WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples

Chapter 1 Simplification Vulgar Fraction Examples

Question 1. From the following table identify the proper fraction, improper fraction, and mixed fraction

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 1

Wbbse Class 6 Maths Solutions:

Identifying the proper fraction, improper fraction, and mixed fraction:

Proper Fraction: \(\frac{1}{5}, \frac{2}{7}, \frac{3}{8}, \frac{6}{13}, \frac{1}{9}, \frac{2}{5}, \frac{5}{9}, \frac{4}{17}, \frac{11}{12}, \frac{3}{7}\)

Improper Fraction: \(\frac{15}{13}, \frac{29}{19}, \frac{23}{17}\)

Mixed Fraction: \(9 \frac{14}{15}, 1 \frac{22}{25}, 11 \frac{1}{9}, 2 \frac{3}{4}, 3 \frac{5}{11}\)

 

Question 2. Reduce \(6 \frac{7}{19}\) in improper fraction.


Class 6 Wb Board Math Solution :

Given:

\(6 \frac{7}{19}\) \(6 \frac{7}{19}=\frac{6 \times 19+7}{19}=\frac{114+7}{19}=\frac{121}{19}\)

Question 2

Question 3. Express in mixed fraction:

Wbbse Class 6 Maths Solutions :

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 3

 

[Division of 123 by 7]

∴ \(\frac{123}{7}\) = \(17 \frac{4}{7}\)

∴ the required mixed fraction = \(17 \frac{4}{7}\)

 

Read And Learn More: WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Solved Problems

 

Question 4. Express with a lowest common denominator: 

\(\frac{5}{8}\), \(\frac{7}{12}\).


Class 6 Wb Board Math Solution:

Given:

\(\frac{5}{8}\), \(\frac{7}{12}\).

The denominators of the given fractions are 8 and 12.

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 4

 

Now 24 ÷ 8 = 3 and 24 ÷ 12 = 2

The common denominator for the given fractions will be 24.

For this, it is required to multiply both the numerator and denominator of the first fraction by 3 and to multiply both the numerator and denominator of the second fraction by 2.

∴ \(\frac{5}{8}=\frac{5 \times 3}{8 \times 3}=\frac{15}{24}\) and \(\frac{7}{12}=\frac{7 \times 2}{12 \times 2}=\frac{14}{24}\)

∴ The given two fractions with the lowest common denominator are \(\frac{15}{24}\) and \(\frac{14}{24}\)

 

Question 5. Express the following fractions with the lowest common numerator:

\(\frac{12}{13}\), \(\frac{18}{23}\)

Wbbse Class 6 Maths Solutions :

Given:

\(\frac{12}{13}\), \(\frac{18}{23}\)

The numerators of the given fractions are 12 and 18.

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 5

 

∴ The L. C. M. of 12, 18 = 2 x 3 x 2 x 3.36.

The lowest common numerator of the given two fractions will be 36.

Now 36 12 3 and 36 18 = 2

Multiplying both the numerator and denominator of the first fraction by 3 and multiplying both the numerator and denominator of the second fraction by 2, we get,

∴ \(\frac{12}{13}=\frac{12 \times 3}{13 \times 3}=\frac{36}{39}\) and \(\frac{7}{12}=\frac{7 \times 2}{12 \times 2}=\frac{14}{24}\)

The required two fractions with the lowest common numerator are \(\frac{36}{39}\) and \(\frac{36}{46}\)

 

Question 6. Write 3 equivalent fractions of each of the following fractions:

1. \(\frac{1}{5}\)

Wbbse Class 6 Maths Solutions:

Given:

\(\frac{1}{5}\)

 We know that, if we multiply both the numerator and denominator of any fraction, then the value of the fraction is not changed.

