representation on a number line:
And as a pie chart:
Also, here is the representation with a tape diagram:
$\frac{5}{6} \times \frac{9}{10}$
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Sign up now$\frac{14}{27} \times \frac{12}{35}$
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Sign up now$2 \frac{3}{5} \times \frac{7}{13}$
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Sign up now$6 \frac{5}{12} \times \frac{6}{11}$
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Sign up now$\frac{8}{21} \times 6 \frac{3}{4}$
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Sign up now$\frac{9}{46} \times 7 \frac{2}{3}$
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Sign up now$28 \times 2 \frac{10}{21}$
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Sign up now$4 \frac{4}{15} \times 3 \frac{1}{8}$
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Sign up now$6 \frac{3}{16} \times 7 \frac{7}{11}$
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Sign up now$3 \frac{6}{25} \times 6 \frac{1}{9}$
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Sign up now$12 \frac{5}{6} \times 1 \frac{5}{22}$
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Sign up now$4 \frac{9}{14} \times 1 \frac{8}{13}$
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Sign up now$15 \frac{3}{10} \times 4 \frac{1}{6}$
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Sign up now$5 \frac{10}{21} \times 1 \frac{17}{46}$
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Sign up now$17 \frac{2}{5} \times 2 \frac{2}{29}$
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Sign up now$23 \frac{7}{16} \times 2 \frac{14}{25}$
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Sign up now$40 \frac{6}{7} \times 2 \frac{19}{22}$
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Sign up now$\frac{3}{5} \times \frac{1}{6} \times \frac{2}{3}$
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Sign up now$2 \frac{1}{4} \times 1 \frac{1}{5} \times 3 \frac{1}{3}$
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Sign up nowExercise 35 - Multiplication and Division of Fractions | R.S. Aggarwal | Mathematics | Class 5
The cost of one pencil is $₹ 3 \frac{13}{20}$. What is the cost of 12 such pencils?
First, let's convert the mixed fraction $3 \frac{13}{20}$ to an improper fraction for ease of multiplication.
The mixed number is composed of a whole number $3$ and a fraction $\frac{13}{20}$. To convert it into an improper fraction, we use the formula:
$$ \text{improper fraction} = \text{whole number} \times \text{denominator} + \text{numerator} $$
Thus, for (3 \frac{13}{20}):
$$ \text{improper fraction} = 3 \times 20 + 13 = 60 + 13 = 73 $$
So, it becomes (\frac{73}{20}).
Now, to find the cost of 12 pencils, we multiply the cost of one pencil by 12:
$$ \text{total cost} = 12 \times \frac{73}{20} $$
Let's compute this value.
The total cost of 12 pencils, each priced at ₹$3 \frac{13}{20}$, is ₹$43 \frac{4}{5}$ or ₹43.8.
If you have any more questions or need further assistance, feel free to ask!
A bag contains $97 \frac{4}{5} \mathrm{~kg}$ of sugar. How much sugar do 10 such bags contain?
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Sign up nowA kilogram of apples cost $₹ 16 \frac{1}{4}$. What is the cost of $3 \frac{1}{5} \mathrm{~kg}$ of apples?
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Sign up nowA metre of cloth costs $₹ 107 \frac{1}{2}$. Find the cost of $2 \frac{1}{5} \mathrm{~m}$ of cloth.
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Sign up nowAn iron rod has been divided into 8 pieces of equal lengths. If the length of each piece is $6 \frac{3}{4} \mathrm{~m}$, what was the original length of the iron rod?
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Sign up nowOne litre of petrol costs ₹ $64 \frac{4}{5}$. What is the cost of 35 litres of petrol?
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Sign up nowA man walks $3 \frac{3}{4} \mathrm{~km}$ in 1 hour. How far does he go in $3 \frac{1}{2}$ hours?
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Sign up nowOne tin holds $16 \frac{3}{5}$ litres of oil. How many litres can 25 such tins hold?
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Sign up nowA water tank can hold $56 \frac{1}{4}$ litres of water. How much water is contained in the tank when it is $\frac{2}{5}$ full?
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Sign up nowAn aeroplane covers $1020 \mathrm{~km}$ in an hour. How much distance will it cover in $4 \frac{1}{6}$ hours?
