NCERT Solutions for Class 7 Maths Chapter 2 Fractions and Decimals

2. Arrange the following fractions in descending order

(i) 2/9, 2/3, 8/21

LCM of 9, 3 and 21 = 63.

29=1463\frac{2}{9}=\frac{14}{63} 23=4263\frac{2}{3}=\frac{42}{63} 821=2463\frac{8}{21}=\frac{24}{63}

Therefore,

4263>2463>1463\frac{42}{63}>\frac{24}{63}>\frac{14}{63}

Answer: 2/3, 8/21, 2/9

(ii) 1/5, 3/7, 7/10

LCM of 5, 7 and 10 = 70.

15=1470\frac{1}{5}=\frac{14}{70} 37=3070\frac{3}{7}=\frac{30}{70} 710=4970\frac{7}{10}=\frac{49}{70}

Answer: 7/10, 3/7, 1/5

3. Is the following a magic square?

The sum of each row is:

1511\frac{15}{11}

The sum of each column is also:

1511\frac{15}{11}

Both diagonals also have the sum:

1511\frac{15}{11}

Answer: Yes, it is a magic square because all rows, columns and diagonals have the same sum.

4. Find the perimeter of the rectangular sheet

Length:

1212=252 cm12\frac{1}{2}=\frac{25}{2}\text{ cm}

Breadth:

1023=323 cm10\frac{2}{3}=\frac{32}{3}\text{ cm}

Perimeter of a rectangle:

P=2(l+b)P=2(l+b) =2(252+323)=2\left(\frac{25}{2}+\frac{32}{3}\right)

LCM of 2 and 3 = 6.

=2(75+646)=2\left(\frac{75+64}{6}\right) =2×1396=1393=2\times\frac{139}{6} =\frac{139}{3}

Answer: 139/3 cm or 46 1/3 cm

5. Find the perimeters of triangle ABE and rectangle BCDE

Given:

• AB = 5/2 cm

• AE = 18/5 cm

• BE = 11/4 cm

• ED = 7/6 cm

(i) Perimeter of triangle ABE

P=52+114+185P=\frac{5}{2}+\frac{11}{4}+\frac{18}{5}

LCM of 2, 4 and 5 = 20.

=50+55+7220=17720 cm=\frac{50+55+72}{20} =\frac{177}{20}\text{ cm}

(ii) Perimeter of rectangle BCDE

P=2(BE+ED)P=2(BE+ED) =2(114+76)=2\left(\frac{11}{4}+\frac{7}{6}\right)

LCM of 4 and 6 = 12.

=2(33+1412)=476 cm=2\left(\frac{33+14}{12}\right) =\frac{47}{6}\text{ cm}

Comparing:

17720=53160\frac{177}{20}=\frac{531}{60} 476=47060\frac{47}{6}=\frac{470}{60}

Therefore,

17720>476\frac{177}{20}>\frac{47}{6}

Answer: The perimeter of triangle ABE is greater.

Students can practise fractions, numerators, denominators, and other maths concepts through interactive learning resources on CuriousJr.

6. How much should the picture be trimmed?

Width of picture:

735=385 cm7\frac{3}{5}=\frac{38}{5}\text{ cm}

Maximum frame width:

7310=7310 cm7\frac{3}{10}=\frac{73}{10}\text{ cm}

Required trimming:

385−7310\frac{38}{5}-\frac{73}{10} =7610−7310=310=\frac{76}{10}-\frac{73}{10} =\frac{3}{10}

Answer: 3/10 cm

7. Ritu ate 3/5 of an apple. What part did Somu eat?

Ritu ate:

35\frac{3}{5}

Remaining part:

1−35=55−35=251-\frac{3}{5} =\frac{5}{5}-\frac{3}{5} =\frac{2}{5}

So, Somu ate 2/5 of the apple.

Difference between their shares:

35−25=15\frac{3}{5}-\frac{2}{5} =\frac{1}{5}

Answer: Ritu ate the larger share by 1/5.

8. Who worked longer?

Michael took:

712 hour\frac{7}{12}\text{ hour}

Vaibhav took:

34=912 hour\frac{3}{4}=\frac{9}{12}\text{ hour}

Since:

912>712\frac{9}{12}>\frac{7}{12}

Vaibhav worked longer.

Difference:

912−712=212=16\frac{9}{12}-\frac{7}{12} =\frac{2}{12} =\frac{1}{6}

Answer: Vaibhav worked longer by 1/6 hour.

Exercise 2.2

1. Which drawings represent the following?

(i) 2 × 1/5

It represents two groups of 1/5.

Answer: Figure (d)

(ii) 2 × 1/2

It represents two groups of 1/2.

Answer: Figure (b)

(iii) 3 × 2/3

It represents three groups of 2/3.

Answer: Figure (a)

(iv) 3 × 1/4

It represents three groups of 1/4.

Answer: Figure (c)

2. Identify the drawings

(i) 3 × 1/5 = 3/5

Answer: Figure (c)

(ii) 2 × 1/3 = 2/3

Answer: Figure (a)

(iii) 3 × 3/4 = 2 1/4

Answer: Figure (b)

3. Multiply and reduce to the lowest form

Multiplication of Fractions

To multiply fractions:

ab×cd=a×cb×d\frac{a}{b}\times\frac{c}{d} =\frac{a\times c}{b\times d}

For example:

23×45=815\frac{2}{3}\times\frac{4}{5} =\frac{8}{15}

Before multiplying, common factors can also be cancelled to simplify the calculation.