∴ \(\frac{1}{5}=\frac{1 \times 2}{5 \times 2}=\frac{1 \times 3}{5 \times 3}=\frac{1 \times 4}{5 \times 4}=\cdots \cdots \text { etc. }\)

or, \(\frac{1}{5}=\frac{2}{10}=\frac{3}{15}=\frac{4}{20}=\cdots \cdots \text { etc. }\)

∴ The required three equivalent fractions are \(\frac{2}{10}, \frac{3}{15}, \frac{4}{20}\)

 

2. \(1 \frac{1}{3}\)

Solution:

Given:

\(1 \frac{1}{3}\) \(1 \frac{1}{3}=\frac{4}{3}=\frac{4 \times 2}{3 \times 2}=\frac{4 \times 3}{3 \times 3}=\frac{4 \times 4}{3 \times 4}=\cdots \cdots \text { etc. }\)

or, \(1 \frac{1}{3}=\frac{8}{6}=\frac{12}{9}=\frac{16}{12}=\cdots \cdots \text { etc. }\)

∴ The required 3 equivalent fractions are [late]\frac{8}{6}, \frac{12}{9}, \frac{16}{12}[/latex]

 

Question 7. Reduce the following fractions into the lowest terms:

1. \({72}{108}\)


Class 6 Wb Board Math Solution :

\(\frac{72}{108}\)

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 7 Q 1

 

 

2. \(\frac{243}{405}\)

Solution:

\(\frac{243}{405}\)

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 7 Q 2

 

Example 8. Arrange the following fractions in ascending order of magnitude:

1. \(\frac{7}{2}, \frac{7}{4}, \frac{7}{5}\)

Solution:

\(\frac{7}{2}, \frac{7}{4}, \frac{7}{5}\)

The denominators of the fractions are 2, 4, and 5.

 

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 8 Q 1

 

∴  L. C. M. of 2, 4, 5 = 2 x 1 x 2 x 5 = 20

20 ÷ 2 = 10 ; 20 ÷ 4 = 5; 20 ÷ 5 = 4.

Multiplying both numerator and denominator of the 1st fraction by 10; the 2nd fraction by 5; the 3rd fraction by 4, we get,

\(\frac{7}{2}=\frac{7 \times 10}{2 \times 10}=\frac{70}{20} ; \quad \frac{7}{4}=\frac{7 \times 5}{4 \times 5}=\frac{35}{20} ; \quad \frac{7}{5}=\frac{7 \times 4}{5 \times 4}=\frac{28}{20}\)

Now the denominators of all the given fractions are 20.

∵ 28 < 35 < 70.

∴ \(\frac{28}{20}<\frac{35}{20}<\frac{70}{20} \text { or, } \frac{7}{5}<\frac{7}{4}<\frac{7}{2}\)

Arranging the fraction in ascending order, we get \(\frac{7}{5}, \frac{7}{4}, \frac{7}{2}\)

 

2. \(5 \frac{3}{4}, 5 \frac{5}{9}, 5 \frac{8}{12}\)

Solution:

\(5 \frac{3}{4}, 5 \frac{5}{9}, 5 \frac{8}{12}\)

Now,

\(5 \frac{3}{4}=\frac{23}{4} ; \quad 5 \frac{5}{9}=\frac{50}{9} ; \quad 5 \frac{8}{12}=\frac{68}{12}\)

The denominators of the given mixed fractions are 4,9,12.

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 8 Q 2

 

∴ L. C. M. of 4, 9, 12 = 2 x 2 x 3 x 3 = 36.

36 ÷ 4 = 9; 36 ÷ 9 = 4; 36 ÷ 12 = 3.

then

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 8 Q 3

 

As 200 < 204 < 207, we get, \(\frac{200}{36}<\frac{204}{36}<\frac{207}{36} \text { or, } 5 \frac{5}{9}<5 \frac{8}{12}<5 \frac{3}{4}\)

∴ Arranging the fractions in ascending order, we get, \(5 \frac{5}{9}, 5 \frac{8}{12}, 5 \frac{3}{4}\)

 

3. \(1 \frac{1}{5}, 1 \frac{1}{7}, 1 \frac{1}{8}\)


Class 6 Wb Board Math Solution :

\(1 \frac{1}{5}, 1 \frac{1}{7}, 1 \frac{1}{8}\) Since each of the fractions has the integral part 1, we take the fractions \(\)

The denominator is 5, 7, and 8.

