NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals

A fraction is a number that represents a part of a whole expressed in the form $\frac{a}{b}$ where $b\ne 0$. Decimals are yet another form of representing fractions, written using a decimal point to separate the whole number part from the fractional part. Through this chapter, students can deeply understand the methods of performing fundamental operations like addition, subtraction, multiplication, and division in fractions and decimals. The NCERT Solutions provide comprehensive step-by-step solutions to every problem in each exercise of this chapter. It is one of the useful study materials as the solutions are provided in an easily understandable manner.

Latest: NCERT Class 7 Maths: Chapterwise Important Formulas with Examples and Points

This Story also Contains

1. NCERT Solutions for Class 7 Maths Chapter 2 - Important Points
2. NCERT Solutions for Class 7 Maths Chapter 2 - Download PDF Below
3. NCERT Solutions for Class 7 Maths Fractions and Decimals (Exercise)
4. Fractions and Decimals Class 7 Maths Chapter 2-Topics
5. NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals - Points to Remember
6. NCERT Solutions for Class 7 Maths Chapter Wise
7. NCERT Solutions for Class 7 Subject-Wise

These NCERT Solutions for Class 7 Maths help students understand fundamental topics of each chapter of Class 7, which are essential in our daily life activities. These solutions are designed by subject matter experts at Careers360, They will boost the confidence of students during exam preparation as the solutions provided are clear, well-structured, and accurate.

NCERT Solutions for Class 7 Maths Chapter 2 - Important Points

Fractions:

• A fraction is written as $\frac{p}{q}$, where p is the numerator and q is the denominator.
• There are three main types of fractions: proper, improper, and mixed.
• Proper fractions have the numerator (p) smaller than the denominator (q).
• Improper fractions have the numerator (p) greater than or equal to the denominator (q).
• Mixed fractions consist of a whole number and a proper fraction.

Conversions:

• Improper fractions can be converted to mixed fractions.
• To convert an improper fraction to a mixed fraction, divide the numerator by the denominator.
• Mixed fractions can be converted to improper fractions.
• To convert a mixed fraction to an improper fraction, multiply the whole number by the denominator and add the numerator.

Operations:

• Multiplication of fractions involves multiplying the numerators and denominators.
• Division of fractions requires finding the reciprocal of the second fraction and then multiplying.
• The reciprocal of a fraction is the fraction flipped, swapping the numerator and denominator.

Addition and Subtraction:

• Adding or subtracting fractions with the same denominator is straightforward.
• When denominators differ, find the least common multiple (LCM) and then proceed.

Decimals:

• Decimals represent fractions with denominators of powers of 10.
• The decimal place value determines the value of each digit in a decimal number.
• Tenth place, hundredth place, thousandth place, etc., indicate positions after the decimal point.

Operations with Decimals:

• Multiplying decimals involves ignoring the decimal points, multiplying the numbers, and then placing the decimal point in the product.
• Dividing decimals requires moving the decimal point in the divisor and dividend to make the divisor a whole number. Then divide as usual.

Comparing Decimals:

• Start comparing decimals from the left and move towards the right.
• If digits match up to a certain place value, compare the next digit to determine which decimal is greater.

NCERT Solutions for Class 7 Maths Chapter 2 - Download PDF Below

NCERT Solutions for Class 7 Maths Fractions and Decimals (Exercise)

1. Which of the drawings (a) to (d) show :

$(i)2\times \frac{1}{5}$ $(ii)2\times \frac{1}{2}$ $(iii)3\times \frac{2}{3}$ $(iv)3\times \frac{1}{4}$

Answer:
i) (d) represents two circles with 1 part shaded out of 5 parts So, it represents

$2\times \frac{1}{5}$ .

ii) b represents two squares one part out of two of both squares is shaded, So it represents

$2\times \frac{1}{2}$

(iii) (a) represents 3 circles 2 parts out of three of all circles are shaded. So it represents $3\times \frac{2}{3}$

(iv) (c) represents 3 squares with one part out of four, shaded in each square hence it represents $3\times \frac{1}{4}$.

2. Some pictures (a) to (c) are given below. Tell which of them show:

$(i)3\times \frac{1}{5}=\frac{3}{5}$ $(ii)2\times \frac{1}{3}=\frac{2}{3}$ $(iii)3\times \frac{3}{4}=2\frac{1}{4}$

Answer:$(i)3\times \frac{1}{5}=\frac{3}{5}$

As in option (c), On the left-hand side, there are three figures in which one part out of three parts is shaded and on the right-hand side, three out of five portions are shaded.

Hence this represents

$3\times \frac{1}{5}=\frac{3}{5}$ .

$(ii)2\times \frac{1}{3}=\frac{2}{3}$

Option (a) represents the equation pictorially.