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Sign up nowFind the perimeter of a square plot of land whose each side is $6 \frac{1}{2}$ metres.
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Sign up nowFind the perimeter of a rectangular park whose length and breadth are $45 \frac{1}{2} \mathrm{~m}$ and $34 \frac{3}{4} \mathrm{~m}$ respectively.
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Sign up nowExercise 36 - Multiplication and Division of Fractions | R.S. Aggarwal | Mathematics | Class 5
$\frac{1}{2}$ of $\frac{1}{3}$
The result of multiplying $ \frac{1}{2} $ by $ \frac{1}{3} $ is:
$$ \frac{1}{6} $$
Here is a visual representation using a pie chart:
$\frac{1}{7}$ of $\frac{1}{9}$
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Sign up now$\frac{2}{3}$ of $\frac{6}{7}$
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Sign up now$\frac{3}{7}$ of $\frac{14}{15}$
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Sign up now$\frac{5}{8}$ of $\frac{16}{25}$
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Sign up now$\frac{2}{5}$ of $1 \frac{9}{16}$
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Sign up now$\frac{4}{11}$ of $4 \frac{2}{5}$
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Sign up now$\frac{3}{4}$ of 56
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Sign up now$\frac{4}{9}$ of 36
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Sign up now$\frac{8}{11}$ of 44
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Sign up now$\frac{9}{13}$ of 78
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Sign up now$\frac{6}{7}$ of 42
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Sign up nowA bag can hold $96$ kg sugar. How much sugar is there in the bag when it is $\frac{5}{8}$ full?
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Sign up nowA test was given to a class of 42 students. If $\frac{6}{7}$ of these students passed, then how many failed?
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Sign up nowThere are 140 members of a committee. In a meeting, three-fourths of the members were present. Ho many members were absent?
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Sign up nowMona's school is $6 \mathrm{~km}$ away from her house. She covers $\frac{2}{3}$ of the distance in a rickshaw. Due to some fault in the rickshaw, she had to cover the remaining distance on foot. How far did she walk?
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Sign up nowThe capacity of a parking lot is that of 84 cars. At a particular time, $\frac{3}{4}$ of the parking lot is occupied How many more cars can be parked at that time?
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Sign up now$\frac{3}{8}$ of the population of a village consists of women. If $\frac{2}{3}$ of the women of that village are illiterate, what fraction of the population in that village consists of illiterate women?
(Hint. Iliterate women $=\frac{2}{3}$ of $\frac{3}{8}$ the population of the village.)
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Sign up nowExercise 37 - Multiplication and Division of Fractions | R.S. Aggarwal | Mathematics | Class 5
Find the multiplicative inverse of each of the following.
(a) $\frac{3}{5}$
(b) $\frac{9}{16}$
(c) $\frac{1}{8}$
(d) $\frac{10}{19}$
(e) 15
(f) $\frac{12}{7}$
(g) $\frac{24}{13}$
(h) $2 \frac{6}{7}$
(i) $3 \frac{9}{14}$
(j) $6 \frac{5}{8}$
(k) 1
(I) 0
Here are the multiplicative inverses for each of the given values:
(a) The multiplicative inverse of $\frac{3}{5}$ is $\frac{5}{3}$.
(b) The multiplicative inverse of $\frac{9}{16}$ is $\frac{16}{9}$.
(c) The multiplicative inverse of $\frac{1}{8}$ is $8$.
(d) The multiplicative inverse of $\frac{10}{19}$ is $\frac{19}{10}$.
(e) The multiplicative inverse of $15$ is $\frac{1}{15}$.
(f) The multiplicative inverse of $\frac{12}{7}$ is $\frac{7}{12}$.
(g) The multiplicative inverse of $\frac{24}{13}$ is $\frac{13}{24}$.
(h) The multiplicative inverse of $2 \frac{6}{7}$ is $\left(\frac{20}{7}\right)^{-1}$ or $\frac{7}{20}$.
(i) The multiplicative inverse of $3 \frac{9}{14}$ is $\left(\frac{51}{14}\right)^{-1}$ or $\frac{14}{51}$.
(j) The multiplicative inverse of $6 \frac{5}{8}$ is $\left(\frac{53}{8}\right)^{-1}$ or $\frac{8}{53}$.
