2.FRACTIONS AND DECIMALS

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EXAMPLES

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Chandu’s mother prepared 15 chapaties and served `3/5` of chapaties to Chandu and his sister, `1/5` of chapaties to Chandu’s father. Can you guess how many chapaties remained to Chandu’s mother?

Solution:

Total number of chapaties = 15
No. of chapaties served to Chandu and his sister = `3/5`of 15

=`3/5` × 15 = 3 × 3 = 9

No. of chapaties served to Chandu’s father = `1/5`of 15

=`1/5` × 15 = 1 × 3 = 3

∴ No. of chapaties remained to Chandu’s mother = 15 – (9 + 3)
= 15 – 12 = 3.

In the school out of 180 students, `4/9` of the students are boys. Find the number of girls in the school?

Solution :

Number of students in the school = 180
Part of the boys in the school = `4/9`

Number of boys = `4/9`of 180

=`4/9` × 180 = 4 × 20 = 80

∴ Number of girls = 180 − 80 = 100

If the cost of 22`1/2`kg of apples (a box) in a wholesale market is ₹ 1170, then find the cost of 5kg of apples.

Solution :

Cost of 22`1/2`kg of apples =₹1170

Cost of 1kg of apple = ₹ 1170 ÷ 22`1/2`

=₹ 1170 ÷ `45/2`

= ₹1170 × `2/45`

=₹26 × 2 = ₹52
∴Cost of 5kg of apples = 5 × ₹52 = ₹260

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EXERCISE- 2.1

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1. In Jagananna Gorumudda (MDM) scheme each student got `3/20` kg rice per day, find the weight of the rice required for 60 students in a class per day.

Solution:

The weight of rice for each student =`3/20`kg

Required rice for 60 students =`3/20 × 60`

=3 × 3
=9 kgs

2. What is a perimeter of a equilateral triangle, if each side of a triangle is 5`3/10`cm?

Solution:

Side of triangle = 5`3/10`cm = `53/10`cm

Equilateral triangle has three equal sides. So,
preimeter = 3 × side

=3 ×`53/10 = 159/10 =`15 `9/10`cm

3. Surya can walk `18/5` km in an hour. How much distance will be walk in 2`1/2` hours?

Solution:

The distance Surya walk in 1 hour =`18/5`km

The distance Surya walk in 2`1/2`hours =`18/5`× 2`1/2`

=`18/5×5/2 = 90/10 =`9 km

4. If the length and breadth of a rectangular garden are `27/2`m and `15/2`m respectively, then find the area of the garden.

Solution:

Length of the garden = `27/2`m

Breadth of the garden =`15/2`m

Garden is in the shape of rectangle.
Rectangle area = length × breadth

So, Garden area = `27/2 × 15/2`

=`405/4`= 101`1/4`sq.m.

5. Gopal bought 3`1/2`kg of potatoes in the market. If he paid ₹84, then find the cost of 1kg of potatoes.

Solution:

Cost of 3`1/2`kg. of potatoes = ₹84

Cost of 1 kg. of potatoes = ₹84 ÷ 3`1/2`

= 84 ÷`7/2`

= 84 ×`2/7`= ₹24

6. A car travelled 225 km in 4`1/2` hours with uniform speed.Find the distance travelled in 1 hour.

Solution:

Distance travelled by a car in 4`1/2`hours = 225 km

Distance travelled by car in 1 hour = 225 ÷ 4`1/2`

= 225 ÷`9/2`

= 255 ×`2/9` = 25×2 = 50 km.

7. If 24 students share 4`4/5` kg of cake, then how much cake does each one get?

Solution:

Weight of the cake shared by 24 students = 4`4/5`kg

weight of the cake got by a student = 4`4/5`kg ÷ 24

= `24/5 ÷ 24 =24/5 × 1/24 =1/5`kg

1 kg = 1000gms
∴ weight of the cake got by a student = `1/5×1000 =`200 grams.

8. Adrum contains 210 liters of water. How many times does the boy get the water for watering the plants with 3`1/2` liters of a full bucket from the drum?

Solution:

Water in a drum = 210 ltr
Water in a bucket = 3`1/2`ltr

No. of times the boy get water with a full bucket of water

=210÷3`1/2` =210÷`7/2`

=`210 × 2/7=30×2`=60

Exercise 2 > < Review Exercise