$(iii)3\times \frac{3}{4}=2\frac{1}{4}$

Option (b) represents this equation pictorially.

3. Multiply and reduce to the lowest form and convert into a mixed fraction:

$(i)7\times \frac{3}{5}$ $(ii)4\times \frac{1}{3}$ $(iii)2\times \frac{6}{7}$ $(iv)5\times \frac{2}{9}$ $(v)\frac{2}{3}\times 4$

$(vi)\frac{5}{2}\times 6$ $(vii)11\times \frac{4}{7}$ $(viii)20\times \frac{4}{5}$ $(ix)13\times \frac{1}{3}$ $(x)15\times \frac{3}{5}$

Answer: $(i)7\times \frac{3}{5}$

On Multiplying, we get

$\Rightarrow \frac{7\times 3}{5}=\frac{21}{5}=\frac{20+1}{5}=\frac{20}{5}+\frac{1}{5}=4+\frac{1}{5}=4\frac{1}{5}$

$(ii)4\times \frac{1}{3}$

On Multiplying, we get

$\Rightarrow \frac{4\times 1}{3}=\frac{4}{3}=\frac{3+1}{3}=\frac{3}{3}+\frac{1}{3}=1+\frac{1}{3}=1\frac{1}{3}$

$(iii)2\times \frac{6}{7}$

On Multiplying, we get

$\Rightarrow \frac{2\times 6}{7}=\frac{12}{7}=\frac{7+5}{7}=\frac{7}{7}+\frac{5}{7}=1+\frac{5}{7}=1\frac{5}{7}$

$(iv)5\times \frac{2}{9}$

On Multiplying, we get

$\Rightarrow \frac{5\times 2}{9}=\frac{10}{9}=\frac{9+1}{9}=\frac{9}{9}+\frac{1}{9}=1+\frac{1}{9}=1\frac{1}{9}$

$(v)\frac{2}{3}\times 4$

On Multiplying, we get

$\Rightarrow \frac{2\times 4}{3}=\frac{8}{3}=\frac{6+2}{3}=\frac{6}{3}+\frac{2}{3}=2+\frac{2}{3}=2\frac{2}{3}$

$(vi)\frac{5}{2}\times 6$

On Multiplying, we get

$\Rightarrow \frac{5\times 6}{2}=\frac{30}{2}=15$

$(vii)11\times \frac{4}{7}$

On Multiplying, we get

$\Rightarrow \frac{11\times 4}{7}=\frac{44}{7}$

Converting this into a mixed fraction, we get

$\Rightarrow \frac{44}{7}=\frac{42+2}{7}=\frac{42}{7}+\frac{2}{7}=6+\frac{2}{7}=6\frac{2}{7}.$

$(viii)20\times \frac{4}{5}$

On Multiplying, we get

$\Rightarrow \frac{20\times 4}{5}=\frac{80}{5}=16$

$(ix)13\times \frac{1}{3}$

On multiplying, we get

$\Rightarrow \frac{13\times 1}{3}=\frac{13}{3}$

Converting this into a mixed fraction,

$\Rightarrow \frac{13}{3}=\frac{12+1}{3}=\frac{12}{3}+\frac{1}{3}=4+\frac{1}{3}=4\frac{1}{3}$ .

$(x)15\times \frac{3}{5}$

On multiplying, we get,

$\Rightarrow \frac{15\times 3}{5}=\frac{45}{5}=9$ .

4. Shade:

$(i)\frac{1}{2}$ 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).

Answer: 1) In Figure (a) there are 12 circles: half of 12 = 6

2) In Figure (b) there are 9 triangles: 2/3 of 9 = 6

3) In Figure (c) there are 15 triangles: 3/5 of 15 = 9

5. Find:

$(a)\frac{1}{2}of(i)24(ii)46$ $(b)\frac{2}{3}of(i)18(ii)27$

$(c)\frac{3}{4}of(i)16(ii)36$ $(d)\frac{4}{5}of(i)20(ii)35$

Answer: $(a)(i)\frac{1}{2}of24$

On Multiplying we get,

$\frac{1}{2}of24=\frac{1}{2}\times 24=\frac{1\times 24}{2}=12$

$(a)ii)\frac{1}{2}of46$

On multiplying, we get

$\Rightarrow \frac{1}{2}of46=\frac{1}{2}\times 46=\frac{1\times 46}{2}=23.$

$(b)(i)\frac{2}{3}of18$

On Multiplying, we get

$\Rightarrow \frac{2}{3}of18=\frac{2}{3}\times 18=\frac{2\times 18}{3}=\frac{36}{3}=12.$

