# Free Fractions Subjective Test 02 Practice Test - 6th grade

Anshu bought a cake from a bakery shop. She has 5 friends to share the cake. In what fraction she should distribute the cake to each of her friends so that every friend gets the same amount of cake? [1 MARK]

#### SOLUTION

Solution :

Concept: 1 Mark

The cake has to be divided among 5 people equally, so the fraction of the cake each friend would get will be 15. Which one of the following is greater? [2 MARKS]

a) 37 and 35

b) 58 and 12

#### SOLUTION

Solution :

Each part: 1 Mark

(a) LCM of 7 and 5 is 35

37=3×57×5=1535

35=3×75×7=2135

Clearly,  2135 is greater than 1535

Hence, 35 is greater than 37

(b) LCM of 8 and 2 is 8

58=5×18×1=58

12=1×42×4=48

Clearly, 58 is greater than 48

Hence, 58 is greater than 12

(a) What fraction of the total pizza is left in the given figure below? [2 MARKS] (b)  What is the product of 6729 and its reciprocal?

#### SOLUTION

Solution :

Each option: 1 Mark

(a) Given pizza has 4 slices

Pizza slices left in total = 3

Fraction of pizza slices left= 34

(b) 6729×7296=1 ( product of a fraction and its reciprocal is always 1)

(a) A piece of wire 78 metre long broke into two pieces. One piece was 14 metre long. How long is the other piece? [3 MARKS]

(b) Sarita bought 25 meters of ribbon and Lalita 34 metre of ribbon. What is the total length of the ribbon they bought?

(c) Simplify: 814256

#### SOLUTION

Solution :

Each option: 1 Mark

(a) Length of the other piece = Total length of the wire - Length of the given piece

(7814)m

(728)m

= (58)m

(b) Total length of ribbon = Length of ribbon bought by Sarita  + Length of ribbon bought by Lalita

25+34

8+1520

2320

=  (1320)m

(c)  814256334176

1986824

13024

6512

5512

In a match of 50 overs, the team batting second was given a target of 310.They lost the match by 10 runs. The team batting second i.e. the losing team, scored one-half of their runs in 30 overs and next five overs they scored one-half of the remaining runs. Later in the next 8 overs, they scored  15th of the remaining runs. In last seven overs, they scored the remaining runs. How many runs did they score in last seven overs?
[3 MARKS]

#### SOLUTION

Solution :

Steps: 2 Marks

Total runs scored by the team that lost = 300

Now, total no. of overs played by them = 50

That is in 30 overs, this team scored =3002

=150 runs

The balance 300 - 150 = 150 runs were scored by this team in balance 20 overs.

By the given condition,

In the next 5 overs, 12 of 150 runs

= 75 runs were scored.

150 runs - 75 runs = 75 runs are still in balance.

Again in the next 8 overs.

15 of 75 = 15 runs were scored.

Now No. of overs left = 20 - (5 + 8)

20 - 13 = 7

In seven overs, runs scored will be 75 - 15 = 60.

Mena finished colouring a picture in 715 hour; Vaibhav finished colouring the same picture in 25 hours. Who worked longer? By what fraction was it longer? [3 MARKS]

#### SOLUTION

Solution :

Steps: 1 Mark
Difference in fractions: 1 Mark
Solution: 1 Mark

Time taken by Mena =
715 hr

Time taken by Vaibhav
25 hr=2×35×3=615

Clearly, 715>615

Vaibhav worked longer.

Time for which Vaibhav has worked more
= 71525=7615=115 hrs longer.

(a) Last month, Shakshi and Shashank sold candy to raise money for their debate team. Shashank sold 25 as much candy as Shakshi did. If Shakshi sold 3 boxes of candy, how many boxes of candy did Shashank sell? [4 MARKS]

(b) Naina was given 112 piece of cake and Najma was given 113 piece of cake. Find the total amount of cake that was given to both of them.

#### SOLUTION

Solution :

Each part: 2 Marks

(a) Shashank sold 25 times 3 boxes of candy  25×3

Simplify the product 65=115

Shashank sold 115 boxes of candy.

(b) Total mount of cake = Naina's share  of cake + Najma's share of cake

=  112+113

=  32+43

9+86

116

=  156

What are proper fractions, improper fractions and mixed fractions? Give Example for each. [4 MARKS]

#### SOLUTION

Solution :

Definitions: 3 Marks
Example: 1 Mark

Proper Fraction: The fractions in which the numerator is less than the denominator are called proper fractions.

e.g. 13,34,21793

Improper Fraction: The fractions in which the numerator is greater than (or equal to) the denominator are called proper fractions.

e.g. 43,94,229

Mixed  Fraction: A whole number and a proper fraction mixed together is called a mixed fraction.

e.g. 213,134,3293

Car A covers 5.5 km in 4 litres of petrol and another car B covers 1800 metres in 1 litre of petrol. Calculate the mileage per litre of petrol,  Now calculate which car travels more and by how much distance compared to the other?  [4 MARKS]

#### SOLUTION

Solution :

Concept: 1 Mark
Application: 3 Marks

Distance covered by car A in 4 litres of petrol is 5500m.

Distance covered by car A in 1 litre of petrol =(5500÷4)= 1375m.

Distance covered by car B in 1 litre of petrol = 1800m.

So car B travels more compared to car A

Difference = 1800-1375 = 425m

Car B travels  425m  more than car A

The length of the shaded rectangle is (1/10) of the bigger rectangle and its breadth is 0.001 times the bigger rectangle . If the area of the bigger rectangle is 10000 m2. Find the area of the shaded rectangle. [4 MARKS] #### SOLUTION

Solution :

Formula: 1 Mark
Steps: 2 Marks

Let the length and breadth of the bigger rectangle be am and bm respectively

Then, the length of the shaded rectangle is (0.1 a)m.