Fraction

Exercise 2.1

Question 1: Solve the following:

(a) `2-3/5`

Solution: `2-3/5=(2xx5-3)/(5)`

`=(10-3)/(5)=7/5=1\2/5`

(b) `4+7/8`

Solution: `4+7/8=(4xx8+7)/(8)`

`=(32+7)/(8)=(39)/(8)=4\5/8`


(c) `3/5+2/7`

Solution: `3/5+2/7`

`=(3xx7+2xx5)/(5xx7)`

`=(21+10)/(35)=(31)/(35)`

(d) `(9)/(11)-(4)/(15)`

Solution: `(9)/(11)-(4)/(15)`

`=(9xx15-4xx11)/(11xx15)`

`=(135-44)/(165)=(91)/(165)`

(e) `(7)/(10)+2/5+3/2`

Solution: `(7)/(10)+2/5+3/2`

`=(7+2xx2+3xx5)/(10)`

`=(7+4+15)/(10)=(26)/(10)`

`=(13)/(5)=2\3/5`

(f) `2\2/3+3\1/2`

Solution: `2\2/3+3\1/2`

`=8/3+7/2=(8xx2+7xx3)/(3xx2)`

`=(16+21)/(6)=(37)/(6)=6\1/6`

(g) `8\1/2-3\5/8`

Solution: `8\1/2-3\5/8`

`=(17)/(2)-(29)/(8)=(17xx4-29)/(8)`

`=(68-29)/(8)=(39)/(8)=4\7/8`

Question 2: Arrange the following in descending order:

(a) `2/9, 2/3, (8)/(21)`

Solution: LCM of 9, 3 and 21 = 63

Hence, `2/9=(2xx7)/(9xx7)=(14)/(63)`

`2/3=(2xx21)/(3xx21)=(42)/(63)`

`(8)/(21)=(8xx3)/(21xx3)=(24)/(63)`

It is clear that: `(42)/(63)>(24)/(63)>(14)/(63)`

Or, `2/3>(8)/(21)>2/9`

(b) `1/5, 3/7, (7)/(10)`

Solution: LCM of 5, 7 and 10 = 70`

Hence, `1/5=(1xx14)/(5xx14)=(14)/(70)`

`3/7=(3xx10)/(7xx10)=(30)/(70)`

`(7)/(10)=(7xx7)/(10xx7)=(49)/(70)`

It is clear that: `(49)/(70)>(30)/(70)>(14)/(70)`

Or, `(7)/(10)>3/7>1/5`


Question 3: In a ‘magic square’ the sum of the numbers in each row, in each column and along the diagonals is the same. Is this a magic square?

magic square

Answer: Let us find the sum of fractions in the first row;

`(4)/(11)+(9)/(11)+(2)/(11)`

`=(4+9+2)/(11)=(15)/(11)`

Sum of fractions in the second row;

`(3)/(11)+(5)/(11)+(7)/(11)`

`=(3+5+7)/(11)=(15)/(11)`

Sum of fractions in the third row;

`(8)/(11)+(1)/(11)+(6)/(11)`

`=(8+1+6)/(11)=(15)/(11)`

Sum of fractions in first column;

`(4)/(11)+(3)/(11)+(8)/(11)`

`=(4+3+8)/(11)=(15)/(11)`

Sum of fractions in second column;

`(9)/(11)+(5)/(11)+(1)/(11)`

`=(9+5+1)/(11)=(15)/(11)`

Sum of fractions in third column;

`(2)/(11)+(7)/(11)+(6)/(11)`

`=(2+7+6)/(11)=(15)/(11)`

Sum of fractions in diagonal from left to right;

`(4)/(11)+(5)/(11)+(6)/(11)`

`=(4+5+6)/(11)=(15)/(11)`

Sum of fractions in diagonal from right to left;

`(2)/(11)+(5)/(11)+(8)/(11)`

`=(2+5+8)/(11)=(15)/(11)`

Since, the sum in each condition is equal hence, this is a magic square.

Question 4: A rectangular sheet of paper is 12 and 1/2 cm long and 10 and 1/2 cm wide. Find its perimeter.

Answer: Length = 12 and 1/2 cm and width = 10 and 1/2 cm

Perimeter = 2(Length + Breadth)

`=2(12\1/2+10\1/2)=2((25)/(2)+(21)/(2))`

`=2((25+21)/(2))=2xx(46)/(2)=46 cm`


Question 5: Find the perimeters of (i) ΔABE (ii) the rectangle BCDE in this figure. Whose perimeter is greater?

fraction for question

Answer: Perimeter of triangle = sum of its sides

`=5/2+2\3/4+3\3/5=5/2+(11)/(4)+(18)/(5)`

`=(50+55+72)/(20)=(177)/(20)=8\(17)/(20)` cm

Perimeter of rectangle can be calculated as follows:

=2(Length + Width)

`=2(2\3/4+7/6)=2((11)/(4)+7/6)`

`=2((33+14)/(12))=2xx(47)/(12)`

`=(47)/(6)=7\5/6` cm

Question 6: Salil wants to put a picture in a frame. The picture is 7 and 3/5 cm wide. To fit in the frame the picture cannot be more than 7 and 3/10 cm wide. How much should the picture be trimmed?

Answer: For finding the width of trimming, we need to subtract the trim’s width from picture’s width.

`7\3/5-7\(3)/(10)=(38)/(5)-(73)/(10)`

`=(76-73)/(10)=(3)/(10)` cm

Question 7: Ritu ate 3/5 part of an apple and the remaining apple was eaten by her brother Somu. How much part of the apple did Somu eat? Who had the larger share? By how much?

Answer: The whole apple can be represented by 1
Hence, part eaten by Somu = 1 – part eaten by Ritu

`1-3/5=(5-3)/(5)=2/5`

In both the cases, denominator is same hence the fraction with larger numerator is a larger fraction.
Difference between them can be calculated as follows:

`3/5-2/5=(3-2)/(5)=1/5`

Ritu ate larger share of apple which is 1/5 more than what was eaten by Somu.

Queston 8: Michael finished colouring a picture in 7/12 hours. Vaibhav finished colouring the same picture in ¾ hour. Who worked longer? By what fraction was it longer?

Answer: First of all, we need to compare the given fractions.
LCM of 12 and 4 = 12

`3/4=(3xx3)/(4xx3)=(9)/(12)`

Here; 9 > 7
Hence, Vaibhav took longer time. Difference can be calculated as follows:

`(9)/(12)-(7)/(12)=(9-7)/(12)`

`=(2)/(12)=1/6`



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