$(b)(ii)\frac{2}{3}of27$

On multiplying, we get

$\Rightarrow \frac{2}{3}of27=\frac{2}{3}\times 27=\frac{2\times 27}{3}=\frac{54}{3}=18$

$(c)(i)\frac{3}{4}of16$

On multiplying, we get

$\Rightarrow \frac{3}{4}of16=\frac{3}{4}\times 16=\frac{3\times 16}{4}=\frac{48}{4}=12.$

$(c)(ii)\frac{3}{4}of36$

$\Rightarrow \frac{3}{4}of36=\frac{3}{4}\times 36=\frac{3\times 36}{4}=\frac{108}{4}=27$

$(d)(i)\frac{4}{5}of20$

On multiplying, we get

$\frac{4}{5}of20=\frac{4}{5}\times 20=\frac{4\times 20}{5}=\frac{80}{5}=16$

$(d)(ii)\frac{4}{5}of35$

On Multiplying, we get,

$\frac{4}{5}of35=\frac{4}{5}\times 35=\frac{4\times 35}{5}=\frac{140}{4}=28$

6. Multiply and express as a mixed fraction :

$(a)3\times 5\frac{1}{5}$ $(b)5\times 6\frac{3}{4}$ $(c)7\times 2\frac{1}{4}$

$(d)4\times 6\frac{1}{3}$ $(e)3\frac{1}{4}\times 6$ $(f)3\frac{2}{5}\times 8$

Answer: $(a)3\times 5\frac{1}{5}$

On multiplying, we get

$\Rightarrow 3\times \frac{5\times 5+1}{5}=3\times \frac{26}{5}=\frac{3\times 26}{5}=\frac{78}{5}$

Converting this into Mixed Fractions,

$\Rightarrow \frac{78}{5}=\frac{75+3}{5}=\frac{75}{5}+\frac{3}{5}=15+\frac{3}{5}=15\frac{3}{5}$

$(b)5\times 6\frac{3}{4}$

On multiplying, we get

$\Rightarrow 5\times \frac{6\times 4+3}{4}=5\times \frac{27}{4}=\frac{5\times 27}{4}=\frac{135}{4}$

Converting this into Mixed Fractions,

$\Rightarrow \frac{135}{4}=\frac{132+3}{4}=\frac{132}{4}+\frac{3}{4}=33+\frac{3}{4}=33\frac{3}{4}$

$(c)7\times 2\frac{1}{4}$

On multiplying, we get

$7\times 2\frac{1}{4}=7\times \frac{4\times 2+1}{4}=7\times \frac{9}{4}=\frac{7\times 9}{4}=\frac{63}{4}$

Converting it into a mixed fraction, we get

$\frac{63}{4}=\frac{60+3}{4}=\frac{60}{4}+\frac{3}{4}=15+\frac{3}{4}=15\frac{3}{4}$

$(d)4\times 6\frac{1}{3}$

On multiplying, we get

$4\times 6\frac{1}{3}=4\times \frac{3\times 6+1}{3}=4\times \frac{19}{3}=\frac{4\times 19}{3}=\frac{76}{3}$

Converting it into a mixed fraction,

$\frac{76}{3}=\frac{75+1}{3}=\frac{75}{3}+\frac{1}{3}=25+\frac{1}{3}=25\frac{1}{3}$

$(e)3\frac{1}{4}\times 6$

Multiplying them, we get

$3\frac{1}{4}\times 6=\frac{4\times 3+1}{4}\times 6=\frac{13}{4}\times 6=\frac{13\times 6}{4}=\frac{78}{4}$

Now, converting the result fraction we got to mixed fraction,

$\frac{78}{4}=\frac{76+2}{4}=\frac{76}{4}+\frac{2}{4}=19+\frac{1}{2}=19\frac{1}{2}$

$(f)3\frac{2}{5}\times 8$

On multiplying, we get

$3\frac{2}{5}\times 8=\frac{5\times 3+2}{5}\times 8=\frac{17}{5}\times 8=\frac{17\times 8}{5}=\frac{136}{5}$

Converting this into a mixed fraction, we get

$\frac{136}{5}=\frac{135+1}{5}=\frac{135}{5}+\frac{1}{5}=27+\frac{1}{5}=27\frac{1}{5}$

7. Find:

$(a)\frac{1}{2}of(i)2\frac{3}{4}(ii)4\frac{2}{9}$ $(b)\frac{5}{8}of(i)3\frac{5}{6}(ii)9\frac{2}{3}$

Answer: $(a)(i)\frac{1}{2}of2\frac{3}{4}$

As we know that, of is equivalent to multiplying,

$\frac{1}{2}of2\frac{3}{4}=\frac{1}{2}\times 2\frac{3}{4}=\frac{1}{2}\times \frac{11}{4}=\frac{11}{8}=1\frac{3}{8}$

