Fraction Test - 1

6 / 11 ÷ 6 / 11

The given expression can be simplified as below

6 / 11 ÷ 6 / 11 = (6 ×11) / (11 × 6)

=1

Hence, the simplified form of the given expression is 1.

Given,

Number of oranges in a box = 500

Rotten oranges out of 500 = 3 / 25

Oranges for guests out of 500 = 1 / 5

Rotten oranges = 3 / 25 of 500

We get,

= 3 / 25 × 500

= 60

Oranges for guests = 1 / 5 of 500

We get,

= 1 / 5 × 500

= 100

Oranges left in box = 500 – 60 – 100

= 340

Hence, 340 oranges are left in the box.

Given

Mr. Vijay spends 7 / 15 of his money

Let us assume he has Rs 1

Amount spent = 7 / 15 of 1 

We get 1 – 7/15

= 8/15

Rs 8 / 15

Since 8 / 15 of the total money = Rs 3280

∴ Total money = Rs (3280 × 15) / 8

= Rs 6150

Hence, the total money Mr. Vijay had was Rs 6150.

Given,

Wheat = Rs 15$\frac{1}{4}$

Rice = Rs 22$\frac{3}{4}$

Vegetables = Rs 8$\frac{1}{4}$

Hence, total amount used to purchase the goods can be calculated as below

Total amount of goods = Rs (15$\frac{1}{4}$ + 22$\frac{3}{4}$+ 8$\frac{1}{4}$)

We get

= 61 / 4 + 91 / 4 + 33 / 4

= Rs 185 / 4

Hence, money returned by shopkeeper can be calculated as below

Money returned = Rs (100 – 185 / 4)

By taking LCM, we get

= Rs (400 – 185) / 4

= Rs 215/ 4

= Rs  53$\frac{3}{4}$

Hence, money returned by the shopkeeper is Rs 53$\frac{3}{4}$

Given,

Sugar = Rs 16$\frac{2}{3}$

Beans = Rs 30$\frac{2}{3}$

Vegetables = Rs 23$\frac{1}{2}$

Hence, total amount used to purchase the goods can be calculated as belowType equation here.

Total amount of goods = Rs (16$\frac{2}{3}$ + 30$\frac{2}{3}$ + 23$\frac{1}{2}$)

We get

= 50 /3  + 92 / 3 + 47 / 2

= Rs 425 / 6

Hence, money returned by shopkeeper can be calculated as below

Money returned = Rs (500 – 425 / 6)

By taking LCM, we get

= Rs (3000 – 425) / 6

= Rs 2575 / 6

= Rs 429$\frac{1}{6}$

3 / 25 of (1 / 6 + 5 / 9) ÷ (4/ 5 – 2 / 7)

The given expression can be simplified as below

3 / 25 of (1 / 6 + 5 / 9) ÷ (4 / 5 – 2 / 7) = 3 / 25 of [(5 + 7) / 15] ÷ [(25 – 18) / 30]

We get

= 7 / 30 of (4 / 5) ÷ (7 / 30)

= 7 / 30 × 4 / 5 × 30 / 7

= 4 / 5

Hence, the simplified form of the given expression is 4 / 5.

The fraction 9/21 can be simplified as below

9/21 = (9  ÷ 3 ) / (21 ÷ 3)

= 3/7

Hence, 3/7 is the simplified form of 9/21.

Given,

Length of piece of cloth = 12 metre

After washing, it shrinks by = 2 / 15 of its length

Hence, the shrinked cloth can be calculated as below

Shrinked cloth = 2 / 15 of 12 m

= 8 / 5 m

Hence, length of cloth after washing can be calculated as below

Length of cloth after washing = 12 – 8 / 5

By taking LCM, we get

= (60 – 8) / 5

= 52 / 5

= 10 $\frac{2}{5}$ m

Hence the length of cloth after washing is

10 $\frac{2}{5}$m 

Given,

Number of mangoes in a box = 840

Rotten mangoes out of 840 = 5 / 21

Mangoes for guests out of 840 = 2 / 7

Rotten mangoes = 5 / 21 of 840

We get,

= 5 / 21 × 840

= 200

Mangoes for guests = 2 / 7 of 840

We get,

= 2 / 7 × 840

= 240

Mangoes left in box = 840 – 240 – 200

= 400

Hence, 400 mangoes are left in the box.

