Fractions and Decimals - Class 7 - Mathematics
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Examples - Fractions and Decimals | NCERT | Mathematics | Class 7
In a class of 40 students $\frac{1}{5}$ of the total number of students like to study English, $\frac{2}{5}$ of the total number like to study Mathematics and the remaining students like to study Science.
(i) How many students like to study English?
(ii) How many students like to study Mathematics?
(iii) What fraction of the total number of students like to study Science?
Let's solve each part of the question step by step.
(i) How many students like to study English?
Given that $\frac{1}{5}$ of the total number of students like to study English, and there are 40 students in total: $$\text{Number of students who like to study English} = \frac{1}{5} \times 40$$
(ii) How many students like to study Mathematics?
Given that $\frac{2}{5}$ of the total number like to study Mathematics, and there are 40 students in total: $$\text{Number of students who like to study Mathematics} = \frac{2}{5} \times 40$$
(iii) What fraction of the total number of students like to study Science?
First, we need to calculate the number of students who like to study Science. Given that the fractions of students liking English and Mathematics add up, we subtract from 1 to find the fraction liking Science: $$\text{Fraction liking Science} = 1 - \left(\frac{1}{5} + \frac{2}{5}\right)$$
Now, let's calculate these values. (i) The number of students who like to study English is 8.
(ii) The number of students who like to study Mathematics is 16.
(iii) The fraction of the total number of students who like to study Science is $\frac{2}{5}$, which is equivalent to 0.4 or 40% of the total number of students.
Sushant reads $\frac{1}{3}$ part of a book in 1 hour. How much part of the book will he read in $2 \frac{1}{5}$ hours?
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Sign up nowThe side of an equilateral triangle is 3.5 cm. Find its perimeter
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Sign up nowThe length of a rectangle is $7.1 \mathrm{~cm}$ and its breadth is $2.5 \mathrm{~cm}$. What is the area of the rectangle?
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Sign up nowFind the average of $4.2$, $3.8$ and $7.6$.
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Sign up nowEach side of a regular polygon is $2.5 \mathrm{~cm}$ in length. The perimeter of the polygon is $12.5 \mathrm{~cm}$. How many sides does the polygon have?
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Sign up nowA car covers a distance of $89.1 \mathrm{~km}$ in 2.2 hours. What is the average distance covered by it in 1 hour?
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Sign up nowExercise 2.1 - Fractions and Decimals | NCERT | Mathematics | Class 7
Which of the drawings (a) to (d) show :
(i) $2 \times \frac{1}{5}$
(ii) $2 \times \frac{1}{2}$
(iii) $3 \times \frac{2}{3}$
(iv) $3 \times \frac{1}{4}$
To determine which drawings represent each of the given expressions, let's analyze each expression and relate it to the characteristics of the drawings:
$2 \times \frac{1}{5}$: This expression represents two fifths. Looking for a figure divided into five equal parts with two parts shaded.
$2 \times \frac{1}{2}$: This represents a whole (1), as two halves make a whole. Look for a figure that is completely shaded or represents a complete set.
$3 \times \frac{2}{3}$: This amounts to 2, meaning three two-thirds combined equal two wholes. Look for two complete sets or an equivalent representation.
$3 \times \frac{1}{4}$: This expression equals three fourths. Look for a figure divided into four equal parts with three parts shaded.
By visually inspecting the provided image:
Drawing (a) is divided into 4 parts, with 3 parts shaded, representing $3 \times \frac{1}{4}$.
Drawing (b) shows 2 complete sets, representing $3 \times \frac{2}{3}$ (since each set resembles two-thirds of a circle, and three such sets make up two wholes).
Drawing (c) is divided into 2 parts, both shaded, representing $2 \times \frac{1}{2}$.
Drawing (d) is divided into 5 parts, with 2 parts shaded, which represents $2 \times \frac{1}{5}$.
Therefore, the matches are:
(i) $2 \times \frac{1}{5}$ is represented by Drawing (d). (ii) $2 \times \frac{1}{2}$ is represented by Drawing (c). (iii) $3 \times \frac{2}{3}$ is represented by Drawing (b). (iv) $3 \times \frac{1}{4}$ is represented by Drawing (a).