$(a)(ii)\frac{1}{2}of4\frac{2}{9}$

As we know that, of is equivalent to multiplying,

$\frac{1}{2}of4\frac{2}{9}=\frac{1}{2}\times 4\frac{2}{9}=\frac{1}{2}\times \frac{38}{9}=\frac{38}{18}=\frac{19}{9}=2\frac{1}{9}$

$(b)(i)\frac{5}{8}of3\frac{5}{6}$

As we know that, of is equivalent to multiplying,

$\frac{5}{8}of3\frac{5}{6}=\frac{5}{8}\times 3\frac{5}{6}=\frac{5}{8}\times \frac{23}{6}=\frac{115}{48}=2\frac{19}{48}$

$(b)(ii)\frac{5}{8}of9\frac{2}{3}$

As we know that, of is equivalent to multiplying,

$\frac{5}{8}of9\frac{2}{3}=\frac{5}{8}\times \frac{29}{3}=\frac{145}{24}=6\frac{1}{24}$

8. Vidya 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?

Answer: Given

Total water = 5 litre.

i) The amount of water vidya consumed :

$=\frac{2}{5}of5litre=\frac{2}{5}\times 5=2litre$

Hence Vidya consumed 2 litres of water from the bottle.

ii) The amount of water Pratap consumed :

$=(1-\frac{2}{5})of5litre=\frac{3}{5}\times 5=3litre$

Hence, Pratap consumed 3 litres of water from the bottle.

1. Find:

$(i)\frac{1}{4}of(a)\frac{1}{4}(b)\frac{3}{5}(c)\frac{4}{3}$

$(ii)\frac{1}{7}of(a)\frac{2}{9}(b)\frac{6}{5}(c)\frac{3}{10}$

Answer: As we know, the term "of " means multiplication. So,

$(i)(a)\frac{1}{4}of\frac{1}{4}=\frac{1}{4}\times \frac{1}{4}=\frac{1}{16}$

$(i)(b)\frac{1}{4}of\frac{3}{5}=\frac{1}{4}\times \frac{3}{5}=\frac{3}{20}$

$(i)(c)\frac{1}{4}of\frac{4}{3}=\frac{1}{4}\times \frac{4}{3}=\frac{4}{12}=\frac{1}{3}$

$(ii)(a)\frac{1}{7}of\frac{2}{9}=\frac{1}{7}\times \frac{2}{9}=\frac{2}{63}$

$(ii)(b)\frac{1}{7}of\frac{6}{5}=\frac{1}{7}\times \frac{6}{5}=\frac{6}{35}$

$(ii)(c)\frac{1}{7}of\frac{3}{10}=\frac{1}{7}\times \frac{3}{10}=\frac{3}{70}$

2. Multiply and reduce to lowest form (if possible) :

$(i)\frac{2}{3}\times 2\frac{2}{3}(ii)\frac{2}{7}\times \frac{7}{9}(iii)\frac{3}{8}\times \frac{6}{4}$

$(iv)\frac{9}{5}\times \frac{3}{5}(v)\frac{1}{3}\times \frac{15}{8}(vi)\frac{11}{2}\times \frac{3}{10}(vii)\frac{4}{5}\times \frac{12}{7}$

Answer: As we know, in the multiplication of fractions, the numerator gets multiplied by the numerator and the denominator gets multiplied by the denominator. So,

$(i)\frac{2}{3}\times 2\frac{2}{3}=\frac{2}{3}\times \frac{8}{3}=\frac{2\times 8}{3\times 3}=\frac{16}{9}=1\frac{7}{9}$

$(ii)\frac{2}{7}\times \frac{7}{9}=\frac{2\times 7}{7\times 9}=\frac{2}{9}$

$(iii)\frac{3}{8}\times \frac{6}{4}=\frac{3\times 6}{8\times 4}=\frac{18}{32}=\frac{9}{16}$

$(iv)\frac{9}{5}\times \frac{3}{5}=\frac{9\times 3}{5\times 5}=\frac{27}{25}=1\frac{2}{25}$

$(v)\frac{1}{3}\times \frac{15}{8}=\frac{1\times 15}{3\times 8}=\frac{15}{24}=\frac{5}{8}$

$(vi)\frac{11}{2}\times \frac{3}{10}=\frac{11\times 3}{2\times 10}=\frac{33}{20}=1\frac{13}{20}$

$(vii)\frac{4}{5}\times \frac{12}{7}=\frac{4\times 12}{5\times 7}=\frac{48}{35}=1\frac{13}{35}$ .