These numbers are prime to each other.

Their L. C. M. = 5 x 7 x 8 = 280.

280 ÷ 5 = 56

280 ÷ 7 = 40

280 ÷ 8 = 35.

∴ \(\frac{1}{5}=\frac{1 \times 56}{5 \times 56}=\frac{56}{280} ; \frac{1}{7}=\frac{1 \times 40}{7 \times 40}=\frac{40}{280} ; \frac{1}{8}=\frac{1 \times 35}{8 \times 35}=\frac{35}{280}\)

As 35 < 40 < 56, we, get \(\frac{35}{280}<\frac{40}{280}<\frac{56}{280} \text { or, } \frac{1}{8}<\frac{1}{7}<\frac{1}{5}\)

∴ \(1 \frac{1}{8}<1 \frac{1}{7}<1 \frac{1}{5}\)

Arranging the fractions in ascending order, we get, \(1 \frac{1}{8}<1 \frac{1}{7}<1 \frac{1}{5}\)

 

4. \(\frac{1}{3}, \frac{4}{5}, \frac{7}{15}\)


Class 6 Wb Board Math Solution :

\(\frac{1}{3}, \frac{4}{5}, \frac{7}{15}\) The denominators of the given fractions are 3, 5, 15.

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 8 Q 4

 

∴ L.C.M. of 3, 5, 15= 3 x 5

=15

15 ÷ 3 = 5

15 ÷ 5 = 3

15 ÷ 15 = 1.

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 8 Q 5

∵ 5 < 7 < 12,

∴ \(\frac{5}{15}<\frac{7}{15}<\frac{12}{15} \text { or, } \frac{1}{3}<\frac{7}{15}<\frac{4}{5}\)

∴ Arranging the fractions in ascending order, we get, \(\frac{1}{3}, \frac{7}{15}, \frac{4}{5}\)

 

5. \(\frac{5}{7}, \frac{3}{4}, \frac{1}{4}\)

Solution:

\(\frac{5}{7}, \frac{3}{4}, \frac{1}{4}\)

∴ The denominators of the given fractions are 7, 4, and 4.

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 8 Q 6

 

∴ L. C. M. of 7, 4, 4 = 4 x 7

= 28.

28 ÷ 2 = 45

90 ÷ 9 = 10

90 ÷ 5 = 18.

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 8 Q 7

 

7 < 20 < 21,

∴ \(\frac{7}{28}<\frac{20}{28}<\frac{21}{28} \text { or, } \frac{1}{4}<\frac{5}{7}<\frac{3}{4}\)

∴ Arranging the fractions in ascending order, we get, \([latex]\frac{1}{4}, \frac{5}{7}, \frac{3}{4}\)[/latex]

 

6. \(3 \frac{1}{2}, 7 \frac{5}{9}, 7 \frac{1}{5}\)

Solution:

\(3 \frac{1}{2}, 7 \frac{5}{9}, 7 \frac{1}{5}\)

Now,

\(3 \frac{1}{2}\) = \(\frac{7}{2}\)

\(7 \frac{5}{9}\) = \(\frac{68}{9}\)

\(7 \frac{1}{5}\) = \(\frac{36}{5}\)

The denominators of the given fractions are 2, 9, and 5.

∴ L. C. M. of 2, 9, 5 = 2 x 9 x 5

= 90. (Here 2, 9, and 5 are prime to each other)

90 ÷ 2 = 45

90 ÷ 9 = 10

90 ÷ 5 = 18.