Some pictures (a) to (c) are given below. Tell which of them show:
(i) $3 \times \frac{1}{5}=\frac{3}{5}$
(ii) $2 \times \frac{1}{3}=\frac{2}{3}$
(iii) $3 \times \frac{3}{4}=2 \frac{1}{4}$
Multiply and reduce to lowest form and convert into a mixed fraction:
(i) $7 \times \frac{3}{5}$
(ii) $4 \times \frac{1}{3}$
(iii) $2 \times \frac{6}{7}$
(iv) $5 \times \frac{2}{9}$
(v) $\frac{2}{3} \times 4$
(vi) $\frac{5}{2} \times 6$
(vii) $11 \times \frac{4}{7}$
(viii) $20 \times \frac{4}{5}$
(ix) $13 \times \frac{1}{3}$
(x) $15 \times \frac{3}{5}$
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Sign up nowShade: (i) $\frac{1}{2}$ of the circles in box (a) (ii) $\frac{2}{3}$ of the triangles in box (b)
(iii) $\frac{3}{5}$ of the squares in box (c).
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Sign up nowFind:
(a) $\frac{1}{2}$ of
(i) 24 (ii) 46
(b) $\frac{2}{3}$ of
(i) 18
(ii) 27
(c) $\frac{3}{4}$ of
(i) 16
(ii) 36
(d) $\frac{4}{5}$ of
(i) 20
(ii) 35
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Sign up nowMultiply and express as a mixed fraction with steps
(a) $3 \times 5 \frac{1}{5}$
(b) $5 \times 6 \frac{3}{4}$
(c) $7 \times 2 \frac{1}{4}$
(d) $4 \times 6 \frac{1}{3}$
(e) $3 \frac{1}{4} \times 6$
(f) $3 \frac{2}{5} \times 8$
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Sign up nowFind: (a) $\frac{1}{2}$ of (i) $2 \frac{3}{4}$ with steps
(ii) $4 \frac{2}{9}$
(b) $\frac{5}{8}$ of
(i) $3 \frac{5}{6}$
(ii) $9 \frac{2}{3}$
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Sign up nowVidya and Pratap went for a picnic. Their mother gave them a water bottle that contained 5 litres of water. Vidya consumed $\frac{2}{5}$ of the water. Pratap consumed the remaining water.
(i) How much water did Vidya drink?
(ii) What fraction of the total quantity of water did Pratap drink?
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Sign up nowExercise 2.2 - Fractions and Decimals | NCERT | Mathematics | Class 7
Find:
(i) $\frac{1}{4}$ of
(a) $\frac{1}{4}$
(b) $\frac{3}{5}$
(c) $\frac{4}{3}$
(ii) $\frac{1}{7}$ of
(a) $\frac{2}{9}$
(b) $\frac{6}{5}$
(c) $\frac{3}{10}$
Here are the results of the specified calculations:
(i) $\frac{1}{4}$ of
(a) $\frac{1}{4} = \frac{1}{16}$ (b) $\frac{3}{5} = \frac{3}{20}$ (c) $\frac{4}{3} = \frac{1}{3}$
(ii) $\frac{1}{7}$ of
(a) $\frac{2}{9} = \frac{2}{63}$ (b) $\frac{6}{5} = \frac{6}{35}$ (c) $\frac{3}{10} = \frac{3}{70}$
Multiply and reduce to lowest form (if possible):
(i) $\frac{2}{3} \times 2 \frac{2}{3}$
(ii) $\frac{2}{7} \times \frac{7}{9}$
(iii) $\frac{3}{8} \times \frac{6}{4}$
(iv) $\frac{9}{5} \times \frac{3}{5}$
(v) $\frac{1}{3} \times \frac{15}{8}$
(vi) $\frac{11}{2} \times \frac{3}{10}$
(vii) $\frac{4}{5} \times \frac{12}{7}$
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Sign up nowMultiply the following fractions:
(i) $\frac{2}{5} \times 5 \frac{1}{4}$
(ii) $6 \frac{2}{5} \times \frac{7}{9}$
(iii) $\frac{3}{2} \times 5 \frac{1}{3}$
(iv) $\frac{5}{6} \times 2 \frac{3}{7}$
(v) $3 \frac{2}{5} \times \frac{4}{7}$
(vi) $2 \frac{3}{5} \times 3$
(vii) $3 \frac{4}{7} \times \frac{3}{5}$
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Sign up nowWhich is greater:
(i) $\frac{2}{7}$ of $\frac{3}{4}$ or $\frac{3}{5}$ of $\frac{5}{8}$
(ii) $\frac{1}{2}$ of $\frac{6}{7}$ or $\frac{2}{3}$ of $\frac{3}{7}$
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Sign up nowSaili plants 4 saplings, in a row, in her garden. The distance between two adjacent saplings is $\frac{3}{4} \mathrm{~m}$. Find the distance between the first and the last sapling.