3. Multiply the following fractions:

$(i)\frac{2}{5}\times 5\frac{1}{4}(ii)6\frac{2}{5}\times \frac{7}{9}(iii)\frac{3}{2}\times 5\frac{1}{3}$
$(iv)\frac{5}{6}\times 2\frac{3}{7}(v)3\frac{2}{5}\times \frac{4}{7}(vi)2\frac{3}{5}\times 3(vii)3\frac{4}{7}\times \frac{3}{5}$

Answer: As we know in the multiplication of fractions, the numerator is multiplied by the numerator and the denominator is multiplied by the denominator.

$(i)\frac{2}{5}\times 5\frac{1}{4}=\frac{2}{5}\times \frac{21}{4}=\frac{2\times 21}{5\times 4}=\frac{42}{20}=\frac{21}{10}=2\frac{1}{10}$

$(ii)6\frac{2}{5}\times \frac{7}{9}=\frac{32}{5}\times \frac{7}{9}=\frac{32\times 7}{5\times 9}=\frac{224}{45}=4\frac{44}{45}$

$(iii)\frac{3}{2}\times 5\frac{1}{3}=\frac{3}{2}\times \frac{16}{3}=\frac{3\times 16}{2\times 3}=\frac{48}{6}=8$

$(iv)\frac{5}{6}\times 2\frac{3}{7}=\frac{5}{6}\times \frac{17}{7}=\frac{5\times 17}{6\times 7}=\frac{85}{42}=2\frac{1}{42}$

$(v)3\frac{2}{5}\times \frac{4}{7}=\frac{17}{5}\times \frac{4}{7}=\frac{17\times 4}{5\times 7}=\frac{68}{35}=1\frac{33}{35}$

$(vi)2\frac{3}{5}\times 3=\frac{13}{5}\times 3=\frac{13\times 3}{5}=\frac{39}{5}=7\frac{4}{5}$

$(vii)3\frac{4}{7}\times \frac{3}{5}=\frac{25}{7}\times \frac{3}{5}=\frac{25\times 3}{7\times 5}=\frac{75}{35}=\frac{15}{7}=2\frac{1}{7}$

4. Which is greater:

$(i)\frac{2}{7}of\frac{3}{4}or\frac{3}{5}of\frac{5}{8}$

$(ii)\frac{1}{2}of\frac{6}{7}or\frac{2}{3}of\frac{3}{7}$

Answer: $(i)\frac{2}{7}of\frac{3}{4}or\frac{3}{5}of\frac{5}{8}$

$\Rightarrow \frac{2}{7}\times \frac{3}{4}or\frac{3}{5}\times \frac{5}{8}$

$\Rightarrow \frac{2\times 3}{7\times 4}or\frac{3\times 5}{5\times 8}$

$\Rightarrow \frac{3}{14}or\frac{3}{8}$

Now, As we Know, When the numerator of two fractions is the same the fraction with a lesser denominator is the bigger fraction. So,

$\Rightarrow \frac{3}{14}<\frac{3}{8}$

Thus,

$\frac{2}{7}of\frac{3}{4}<\frac{3}{5}of\frac{5}{8}$ .

$(ii)\frac{1}{2}of\frac{6}{7}or\frac{2}{3}of\frac{3}{7}$

$\Rightarrow \frac{1}{2}\times \frac{6}{7}or\frac{2}{3}\times \frac{3}{7}$

$\Rightarrow \frac{1\times 6}{2\times 7}or\frac{2\times 3}{3\times 7}$

$\Rightarrow \frac{3}{7}or\frac{2}{7}$

As we know, When the denominator of two fractions is the same, the fraction with the bigger numerator is the bigger fraction, so,

$\Rightarrow \frac{3}{7}>\frac{2}{7}$

Thus,

$\frac{1}{2}\times \frac{6}{7}>\frac{2}{3}\times \frac{3}{7}$ .

5. Saili plants 4 saplings, in a row, in her garden. The distance between two adjacent saplings is $\frac{3}{4}m$. Find the distance between the first and the last sapling.

Answer: distance between two adjacent saplings = $\frac{3}{4}m$

distance between the first and the last sapling :

$=3\times \frac{3}{4}$

$=\frac{3\times 3}{4}$

$=\frac{9}{4}$ .

6. Lipika 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?

Answer: Number of time spent in one day = $1\frac{3}{4}$ hour

The number of time spent in 6 days :

$=6\times 1\frac{3}{4}=6\times \frac{7}{4}=\frac{6\times 7}{4}=\frac{42}{4}=\frac{21}{2}=10\frac{1}{2}hours$

Hence $10\frac{1}{2}hours$ are required by Lipika to complete the book.