(k) The multiplicative inverse of $1$ is $1$.
(l) The multiplicative inverse of $0$ is undefined (often notated as infinity symbolically).
These results provide the reciprocal for each fraction or number, effectively reversing the numerator and denominator where applicable.
Divide and find the quotient.
$\frac{6}{7} \div 3$
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Sign up nowDivide and find the quotient.
$\frac{7}{12} \div 21$
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Sign up nowDivide and find the quotient.
$4 \frac{2}{3} \div 7$
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Sign up nowDivide and find the quotient.
$17 \frac{3}{5} \div 33$
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Sign up nowDivide and find the quotient.
$\frac{7}{9} \div \frac{2}{3}$
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Sign up nowDivide and find the quotient.
$\frac{7}{24} \div \frac{5}{12}$
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Sign up nowDivide and find the quotient.
$\frac{9}{26} \div 4 \frac{2}{13}$
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Sign up nowDivide and find the quotient.
$8 \frac{1}{6} \div 4 \frac{2}{3}$
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Sign up nowDivide and find the quotient.
$10 \frac{5}{7} \div 1 \frac{11}{14}$
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Sign up nowDivide and find the quotient.
$100 \div 33 \frac{1}{3}$
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Sign up nowDivide and find the quotient.
$88 \div 3 \frac{1}{7}$
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Sign up nowDivide and find the quotient.
$84 \div 7 \frac{7}{8}$
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Sign up nowDivide and find the quotient.
$15 \frac{8}{9} \div 3 \frac{2}{3}$
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Sign up nowDivide and find the quotient.
$16 \frac{2}{3} \div 2 \frac{2}{9}$
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Sign up nowDivide and find the quotient.
$5 \frac{7}{10} \div 3 \frac{1}{6}$
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Sign up nowExpress 25 minutes as a fraction of an hour.
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Sign up nowExpress 35 paise as a fraction of a rupee.
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Sign up nowExpress $325 \mathrm{~mL}$ as a fraction of a litre.
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Sign up nowExpress $65 \mathrm{~cm}$ as a fraction of a metre.
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Sign up nowExpress $125 \mathrm{~m}$ as a fraction of a km.
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Sign up nowExercise 38 - Multiplication and Division of Fractions | R.S. Aggarwal | Mathematics | Class 5
If the cost of $3 \frac{1}{4} \mathrm{~kg}$ of sugar is $₹ 106 \frac{3}{5}$, find the cost of $1 \mathrm{~kg}$ of sugar.
To find the cost of 1 kg of sugar, we start by converting the mixed fractions into improper fractions for easier calculations.
First, convert $3 \frac{1}{4}$ kg to an improper fraction:
$$ 3 \frac{1}{4} = 3 + \frac{1}{4} = \frac{3 \times 4}{4} + \frac{1}{4} = \frac{12}{4} + \frac{1}{4} = \frac{13}{4} $$
Next, convert $₹ 106 \frac{3}{5}$ to an improper fraction:
$$ 106 \frac{3}{5} = 106 + \frac{3}{5} = \frac{106 \times 5}{5} + \frac{3}{5} = \frac{530}{5} + \frac{3}{5} = \frac{533}{5} $$
Now, to find the cost of 1 kg of sugar, divide the total cost by the total weight in kg:
The cost of $\frac{13}{4} $ kg of sugar is $\frac{533}{5} $ rupees. Let $ x$ be the cost for 1 kg:
$$ x = \frac{\frac{533}{5}}{\frac{13}{4}} $$
Computing $x $, the cost of 1 kg of sugar:
$$ x = \frac{533}{5} \times \frac{4}{13} $$
Let's calculate this value.
The cost of 1 kg of sugar is $₹ 32 \frac{4}{5} $.
This is approximately ₹ 32.8 for 1 kg of sugar.
If the cost of $2 \frac{3}{4}$ litres of petrol is $₹ 145 \frac{1}{5}$, find the cost of 1 litre of petrol.
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Sign up nowA bag of salt weighs $2 \frac{1}{4} \mathrm{~kg}$. If $40 \frac{1}{2} \mathrm{~kg}$ of salt is to be put in such bags, how many bags will be required?