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 8 Q 8

 

As 315 648 < 680, we get, \(\frac{315}{90}<\frac{648}{90}<\frac{680}{90} \text { or, } 3 \frac{1}{2}<7 \frac{1}{5}<7 \frac{5}{9}\)

∴ Arranging the fractions in ascending order, we get, \(3 \frac{1}{2}, 7 \cdot \frac{1}{5}, 7 \frac{5}{9}\)

 

7. \(\frac{1}{8}, \frac{7}{10}, \frac{3}{5}\)

Solution:

\(\frac{1}{8}, \frac{7}{10}, \frac{3}{5}\) The denominators of the given fractions are 8, 10, and 5.

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 8 Q 9

 

 L. C. M. of 8, 10, 5 = 2 x 5 x 4 = 40.

40 ÷ 8 = 5

40 ÷ 10 = 4

40 ÷ 5 = 8.

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 8 Q 10

∵ 5 < 24, < 28,

∴ \(\frac{5}{40}<\frac{24}{40}<\frac{28}{40} \quad \text { or, } \frac{1}{8}<\frac{3}{5}<\frac{7}{10}\)

∴ Arranging the fractions in ascending order, we get, \(\frac{1}{8}, \frac{3}{5}, \frac{7}{10}\) 

 

3. \(3 \frac{1}{2}, 3 \frac{5}{9}, 3 \frac{1}{5}\)

Solution:

\(3 \frac{1}{2}, 3 \frac{5}{9}, 3 \frac{1}{5}\)

Since such of the given fractions has the integer 3.

So we have to test the fractions \(\frac{1}{2}, \frac{5}{9}, \frac{1}{5}\)

Now the denominators of the fractions \(\frac{1}{2}, \frac{5}{9}, \frac{1}{5}\) are 2, 9, 5.

L. C M of 2, 9, 5 = 2 x 9 x 5

= 90

∴ 90 ÷ 2 = 45

90 ÷ 9 = 10

90 ÷ 5 = 18

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 8 Q 11

 

As, 18< 45 < 50;

∴ \(\frac{18}{90}<\frac{45}{90}<\frac{50}{90} \quad \text { or, } \quad \frac{1}{5}<\frac{1}{2}<\frac{5}{9}\)

or, \(3+\frac{1}{5}<3+\frac{1}{2}<3+\frac{5}{9} \quad \text { or, } \quad 3 \frac{1}{5}<3 \frac{1}{2}<3 \frac{5}{9}\)

Arranging the fractions in ascending order, we get, \(3 \frac{1}{5}, 3 \frac{1}{2}, 3 \frac{5}{9}\)

 

Example 9. Add: \(\frac{7}{2}+\frac{2}{3}+1 \frac{1}{2}\)

Solution:

Given:

\(\frac{7}{2}+\frac{2}{3}+1 \frac{1}{2}\)

 

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 9

 

Example 10. Subtract: \(10 \frac{2}{3}-7 \frac{2}{5}\)

Solution:

Given:

\(10 \frac{2}{3}And7 \frac{2}{5}\)

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 10

 

Example 11. Simplify: \(4 \frac{2}{15}+8 \frac{3}{5}-9 \frac{4}{25}\)

Solution:

The given quality = \(4 \frac{2}{15}+8 \frac{3}{5}-9 \frac{4}{25}\)

 

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 11

 

The required answer = \(3 \frac{43}{75}\)

 

Example 12. Find the value of the following:

1. \(\frac{2}{7}-\frac{2}{3}+1 \frac{1}{2}\)

Solution:

\(\frac{2}{7}-\frac{2}{3}+1 \frac{1}{2}\)

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 12 Q 1

 

2. \(1 \frac{2}{5}-\frac{3}{8}+\frac{1}{4}\)

Solution:

\(1 \frac{2}{5}-\frac{3}{8}+\frac{1}{4}\)

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 12 Q 2

 

[ L.C.M of 5, 8, 4 :

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 12 Q 3

 

∴ L.C.M. of 5, 8, 4 = 2 x 2 x 5 x 2 = 40]

 

3. \(\frac{2}{5}+\frac{3}{8}-\frac{1}{4}\)

Solution:

\(\frac{2}{5}+\frac{3}{8}-\frac{1}{4}\)

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 12 Q 4

 