7. A car runs 16 km using 1 litre of petrol. How much distance will it cover using $2\frac{3}{4}$ litres of petrol?

Answer: Distance covered in 1-litre petrol = 16 km

The distance that will be covered in $2\frac{3}{4}$ litre petrol.

$=16\times 2\frac{3}{4}$

$=16\times \frac{11}{4}$

$=\frac{11\times 16}{4}$

$=11\times 4$

$=44km$

Hence 44 km can be covered using $2\frac{3}{4}$ litre petrol.

8. (a) (i) Provide the number in the box , such that $\frac{2}{3}\times$ = $\frac{10}{30}$.

(ii) The simplest form of the number obtained is _________.

(b) (i) Provide the number in the box , such that $\frac{3}{5}\times$ = $\frac{24}{75}$.

(ii) The simplest form of the number obtained in is _________.

Answer: As we know, in the multiplication of fractions, the numerator of both fractions is multiplied to give the numerator of the new fraction, and the denominator of both fractions is multiplied to give the denominator of the answer fraction. So,

$\frac{2}{3}\times$ = $\frac{10}{30}$ .

We have to multiply 5 with 2 in the numerator to get 10 and 10 with 3 in the denominator to get 30. So,

$\Rightarrow \frac{2}{3}\times \frac{5}{10}=\frac{10}{30}$

The Simplest Form :

$\Rightarrow \frac{5}{10}=\frac{1}{2}$ .

1. Find:

$(i)12÷\frac{3}{4}$ $(ii)14÷\frac{5}{6}$ $(iii)8÷\frac{7}{3}$ $(iv)4÷\frac{8}{3}$ $(v)3÷2\frac{1}{3}$ $(vi)5÷3\frac{4}{7}$

Answer: As we know, The division of a number by a / b is equivalent to the multiplication of that number with b / a. So,

$(i)12÷\frac{3}{4}$

$\Rightarrow 12÷\frac{3}{4}=12\times \frac{4}{3}=\frac{48}{3}=16$

$(ii)14÷\frac{5}{6}$

$\Rightarrow 14÷\frac{5}{6}=14\times \frac{6}{5}=\frac{84}{5}=16\frac{4}{5}$

$(iii)8÷\frac{7}{3}$

$\Rightarrow 8÷\frac{7}{3}=8\times \frac{3}{7}=\frac{24}{7}=3\frac{3}{7}$

$(iv)4÷\frac{8}{3}$

$\Rightarrow 4÷\frac{8}{3}=4\times \frac{3}{8}=\frac{12}{8}=\frac{3}{2}=1\frac{1}{2}$

$(v)3÷2\frac{1}{3}$

$\Rightarrow 3÷2\frac{1}{3}=3÷\frac{7}{3}=3\times \frac{3}{7}=\frac{9}{7}=1\frac{2}{7}$

$(vi)5÷3\frac{4}{7}$

$\Rightarrow 5÷3\frac{4}{7}=5÷\frac{25}{7}=5\times \frac{7}{25}=\frac{35}{25}=\frac{7}{5}=1\frac{2}{5}$

2. Find the reciprocal of each of the following fractions. Classify the reciprocals as proper fractions, improper fractions and whole numbers.

$(i)\frac{3}{7}$ $(ii)\frac{5}{8}$ $(iii)\frac{9}{7}$ $(iv)\frac{6}{5}$ $(v)\frac{12}{7}$ $(vi)\frac{1}{8}$ $(vii)\frac{1}{11}$

Answer: As we know, in the reciprocal of any fraction, the numerator and denominator get exchanged. Basically, we flip the number upside down. So

$i)Reciprocalof\frac{3}{7}=\frac{7}{3}$

As the numerator is greater than the denominator, it is an improper fraction.

$ii)Reciprocalof\frac{5}{8}=\frac{8}{5}$

As the numerator is greater than the denominator, it is an improper fraction.

$iii)Reciprocalof\frac{9}{7}=\frac{7}{9}$

As the denominator is greater than the numerator, it is a proper fraction.

$iv)Reciprocalof\frac{6}{5}=\frac{5}{6}$

As the denominator is greater than the numerator, it is a proper fraction.

$v)Reciprocalof\frac{12}{7}=\frac{7}{12}$

As the denominator is greater than the numerator, it is a proper fraction.

$vi)Reciprocalof\frac{1}{8}=\frac{8}{1}=8$

It is an integer and hence a whole number.

$vii)Reciprocalof\frac{1}{11}=\frac{11}{1}=11$

It is an integer and hence a whole number.