4. Find the fraction of the given numbers

For questions involving “of”, multiplication is used.

For example:

17 of 29=17×29=263\frac{1}{7}\text{ of }\frac{2}{9} =\frac{1}{7}\times\frac{2}{9} =\frac{2}{63}

Similarly:

17 of 65=635\frac{1}{7}\text{ of }\frac{6}{5} =\frac{6}{35}

and

17 of 310=370\frac{1}{7}\text{ of }\frac{3}{10} =\frac{3}{70}

Check: Integers: Definition, Types, Rules, Properties and Examples

5. Multiply and reduce to the lowest form

(i) 2/3 × 2 2/3

Convert the mixed fraction:

223=832\frac{2}{3}=\frac{8}{3}

Therefore,

23×83=169\frac{2}{3}\times\frac{8}{3} =\frac{16}{9}

Answer: 16/9 or 1 7/9

(ii) 2/7 × 7/9

27×79=29\frac{2}{7}\times\frac{7}{9} =\frac{2}{9}

Answer: 2/9

(iii) 3/8 × 6/4

38×64=1832=916\frac{3}{8}\times\frac{6}{4} =\frac{18}{32} =\frac{9}{16}

Answer: 9/16

(iv) 9/5 × 3/5

95×35=2725\frac{9}{5}\times\frac{3}{5} =\frac{27}{25}

Answer: 27/25 or 1 2/25

(v) 1/3 × 15/8

13×158=1524=58\frac{1}{3}\times\frac{15}{8} =\frac{15}{24} =\frac{5}{8}

Answer: 5/8

(vi) 11/2 × 3/10

112×310=3320\frac{11}{2}\times\frac{3}{10} =\frac{33}{20}

Answer: 33/20 or 1 13/20

(vii) 4/5 × 12/7

45×127=4835\frac{4}{5}\times\frac{12}{7} =\frac{48}{35}

Answer: 48/35 or 1 13/35

Important Concepts from Class 7 Maths Chapter 2

Proper, Improper and Mixed Fractions

A proper fraction has a numerator smaller than its denominator.

Example:

35\frac{3}{5}

An improper fraction has a numerator greater than or equal to its denominator.

Example:

75\frac{7}{5}

A mixed fraction contains a whole number and a proper fraction.

Example:

1251\frac{2}{5}

Converting a Mixed Fraction into an Improper Fraction

To convert a mixed fraction into an improper fraction:

(whole number×denominator)+numeratordenominator\frac{(\text{whole number}\times\text{denominator})+\text{numerator}} {\text{denominator}}

For example:

213=(2×3)+13=732\frac{1}{3} =\frac{(2\times3)+1}{3} =\frac{7}{3}

Read More: Vulgar Fraction

Comparing Fractions

When denominators are different, one method is to convert the fractions to equivalent fractions with a common denominator.

For example:

23and35\frac{2}{3}\quad\text{and}\quad\frac{3}{5}

LCM of 3 and 5 = 15.

23=1015\frac{2}{3}=\frac{10}{15} 35=915\frac{3}{5}=\frac{9}{15}

Therefore:

23>35\frac{2}{3}>\frac{3}{5}

Multiplication of Fractions

Multiply the numerators together and the denominators together:

ab×cd=acbd\frac{a}{b}\times\frac{c}{d} =\frac{ac}{bd}

A whole number can be written over 1 before multiplication.

For example:

5×23=51×23=1035\times\frac{2}{3} =\frac{5}{1}\times\frac{2}{3} =\frac{10}{3}

Division of Fractions

To divide one fraction by another, multiply the first fraction by the reciprocal of the second fraction.

For example:

23÷45\frac{2}{3}\div\frac{4}{5}

becomes

23×54=1012=56\frac{2}{3}\times\frac{5}{4} =\frac{10}{12} =\frac{5}{6}

Also, check: Consecutive Numbers: Meaning, Types, Formulas and Examples

What Does “Of” Mean in Fractions?

In fraction calculations, “of” generally indicates multiplication.

For example:

12 of 14=12×14=18\frac{1}{2}\text{ of }\frac{1}{4} =\frac{1}{2}\times\frac{1}{4} =\frac{1}{8}

Decimals

Decimals represent parts of a whole using place values such as tenths, hundredths and thousandths.

For example:

• 0.5 = 5/10

• 0.25 = 25/100

• 0.125 = 125/1000

Read More: Numerator and Denominator

When multiplying decimals, multiply the numbers and then place the decimal point according to the total number of decimal places in the factors.

When dividing decimals, the divisor can be converted into a whole number by multiplying both the divisor and dividend by the same power of 10.

Quick Revision: Class 7 Maths Chapter 2

• A proper fraction has a numerator smaller than its denominator.

• An improper fraction has a numerator greater than or equal to its denominator.

• A mixed fraction contains a whole number and a proper fraction.

• To compare unlike fractions, a common denominator can be used.

• To multiply fractions, multiply numerators and denominators.

• To divide fractions, multiply by the reciprocal of the divisor.

• In fraction problems, “of” generally means multiplication.

• Decimals use place values such as tenths, hundredths and thousandths.

• Always simplify the final fraction whenever possible.