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Sign up nowLipika reads a book for $1 \frac{3}{4}$ hours everyday. She reads the entire book in 6 days. How many hours in all were required by her to read the book?
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Sign up nowA car runs $16 \mathrm{~km}$ using 1 litre of petrol. How much distance will it cover using $2 \frac{3}{4}$ litres of petrol.
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Sign up now(a) (i) Provide the number in the box $\square$, such that $\frac{2}{3} \times \square=\frac{10}{30}$.
(ii) The simplest form of the number obtained in $\square$ is
(b) (i) Provide the number in the box $\square$, such that $\frac{3}{5} \times \square=\frac{24}{75}$.
(ii) The simplest form of the number obtained in $\square$ is
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Sign up nowExercise 2.3 - Fractions and Decimals | NCERT | Mathematics | Class 7
Find:
(i) $12 \div \frac{3}{4}$
(ii) $14 \div \frac{5}{6}$
(iii) $8 \div \frac{7}{3}$
(iv) $4 \div \frac{8}{3}$
(v) $3 \div 2 \frac{1}{3}$
(vi) $5 \div 3 \frac{4}{7}$
For each division problem involving fractions, we use the same steps to solve. Here’s how we can solve these:
Convert any mixed numbers to improper fractions.
Multiply the first number (dividend) by the reciprocal of the second number (divisor).
Let’s apply these steps to each division problem:
(i) $$12 \div \frac{3}{4}$$
The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$.
Then, multiply $12$ by $\frac{4}{3}$: $$12 \times \frac{4}{3} = \frac{12 \times 4}{3} = \frac{48}{3} = 16.$$
(ii) $$14 \div \frac{5}{6}$$
The reciprocal of $\frac{5}{6}$ is $\frac{6}{5}$.
Then, multiply $14$ by $\frac{6}{5}$: $$14 \times \frac{6}{5} = \frac{14 \times 6}{5} = \frac{84}{5} = 16.8.$$
(iii) $$8 \div \frac{7}{3}$$
The reciprocal of $\frac{7}{3}$ is $\frac{3}{7}$.
Then, multiply $8$ by $\frac{3}{7}$: $$8 \times \frac{3}{7} = \frac{8 \times 3}{7} = \frac{24}{7} = 3\frac{3}{7}.$$
(iv) $$4 \div \frac{8}{3}$$
The reciprocal of $\frac{8}{3}$ is $\frac{3}{8}$.
Then, multiply $4$ by $\frac{3}{8}$: $$4 \times \frac{3}{8} = \frac{4 \times 3}{8} = \frac{12}{8} = 1\frac{1}{2}.$$
(v) $$3 \div 2\frac{1}{3}$$
First, convert $2\frac{1}{3}$ to an improper fraction: $2\frac{1}{3} = \frac{7}{3}$.
The reciprocal of $\frac{7}{3}$ is $\frac{3}{7}$.
Then, multiply $3$ by $\frac{3}{7}$: $$3 \times \frac{3}{7} = \frac{3 \times 3}{7} = \frac{9}{7} = 1\frac{2}{7}.$$
(vi) $$5 \div 3\frac{4}{7}$$
First, convert $3\frac{4}{7}$ to an improper fraction: $3\frac{4}{7} = \frac{25}{7}$.