3. Find:

$(i)\frac{7}{3}÷2$ $(ii)\frac{4}{9}÷5$ $(iii)\frac{6}{13}÷7$ $(iv)4\frac{1}{3}÷3$

$(v)3\frac{1}{2}÷4$ $(vi)4\frac{3}{7}÷7$

Answer: As we know, The division of a number by a / b is equivalent to the multiplication of that number with b / a which is also called the reciprocal of a / b. So,

$(i)\frac{7}{3}÷2$

$\Rightarrow \frac{7}{3}÷2=\frac{7}{3}\times \frac{1}{2}=\frac{7}{6}=1\frac{1}{6}$

$(ii)\frac{4}{9}÷5$

$\Rightarrow \frac{4}{9}÷5=\frac{4}{9}\times \frac{1}{5}=\frac{4}{45}$

$(iii)\frac{6}{13}÷7$

$\Rightarrow \frac{6}{13}÷7=\frac{6}{13}\times \frac{1}{7}=\frac{6}{91}$

$(iv)4\frac{1}{3}÷3$

$\Rightarrow 4\frac{1}{3}÷3=\frac{13}{3}÷3=\frac{13}{3}\times \frac{1}{3}=\frac{13}{9}=1\frac{4}{9}$

$(v)3\frac{1}{2}÷4$

$\Rightarrow 3\frac{1}{2}÷4=\frac{7}{2}÷4=\frac{7}{2}\times \frac{1}{4}=\frac{7}{8}$

$(vi)4\frac{3}{7}÷7$

$\Rightarrow 4\frac{3}{7}÷7=\frac{31}{7}÷7=\frac{31}{7}\times \frac{1}{7}=\frac{31}{49}$

4. Find:

$(i)\frac{2}{5}÷\frac{1}{2}$ $(ii)\frac{4}{9}÷\frac{2}{3}$ $(iii)\frac{3}{7}÷\frac{8}{7}$ $(iv)2\frac{1}{3}÷\frac{3}{5}$ $(v)3\frac{1}{2}÷\frac{8}{3}$ $(vi)\frac{2}{5}÷1\frac{1}{2}$ $(vii)3\frac{1}{5}÷1\frac{2}{3}$ $(viii)2\frac{1}{5}÷1\frac{1}{5}$

Answer: As we know, The division of a number by a / b is equivalent to the multiplication of that number with b / a which is also called the reciprocal of a / b. So,

$(i)\frac{2}{5}÷\frac{1}{2}$

$\Rightarrow \frac{2}{5}÷\frac{1}{2}=\frac{2}{5}\times \frac{2}{1}=\frac{4}{5}$

$(ii)\frac{4}{9}÷\frac{2}{3}$

$\Rightarrow \frac{4}{9}÷\frac{2}{3}=\frac{4}{9}\times \frac{3}{2}=\frac{12}{18}=\frac{2}{3}$

$(iii)\frac{3}{7}÷\frac{8}{7}$

$\Rightarrow \frac{3}{7}÷\frac{8}{7}=\frac{3}{7}\times \frac{7}{8}=\frac{3}{8}$

$(iv)2\frac{1}{3}÷\frac{3}{5}$

$\Rightarrow 2\frac{1}{3}÷\frac{3}{5}=\frac{7}{3}÷\frac{3}{5}=\frac{7}{3}\times \frac{5}{3}=\frac{35}{9}=3\frac{8}{9}$

$(v)3\frac{1}{2}÷\frac{8}{3}$

$3\frac{1}{2}÷\frac{8}{3}=\frac{7}{2}÷\frac{8}{3}=\frac{7}{2}\times \frac{3}{8}=\frac{21}{16}=1\frac{5}{16}$

$(vi)\frac{2}{5}÷1\frac{1}{2}$

$\Rightarrow \frac{2}{5}÷1\frac{1}{2}=\frac{2}{5}÷\frac{3}{2}=\frac{2}{5}\times \frac{2}{3}=\frac{4}{15}$

$(vii)3\frac{1}{5}÷1\frac{2}{3}$

$\Rightarrow 3\frac{1}{5}÷1\frac{2}{3}=\frac{16}{5}÷\frac{5}{3}=\frac{16}{5}\times \frac{3}{5}=\frac{48}{25}=1\frac{23}{25}$

$(viii)2\frac{1}{5}÷1\frac{1}{5}$

$\Rightarrow 2\frac{1}{5}÷1\frac{1}{5}=\frac{11}{5}÷\frac{6}{5}=\frac{11}{5}\times \frac{5}{6}=\frac{11}{6}=1\frac{5}{6}$

1. Find:

(i) 0.2 × 6 (ii) 8 × 4.6 (iii) 2.71 × 5 (iv) 20.1 × 4

(v) 0.05 × 7 (vi) 211.02 × 4 (vii) 2 × 0.86

Answer: As we know, The multiplication of the decimal number is just like the multiplication of a normal number, we just have to put a decimal before a digit such that the number of digits after the decimal should remain the same.