4. \(7-3 \frac{1}{8}-2 \frac{1}{3}\)

Solution:

\(7-3 \frac{1}{8}-2 \frac{1}{3}\)

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 12 Q 5

 

5. \(\frac{4}{5}+\frac{5}{8}-1 \frac{1}{3}\)

Solution:

\(\frac{4}{5}+\frac{5}{8}-1 \frac{1}{3}\)

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 12 Q 6

 

6. \(1 \frac{3}{10}+1 \frac{4}{5}-1 \frac{1}{4}\)

Solution:

\(1 \frac{3}{10}+1 \frac{4}{5}-1 \frac{1}{4}\)

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 12 Q 7

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 12 Q 8

 

∴ L.C.M of 10, 5, 4 = 2 x 5 x 2

= 20.

 

7. \(2 \frac{5}{6}-1 \frac{8}{9}+1 \frac{3}{4}\)

Solution:

\(2 \frac{5}{6}-1 \frac{8}{9}+1 \frac{3}{4}\)

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 12 Q 9

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 12 Q 10

∴ L.C.M of 6, 9, 4 = 2 x 3 x 3 x 2

= 36.

 

8. \(4 \frac{1}{7}+2 \frac{2}{5}-5\)

Solution:

Given

\(4 \frac{1}{7}+2 \frac{2}{5}-5\)

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 12 Q 11

 

Example 13. Simplify: \(8 \frac{1}{4} \div 1 \frac{4}{17} \div 5 \frac{7}{8} \text { of } 1 \frac{2}{15}\)

Solution:

Given expression =  \(8 \frac{1}{4} \div 1 \frac{4}{17} \div 5 \frac{7}{8} \text { of } 1 \frac{2}{15}\)

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 13

 

∴ The required answer = \(1 \frac{1}{329}\)

 

Example 14. Simplify: \(1 \frac{1}{4}+\frac{1}{3}\left[2 \frac{1}{4}+1 \frac{1}{2}\left\{3 \frac{1}{2} \div 2 \frac{1}{3}\left(4 \frac{1}{4} \div \overline{2+3 \frac{2}{3}}\right)\right\}\right]\)

Solution:

The given expression = \(1 \frac{1}{4}+\frac{1}{3}\left[2 \frac{1}{4}+1 \frac{1}{2}\left\{3 \frac{1}{2} \div 2 \frac{1}{3}\left(4 \frac{1}{4} \div \overline{2+3 \frac{2}{3}}\right)\right\}\right]\)

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 14

 

∴ The required answer = 3

 

Example 15. Simplify: \(\frac{4 \frac{1}{2}}{32} \times \frac{2 \frac{2}{3} \div \frac{5}{8}}{1 \frac{1}{5} \text { of } \frac{5}{6} \div 8 \frac{1}{3}} \times \frac{2}{5}\)

Solution:

\(\frac{4 \frac{1}{2}}{32} \times \frac{2 \frac{2}{3} \div \frac{5}{8}}{1 \frac{1}{5} \text { of } \frac{5}{6} \div 8 \frac{1}{3}} \times \frac{2}{5}\)

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 15 Q 1

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 15 Q 2

 

∴ The required answer = 2.

 

Example 16. Simplify: \(\frac{1 \frac{1}{4}-\frac{5}{12}}{1 \frac{1}{4}+\frac{5}{12}}-4 \div \frac{6 \frac{1}{2}}{2+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}}+4 \frac{5}{7 \frac{2}{3}}\)

Solution:

The given expression = \(\frac{1 \frac{1}{4}-\frac{5}{12}}{1 \frac{1}{4}+\frac{5}{12}}-4 \div \frac{6 \frac{1}{2}}{2+\frac{1}{1+\frac{1}{1+\frac{1}{2}}}}+4 \frac{5}{7 \frac{2}{3}}\)

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 16 Q 1

 

WBBSE Solutions For Class 6 Maths Chapter 1 Simplification Vulgar Fraction Examples Question 16 Q 2

 

 

 

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