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Sign up now14 tins hold $178 \frac{1}{2}$ litres of oil. How much oil is there in 1 tin?
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Sign up nowIf a car travels $283 \frac{1}{2} \mathrm{~km}$ in $4 \frac{2}{3}$ hours, how far does it go in 1 hour?
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Sign up nowIf $367 \frac{1}{2} \mathrm{~kg}$ of rice is contained in 35 bags of equal weights, how much does each bag weigh?
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Sign up nowSuchi cuts $54 \mathrm{~m}$ of cloth into pieces, each of length $3 \frac{3}{8}$ metres. How many pieces does she get?
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Sign up nowMona cuts $36 \frac{1}{8} \mathrm{~m}$ of cloth into 17 pieces of equal lengths. What is the length of each piece?
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Sign up nowThe area of a rectangle is $37 \frac{4}{5} \mathrm{sq}$. $\mathrm{cm}$. If its length is $6 \frac{3}{4} \mathrm{~cm}$, find its breadth.
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Sign up nowThe product of two fractions is 5 . If one of them is $13 \frac{4}{7}$, find the other.
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Sign up nowQuestion Bag 1 - Multiplication and Division of Fractions | R.S. Aggarwal | Mathematics | Class 5
Rita had $\frac{5}{6}$ of a cake. She ate $\frac{2}{3}$ of it. What part of the cake did she eat?
(a) $\frac{5}{9}$
(b) $\frac{3}{10}$
(c) $\frac{4}{5}$
(d) $\frac{10}{12}$
Rita ate $\frac{5}{9} $ of the entire cake. This corresponds to option (a) $\frac{5}{9}$.
Reciprocal of $3 \frac{1}{2}$ is
(a) $\frac{7}{2}$
(b) $\frac{2}{7}$
(c) $1 \frac{2}{3}$
(d) $2 \frac{1}{3}$
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Sign up nowQuestion Bag 2 - Multiplication and Division of Fractions | R.S. Aggarwal | Mathematics | Class 5
Fill in the blanks.
(a) $\frac{1}{4}$ of a rupee $=$ __________ P
(b) $\frac{2}{3}$ of a year $=$ __________ months
(c) $\frac{5}{6}$ of a day $=$ __________hours
(d) $\frac{3}{8}$ of a $\mathrm{kg}=$ ___________ gm
(e) $\frac{11}{25}$ of a litre $=$ _____________$\mathrm{mL}$
(f) $\frac{7}{15}$ of an hour $=$ ___________min
Here are the answers to the queries:
(a) $\frac{1}{4}$ of a rupee $=$ 25 P
(b) $\frac{2}{3}$ of a year $=$ 8 months
(c) $\frac{5}{6}$ of a day $=$ 20 hours
(d) $\frac{3}{8}$ of a $\mathrm{kg}=$ 375 gm
(e) $\frac{11}{25}$ of a litre $=$ **440 \mathrm{mL}$
(f) $\frac{7}{15}$ of an hour $=$ 28 min
Fill in the placeholders.
(a) _________ $\div 2 \frac{3}{4}=0$
(b) $\frac{6}{7} \div \square=1$
(c) $3 \frac{2}{5} \div 3 \frac{2}{5}=\square$ ______
(e) $0 \div 7 \frac{5}{6}=$ _________
(f) $\frac{3}{8} \div \frac{2}{3} = \frac{3}{8} \times \square$
(g) $9 \frac{2}{7} \times 3 \frac{5}{9} \times 0 \times 1 \frac{2}{3}= \square$
(h) $ 100 \div 3 \frac{1}{3} = \square$
(i) $5 \div \frac{1}{5}=\square$
(j) $11 \div \frac{1}{11}=\square$
(k) $\frac{1}{2} \div \frac{1}{10} \square$
(l) $\frac{1}{5} \div \frac{1}{20}=\square$
(m) $1 \div \frac{3}{5}=\square$
(n) $\frac{5}{6} \div \frac{6}{5}=$
(o) $8 \frac{8}{9} \div 0$
(p) $49 \div \frac{7}{9}=$
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Sign up nowDivide the product of $1 \frac{4}{13}$ and $7 \frac{4}{3}$ by $3 \frac{2}{13}$
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