The reciprocal of $\frac{25}{7}$ is $\frac{7}{25}$.
Then, multiply $5$ by $\frac{7}{25}$: $$5 \times \frac{7}{25} = \frac{5 \times 7}{25} = \frac{35}{25} = 1\frac{10}{25} = 1\frac{2}{5}.$$
These steps provide a systematic way to divide numbers by fractions or mixed numbers and can be applied to similar problems as well.
Find:
(i) $\frac{7}{3} \div 2$
(ii) $\frac{4}{9} \div 5$
(iii) $\frac{6}{13} \div 7$
(iv) $4 \frac{1}{3} \div 3$
(v) $3 \frac{1}{2} \div 4$
(vi) $4 \frac{3}{7} \div 7$
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Sign up nowFind:
(i) $\frac{2}{5} \div \frac{1}{2}$
(ii) $\frac{4}{9} \div \frac{2}{3}$
(iii) $\frac{3}{7} \div \frac{8}{7}$
(iv) $2 \frac{1}{3} \div \frac{3}{5}$
(v) $3 \frac{1}{2} \div \frac{8}{3}$
(vi) $\frac{2}{5} \div 1 \frac{1}{2}$
(vii) $3 \frac{1}{5} \div 1 \frac{2}{3}$
(viii) $2 \frac{1}{5} \div 1 \frac{1}{5}$
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Sign up nowExercise 2.4 - Fractions and Decimals | NCERT | Mathematics | Class 7
Find:
(i) $0.2 \times 6$
(ii) $8 \times 4.6$
(v) $0.05 \times 7$
(vi) $211.02 \times 4$
(iii) $2.71 \times 5$
(iv) $20.1 \times 4$
Here are the results for the given multiplications:
(i) $0.2 \times 6 = 1.2$
(ii) $8 \times 4.6 = 36.8$
(iii) $2.71 \times 5 = 13.55$
(iv) $20.1 \times 4 = 80.4$
(v) $0.05 \times 7 = 0.35$
(vi) $211.02 \times 4 = 844.08$
Find the area of rectangle whose length is $5.7 \mathrm{~cm}$ and breadth is $3 \mathrm{~cm}$ also write with steps.
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Sign up nowFind:
(i) $1.3 \times 10$
(ii) $36.8 \times 10$
(iii) $153.7 \times 10$
(iv) $168.07 \times 10$
(v) $31.1 \times 100$
(vi) $156.1 \times 100$
(vii) $3.62 \times 100$
(viii) $43.07 \times 100$
(ix) $0.5 \times 10$
(x) $0.08 \times 10$
(xi) $0.9 \times 100$
(xii) $0.03 \times 1000$
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Sign up nowA two-wheeler covers a distance of $55.3 \mathrm{~km}$ in one litre of petrol. How much distance will it cover in 10 litres of petrol?