In other words,

The number of digits after the decimal should be the same before and after the multiplication.

So.

(i) 0.2 × 6 = 1.2

(ii) 8 × 4.6 = 36.8

(iii) 2.71 × 5 = 13.55

(iv) 20.1 × 4 = 80.4

(v) 0.05 × 7 = 0.35

(vi) 211.02 × 4 = 844.08

(vii) 2 × 0.86 = 1.72

2. Find the area of a rectangle whose length is 5.7cm and breadth is 3 cm.

Answer: Given the length of the rectangle = 5.7 cm.

Width of rectangle = 3 cm

Area of the rectangle = Length x width

= 5.7 x 3

= 17.1 $c{m}^2$ .

Hence Area of the rectangle is 17.1 $c{m}^2$.

3. Find:

(i) 1.3 × 10 (ii) 36.8 × 10 (iii) 153.7 × 10 (iv) 168.07 × 10

(v) 31.1 × 100 (vi) 156.1 × 100 (vii) 3.62 × 100 (viii) 43.07 × 100

(ix) 0.5 × 10 (x) 0.08 × 10 (xi) 0.9 × 100 (xii) 0.03 × 1000

Answer: As we know, The multiplication of the decimal number is just like the multiplication of a normal number, we just have to put a decimal before a digit such that the number of digits after the decimal should remain the same.

In other words,

The number of digits after the decimal should be the same before and after the multiplication.

So.

(i) 1.3 × 10 = 13

(ii) 36.8 × 10 = 368

(iii) 153.7 × 10 = 1537

(iv) 168.07 × 10 = 1680.7

(v) 31.1 × 100 = 3110

(vi) 156.1 × 100 =15610

(vii) 3.62 × 100 = 362

(viii) 43.07 × 100 = 4307

(ix) 0.5 × 10 = 5

(x) 0.08 × 10 = 0.8

(xi) 0.9 × 100 = 90

(xii) 0.03 × 1000 =30

4. A two-wheeler covers a distance of 55.3 km in one litre of petrol. How much distance will it cover in 10 litres of petrol?

Answer: Distance covered by two-wheeler in 1 litre of petrol = 55.3 km.

Distance two-wheeler will cover in 10 litres of petrol = 10 x 55.3 km

= 553 km

Hence two-wheeler will cover a distance of 553 km in 10 litres of petrol.

5. Find:

(i) 2.5 × 0.3 (ii) 0.1 × 51.7 (iii) 0.2 × 316.8 (iv) 1.3 × 3.1 (v) 0.5 × 0.05 (vi) 11.2 × 0.15 (vii) 1.07 × 0.02

(viii) 10.05 × 1.05 (ix) 101.01 × 0.01 (x) 100.01 × 1.1

Answer: As we know, The multiplication of the decimal number is just like the multiplication of a normal number, we just have to put a decimal before a digit such that the number of digits after the decimal should remain the same.

In other words,

The number of digits after the decimal should be the same before and after the multiplication.

So,

(i) 2.5 × 0.3 = 0.75

(ii) 0.1 × 51.7 = 5.17

(iii) 0.2 × 316.8 = 63.36

(iv) 1.3 × 3.1 = 4.03

(v) 0.5 × 0.05 = 0.025

(vi) 11.2 × 0.15 = 1.680

(vii) 1.07 × 0.02 = 0.0214

(viii) 10.05 × 1.05 = 10.5525

(ix) 101.01 × 0.01 = 1.0101

(x) 100.01 × 1.1 = 110.11

1. Find:

$(i)0.4÷2$ $(ii)0.35÷5$ $(iii)2.48÷4$ $(iv)65.4÷6$

$(v)651.2÷4$ $(vi)14.49÷7$ $(vii)3.96÷4$ $(viii)0.80÷5$

Answer: As we know, while dividing decimals, we first express the decimal in terms of fractions and then divide it,

Dividing by a number is equivalent to multiplying by the reciprocal of that number. So

$(i)0.4÷2$

$0.4÷2=\frac{4}{10}÷2=\frac{4}{10}\times \frac{1}{2}=\frac{2}{10}=\frac{1}{5}$

$(ii)0.35÷5$

$0.35÷5=\frac{35}{100}÷5=\frac{35}{100}\times \frac{1}{5}=\frac{7}{100}=0.07$

$(iii)2.48÷4$

$2.48÷4=\frac{248}{100}÷4=\frac{248}{100}\times \frac{1}{4}=\frac{62}{100}=0.62$

$(iv)65.4÷6$

$65.4÷6=\frac{654}{100}÷6=\frac{654}{100}\times \frac{1}{6}=\frac{109}{100}=1.09$