# Free Fractions Subjective Test 01 Practice Test - 6th grade

In a cake eating contest, Saumya got through 34 of a cake before time was called;
Shreya finished just 14 of her cake. How much more cake Saumya ate? [1 MARK]

#### SOLUTION

Solution :

Solution: 1 Mark

The amount of cake Saumya ate more than Shreya was ;

3414=24=12 more cake.

Nimmi was asked to solve all these questions by her teacher. [2 MARKS]

(i) 2+35

(ii) 5+15

(iii) 1+45

Help her solve these questions.

#### SOLUTION

Solution :

Steps: 1 Mark

(i) 2+35=10+35=135.

(ii) 5+15=25+15=265.

(iii) 1+45=5+45=95.

Last week, Suman spent 10 hours watching television. Shobha watched television for 13 as many hours as Suman did. How many hours did Shobha spend watching television? [2 MARKS]

#### SOLUTION

Solution :

Steps: 1 Mark

Shobha spent 13 times of 10 hours watching television.

13×10=103 or 313

Shobha spent 103 hours or  313 hours (which is 3 hours 20 minutes)  watching  television.

What fraction of a day is passed in 6 hours? Express the fraction in the simplest form.  [3 MARKS]

#### SOLUTION

Solution :

Steps: 1 Mark
Fraction: 1 Mark

There are 24 hours in a day.
6 hours of a day
=624
=14 (expressed in the simplest form)
624 and 14 are equivalent fractions.
6 hours of a day represents 14th of a day.

Out of the following fractions which is the smallest and which the greatest? [3 MARKS]
12,34,45,32,63

#### SOLUTION

Solution :

Smallest Fraction: 1 Mark
Greatest Fraction: 1 Mark
Steps: 1 Mark

63=2=21

LCM for the fractions 12,34,45,32,21 is 20

12=1020

34=1520

45=1620

32=3020

21=4020

Now that the denominator is equal, we can compare the fractions. The numerator 40 is the greatest and 10 is the least. Hence, the corresponding original fractions will be the greatest and the least.
Greatest fraction = 63 = 2
Smallest fraction = 12 = 0.5

2 multiplied by 12= ?,
3 multiplied by 14= ?,
7 multiplied by 13= ? and
17 multiplied by 15= ?
Simplify your answer and write it as a proper fraction or as a whole or mixed number. [3 MARKS]

#### SOLUTION

Solution :

Steps: 2 Marks

21×12=1

31×14=34

71×13=73=213

171×15=175=325

Out of the numbers from 0 to 10, what fraction of them are:  [4 MARKS]

1) Odd numbers
2) Prime numbers
3) Even numbers

#### SOLUTION

Solution :

Each option: 1 Mark

There are total of 11 numbers from 0 to 10

1) Number of odd numbers (1,3,5,7,9) = 5.

Fraction of odd numbers = 511

2) Number of prime numbers (2,3,5,7) = 4

Fraction of prime numbers 411

3) Number of even numbers (2,4,6,8,10) = 5

Fraction of even numbers 511

(a) Show the fractions 44,24,34 on a number line and simplify.
(b) A 9.85m long rope is divided into 5 equal parts. Find the length of each part.  [4 MARKS]

#### SOLUTION

Solution :

Each option: 2 Marks

(a) 44=1

24=12

34 is in its simplest form

Representation of the fractions on the number line is shown below

(b) Length of rope = 9.85m

After dividing the rope into 5 equal parts each part will be 15th of the total part.

15×9.85=9.855=1.97m

(a) Nisha had 55 balloons; she gave 46 balloons to Astha. What fraction of the balloons is left with Nisha? If Ashta loses 6 ballons what fraction of balloons in left with her?

(b)
Sameera purchased 312 kg apples and 434 kg oranges. What is the total weight of fruits purchased by her?

(c) Solve : 223+312 [4 MARKS]

#### SOLUTION

Solution :

(a) Concept: 1 Mark
Solution: 1 Mark
(b) Solution: 1 Mark
(c) Solution: 1 Mark

(a) Total no of balloons = 55

Balloons left with Nisha = 55 - 46 = 9

Fraction of balloon left = 955

Balloons left with Nisha = 46 - 6 = 40

Fraction of balloon left with Nisha = 4046=2023

(b)The total weight of the fruits = 312+434

= 72+194

144+194

334

814

(c) 223+312=83+72

=8×2+7×36

=16+216

=376

=616

(a) Aashu's elder sister divided a watermelon into 6 equal parts and Aarush eats 4 of them. What fraction of watermelon has he eaten hand what fraction is remaining? What is the name given to the fractions obtained?

(b)
Suman studies for 523 hours daily. She devotes 245 hours of her time for Science and Mathematics. How much time does she devote for other subjects?   [4 MARKS]

#### SOLUTION

Solution :

(a) Solution: 1 Mark
Name: 1 Mark
(b) Concept: 1 Mark
Steps: 1 Mark

(a) No of parts Arush has eaten = 4

Total no of parts = 6

So fraction of parts he has eaten = 46=23

Fraction of watermelon remaining = 123=323=13

The fractions 23 and 13 are called proper fractions.

(b) Total time of Suman’s study =  523=173 hours

Time devoted by her for Science and Mathematics =  245=145 hours

Thus, time devoted by her for other subjects = 173145

= 17×51514×315

4315

= 21315