Given,

Length of piece of cloth = 8 metres

After washing, it shrinks by = 1 / 16 of its length

Hence, the shrinked cloth can be calculated as below

Shrinked cloth = 1 / 16 of 8 m

= 1 / 2 m

Hence, length of cloth after washing can be calculated as below

Length of cloth after washing = 8 – 1/2

By taking LCM, we get

= (16 – 1) / 2

= 15 / 2

= 7$\frac{1}{2}$

Hence the length of cloth after washing is 7$\frac{1}{2}$

Given,

Total number of products = 48

Number of products broken = 14                         

Remaining products = 48 – 14

= 34

The fraction of total number of products and the products broken = 48 / 14

= 24 / 7

Let the total journey = x km

Given total distance covered = 21 km

Journey left = 1 / 5 of x

Hence, according to the question, the total distance of journey can be calculated as below

1 / 5 of x = x – 21

x – x / 5 = 21

By calculating further, we get

(5x – x) / 5 = 21

4x / 5 = 21

4x = 105

x = 105 / 4

x = 26.25

Hence, the full length of the journey is 26.25 km.

Given,

Number of oranges bought = 3 dozen

We know there are 12 oranges in a dozen.

Total oranges = 3  12 = 36

Number of oranges eaten = 15

Number of oranges left = 36 – 15

= 21

Therefore, the required fraction is 21/ 36

⇒ 7/12

(1 / 3 + 1 / 4) ÷ (1 / 5 – 1 / 6)

The given expression can be simplified as follows

(1 / 3 + 1 / 4) ÷ (1 / 5 – 1 / 6) = [(4 + 3) / 12] ÷ [(6 – 5) / 30]

On further calculation, we get

= (7/ 12) ÷ (1 / 30)

= 7 / 12 × 30 / 1

= 35/2

= 17 1/2

Hence, the simplified form of the given expression is 17 1/2

Given,

Length of the rope =

12$\frac{3}{4}$m

Length of cut off rope =

3$\frac{2}{5}$m

Remaining rope = 12$\frac{3}{4}$ – 3$\frac{2}{5}$

We get

= 51 / 4 – 17 / 5

By taking LCM, we get

= (255 – 68) / 20

= 187 / 20 m

= 8$\frac{17}{20}$

Hence, the length of the remaining rope is 8$\frac{17}{20}$

7 – (6 / 13 – $\frac{2}{13}$)

The given expression can be simplified as below

7 – (6 / 13 – 4 $\frac{2}{13}$) = 7 – (6 / 13 – 54 / 13)

= 7 – (6 – 54) / 13

= 7 – (-48 / 13)

On further calculation, we get

= 7/ 1 + 48 / 13

= 139 / 13

= 10 $\frac{9}{13}$

Hence is 10 $\frac{9}{13}$ the simplified form of the given expression.

Given,

Total number of females = 210

Number of males = 2 / 5

Let us assume the total number of males and females be x

Total number of males = 2 / 5 of x

We get,

= 2x / 5

x – 2x/5 = 210

(5x – 2x)/5 = 210

3x/5 = 210

X = 210 X 5/3

X = 350

According to question, total strength can be calculate as below

Number of males = Total strength – females

= 350 - 210

=  140

Hence, the total number of males is 140.

Given

Money earned by Aman in a particular month = Rs 12400

Amount spend on food, rent, insurance and holidays by him are 1 / 8, 1 / 5, 1 / 16 and 3 / 20 respectively

Amount spend on food = 1 / 8 of 12400

= 1 / 8 × 12400

= Rs 1550

Amount spend on rent = 1 / 5 of 12400

= 1 / 5 × 12400

= Rs 2480

Amount spend on insurance = 1 / 16 of 12400

= 1 / 16 × 12400

= Rs 775

Amount spend on holidays = 3 / 20 of 12400

= 3 / 20 × 12400

= Rs 1860

Total amount spend = Rs (1550 + 2480 + 775 + 1860)

= Rs 6665

Amount saved by man = 12400 – 6665

= Rs 5735

Hence, amount saved by Aman in a month is Rs 5735.

The fraction 245 / 70 can be simplified as below

245 / 70 = (245 ÷ 35) / (70 ÷ 35)

= 7 / 2

Hence, 7 / 2 is the simplified form of 245 / 70.

