Worksheet Solution: Fractions

Q1: Compare the following pairs of fractions:

1.  3/11 and 8/11

2.  2/11 and 5/24

The denominators are 15 and 19.
Since 15 and 19 are co-prime, the LCM is $15\; \backslash times\; 19\; =\; 285$15×19=285.

3.  4/15 and 7/19

The denominators are 15 and 19.

Since 15 and 19 are co-prime, the LCM is $15\times 19$ = 285.

Therefore,

Q2: In each of the following, identify the sets of like fractions.

1. 
   All are like fractions as the denominator is the same.
2. 
   No like fractions.
3. 
   Like Fractions, as the denominator same.

Q3: In the following set of fractions, identify the unit fractions.

A unit fraction is any fraction with 1 as its numerator

1/5, 1/21, 1/19, 1/48, 1/62

Q4: Fill in the blanks in each of the following by the correct number:

Question 5: Find the equivalent fraction of 64/84 with:

1. Denominator 63
   64/84 in lowest terms is,64/84 = 16/21
   21*3 = 63(63 is the new denominator )
   So 16 should be also multiplied by 3
   = 16/21*3/3 = 48/63
2. Denominator 147
   64/84 in lowest terms is,64/84=16/21
   16/21 x 3 = 112/147
3. Numerator 16
   64/84 in lowest terms is,
   64/84=16/21

Q6:  Subtract 2$\frac{2}{3}$ from 5, we get?

Q 7: Fill in the blanks by putting >,<or = in each of the following to make the statement true:

Q8: Which is smaller in each of the following pairs of fractions?

1. 3/16, 21/32
   Make the fractions equal
   3/16 x 2 = 6/32
   Thus, 3/16 is smaller.
2. 2/5, 7/12
   Make the fractions equal2/5 x 12 = 24/60
   7/12 x 5 = 35/60
   Thus, 2/5 is smaller.
3. 10/33, 1/3
   Make the fractions equal1/3 x 11 = 11/33
   Thus, 10/33 is smaller.

Q 9:Add together:

Question 10: Find the sum:

1. 
   Converting the mixed fractions into improper fractions 
   9/5 + 49/15 + 53/10 
   Now, making the denominator equal by LCM. 
   LCM = 30 
   9/5 x 6 = 54/30 
   49/15 x 2 = 98/30 
   53/10 x 3 = 159/30 
   Now the fractions are equal, adding them we get 
   54 + 98 + 159/30 =311/30 = 10(11/30)
   
   
2. 
   Converting the mixed fractions into improper fractions 

   3/5 + 36/7 + 11/2 

   Now, making the denominator equal by LCM. 

   LCM = 70 

   3/5 x 14 = 42/70

   36/7 x 10 = 360/70

   11/2 x 35 = 385/70

   Now the fractions are equal, adding them we get 

   42/70 + 360/70 +  385/70 = 787/70
   
   

3. 
   Converting the mixed fractions into improper fractions 

   19/8 + 29/16 + 3/4 

   Now, making the denominator equal by LCM. 

   LCM = 16 

   19/8 x 2 = 38/16

   3/4 x 4 = 12/16 

   Now the fractions are equal, adding them we get 

   38/16 + 29/16 + 12/16 = 79/16
   
   

4. 
   Converting the mixed fractions into improper fractions 12/9 + 2/24 + 7/36 
   Now, making the denominator equal by LCM. 
   LCM = 72 
   12/9 x 8 = 96/72
   5/24 x 3 = 15/72
   7/36 x 2 = 14/72 
   Now the fractions are equal, adding them we get 
   96/72 + 15/72 + 14/72 = 125/72
   

Question 11: Mukesh bought a pencil for Rs 2 (1/4) and a sharpener for Rs 1 (1/2). How much money did he spend on both these items?

Ans: Mukesh bought a pencil for = Rs 2(1/4)

Mukesh bought a sharpener for = Rs 1(1/2). 

Total money spent =  2(1/4) + 1(1/2). 

Converting the mixed fractions into improper fractions 

9/4 + 3/2 

LCM = 4    

3/2 x 2 = 6/4 

9/4 + 6/4 = Rs. 15/4

Question 12: Pankaj bought 5(1/9) litres of petrol on Monday, 2(5/6) litres on Tuesday, and 1(2/9) litres on Wednesday. How many litres of petrol did he buy on these three days?

Ans: Pankaj bought petrol on Monday = 5(1/9) litres 

Pankaj bought petrol on Tuesday = 2(5/6) litres

Pankaj bought petrol on Wednesday = 1(2/9)litres

Total petrol on three days = 5(1/9) + 2(5/6) + 1(2/9)

Converting the mixed fractions into improper fractions 

46/9 + 15/6 + 11/9 

LCM = 18 

46/9 x 2 = 92/18 

15/6 x 3 = 51/18

11/9 x 2 = 22/18 

Adding them we get total petrol on three days = 165/18 

Q13: Fill in the blanks:

1. 1.
2. 2/11 x 11/2 = 1.
3. 17/3 x 3/17 = 1.

Q14:Ring the improper fractions:

Q15:is the same as. Is it true?

Dividing two fractions is equivalent to multiplying the first fraction by the reciprocal of the second:
On the other hand, the right-hand side expression is:Comparing the two results:Hence , statement is false.