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Sign up nowFind:
(i) $2.5 \times 0.3$
(ii) $0.1 \times 51.7$
(iii) $0.2 \times 316.8$
(iv) $1.3 \times 3.1$
(v) $0.5 \times 0.05$
(vi) $11.2 \times 0.15$
(vii) $1.07 \times 0.02$
(viii) $10.05 \times 1.05$
(ix) $101.01 \times 0.01$
(x) $100.01 \times 1.1$
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Sign up nowExercise 2.5 - Fractions and Decimals | NCERT | Mathematics | Class 7
Find:
(i) $0.4 \div 2$
(ii) $0.35 \div 5$
(iii) $2.48 \div 4$
(iv) $65.4 \div 6$
(v) $651.2 \div 4$
(vi) $14.49 \div 7$
(vii) $3.96 \div 4$
(viii) $0.80 \div 5$
Below are the results for each division:
(i) $0.4 \div 2 = 0.2$
(ii) $0.35 \div 5 = 0.07$
(iii) $2.48 \div 4 = 0.62$
(iv) $65.4 \div 6 = 10.9$
(v) $651.2 \div 4 = 162.8$
(vi) $14.49 \div 7 = 2.07$
(vii) $3.96 \div 4 = 0.99$
(viii) $0.80 \div 5 = 0.16$
Find:
(i) $4.8 \div 10$
(ii) $52.5 \div 10$
(iii) $0.7 \div 10$
(v) $272.23 \div 10$
(vi) $0.56 \div 10$
(vii) $3.97 \div 10$
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Sign up nowFind:
(i) $2.7 \div 100$
(ii) $0.3 \div 100$
(iii) $0.78 \div 100$
(iv) $432.6 \div 100$
(v) $23.6 \div 100$
(vi) $98.53 \div 100$
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Sign up nowFind:
(i) $7.9 \div 1000$
(ii) $26.3 \div 1000$
(iii) $38.53 \div 1000$
(iv) $128.9 \div 1000$
(v) $0.5 \div 1000$
(iv) $33.1 \div 10$
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Sign up nowFind:
(i) $7 \div 3.5$
(ii) $36 \div 0.2$
(v) $0.5 \div 0.25$
(vi) $7.75 \div 0.25$
(iii) $3.25 \div 0.5$
(iv) $30.94 \div 0.7$
(ix) $2.73 \div 1.3$
(vii) $76.5 \div 0.15$
(viii) $37.8 \div 1.4$
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Sign up nowA vehicle covers a distance of $43.2 \mathrm{~km}$ in 2.4 litres of petrol. How much distance will it cover in one litre of petrol?
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Sign up nowExtra Questions - Fractions and Decimals | NCERT | Mathematics | Class 7
Are reciprocals of each other?
A. 1 and -1 B. 1 and 0 C. -1 and 0 D. 1 and 1
The correct option is D. 1 and 1
The definition of a reciprocal is one divided by a given number. This can be mathematically expressed as: $$ \text{reciprocal of } x = \frac{1}{x} $$ Let's analyze each option:
Option A: The reciprocal of 1 is $\frac{1}{1} = 1$ and of -1 is $\frac{1}{-1} = -1$. Thus, 1 and -1 are not reciprocals of each other.
Option B: The reciprocal of 0 is undefined, as division by zero is not allowed in mathematics. Hence, 1 and 0 cannot be reciprocals.
Option C: Similarly to Option B, the reciprocal of 0 does not exist, making -1 and 0 not reciprocals.
Option D: The reciprocal of 1 is $\frac{1}{1} = 1$. Therefore, 1 is the reciprocal of itself.
Based on this analysis, option D is correct because both numbers are indeed reciprocals of each other.
Divide the sum of $65/12$ and $12/7$ by their difference.
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Sign up nowIf $x=0.\overline{18}$, which of the following statements are true? (i) $100x=18.\overline{18}$ (ii) $100x-x=17.18$ (iii) $99x=18$
A. (i) only
B. (i) and (iii)
C. (ii) only
D. (i) and (ii)
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Sign up nowEvaluate: $$ 152.55 \div 2.5 $$
(A) 61.2 (B) 61.02
(C) 61.5 (D) 610.5
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Sign up nowArrange the fractions in ascending order: $$ \frac{2}{3}, \frac{4}{5}, \frac{6}{5}, \frac{9}{8} $$
(A) $\frac{2}{3}, \frac{4}{5}, \frac{6}{5}, \frac{9}{8}$ (B) $\frac{2}{3}, \frac{4}{5}, \frac{6}{5}, \frac{9}{8}$ (C) $\frac{2}{3}, \frac{6}{5}, \frac{4}{5}, \frac{9}{8}$ (D) $\frac{6}{5}, \frac{2}{3}, \frac{4}{5}, \frac{9}{8}$
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Sign up now$\frac{1}{2} \times \left(1+\frac{1}{4}\right) \times \left(1+\frac{2}{4}\right) \times \left(1+\frac{3}{4}\right) \times \left(1+\frac{5}{4}\right)$ is equal to:
(A) $44 / 256$
(B) $948 / 255$
(C) $255 / 948$
(D) $945 / 256$
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