The given expression can be simplified as below

4 / 1 + 7 / 10 – 54 / 25 = {(4  x 50) + (7 × 5) – (54 x 2)}/50

= (200 + 35 -108)/ 50

= 127 / 50

= 2 $\frac{27}{50}$

Hence, simplified form of the given expression is 2$\frac{27}{50}$  

Given,

Length of the bundle of wire = 12$\frac{2}{3}$m

Length of wire cut off  = 5$\frac{3}{5}$ m

Remaining wire = 12$\frac{2}{3}$ – 5$\frac{3}{5}$  

We get

= 38 / 3 – 28 / 5

By taking LCM, we get

= (190 – 84) / 15

= 106 / 15 m

= 7$\frac{1}{15}$ m

Hence, the length of the remaining wire is

7$\frac{1}{15}$m

(1 / 2 + 1 / 3) ÷ (1 / 4 – 1 / 6)

The given expression can be simplified as follows

(1 / 2 + 1 / 3) ÷ (1 / 4 – 1 / 6) = [(3 + 2) / 6] ÷ [(3 – 2) / 12]

On further calculation, we get

= (5 / 6) ÷ (1 / 12)

= 5 / 6 × 12 / 1

= 5 × 2

= 10

Hence, the simplified form of the given expression is 10

Given,

Weight  = 112 g

Weight of copper = 5 / 14 of 112 g

Weight of copper = 5 / 14 × 112

We get,

= 40 g

Weight of gold = 112 – 40

= 72 g

Hence, the weight of gold in ornament is 72 g

Given,

Weight of an ornament = 63 g

Weight of copper = 4 / 9 of 63 g

Weight of copper = 4 / 9 × 63

We get,

= 28 g

Weight of gold = 63 – 28

= 35 g

Hence, the weight of gold in ornament is 35 g

Given

Women spends 7 / 9 of her money

Let us assume she has Rs 1

Amount spent = 7 / 9 of 1

Amount left = 1 – 7 / 9

We get,

= (9 – 7) / 9

= Rs 2 / 9

Since 2 / 9 of her total money = Rs 1710

∴ Total money = Rs (1710 × 9) / 2

= Rs 15390 / 2

= Rs 7695

Hence, the total money she had was Rs 7695.

7 / 20 of (1 / 3 + 5 / 12) ÷ (5 / 8 – 1/ 4)

The given expression can be simplified as below

7 / 20 of (1 / 3 + 5 / 12) ÷ (5 / 8 – 1 / 4) = 7 / 20 of [(4 + 5) / 12] ÷ [(5 – 2) / 8]

We get

= 7 / 20 of (3 / 4) ÷ (3 / 8)

= 7 / 20 × 3 / 4 × 8 / 3

= 7/ 5

Hence, the simplified form of the given expression is 7 / 5.

Given,

Half of work is done on Monday and one-fifth on Tuesday

Let total work done by a boy is 1

Work done on Monday = 1 / 2

Work done on Tuesday = 1 / 5

Hence, remaining work done on Wednesday to complete the work is calculated as below

Remaining work done = 1 – [(1 / 2 + 1 / 5)]

Taking LCM, we get

= 1 – [(5 + 2) / 10]

= 1 – 7 / 10

= (10 – 7) / 10

= 3 / 10

Hence, work done by the boy on Wednesday to complete the entire work is is 3 / 10.

Given,

Half of work is done on Friday and one-fourth on Saturday by Amit

Let total work done by Amit is 1

Work done on Friday = 1 / 2

Work done on Saturday = 1 / 4

Hence, remaining work done on Sunday to complete the work is calculated as below

Remaining work done = 1 – [(1 / 2 + 1 / 4)]

Taking LCM, we get

= 1 – [(2 + 1) / 4]

= 1 – (3 / 4)

= (4 – 3) / 4

= 1 / 4

Hence, work done by Amit on Sunday to complete the entire work is is 1 / 4.

2$\frac{4}{5}$ and 5 / 6

The given fractions are 14/8 and 5/6 

LCM of 5 and 6 is 30.

= (84 + 25)/30

109/30

= 3$\frac{19}{30}$

Hence, 3$\frac{19}{30}$    is the addition of the given fractions.

Total number of children = 35

Number of senior citizens = 3 / 8

Let us assume the total number of people be x

Total number of senior citizens   = 3 / 8 of x

We get,

= 3x / 8

According to question, total number of people can be calculate as below

x – 3x/8 = 35

⇒ (8x – 3x)/8 = 35

⇒ 5x/8 =35

⇒ X = 35 X 8 / 5

⇒ 56

= 56 – 35

= 21

Hence, the total number of senior citizens  is 21.