Key Ideas
Conversions: ₹ 1 = 100 paise; 1 m = 100 cm; 1 cm = 10 mm; 1 km = 1000 m; 1 kg = 1000 g; 1 g = 1000 mg; 1 litre (l) = 1000 ml.
Adding: add the smaller units first. If the total reaches the conversion number (100 or 1000), change it into 1 bigger unit and carry it.
Subtracting: if the smaller unit above is too small, borrow 1 bigger unit and change it into 100 or 1000 smaller units.
Speed: distance covered = speed × time. For part of an hour, take that part of the speed (half an hour → half the distance).
Problem Set 46
1Add:
(1) ₹ paise 9 50+ 14 60 23 110 24 10
(2) cm mm 6 5+ 7 9 13 14 14 4
(3) m cm 22 50+ 25 75 47 125 48 25
(4) km m 15 740+ 13 950 28 1690 29 690
(5) kg g 25 650+ 29 770 54 1420 55 420
(6) l ml 19 840+ 25 250 44 1090 45 90
- ₹ 9 and 50 paise + ₹ 14 and 60 paise = ₹ 24 and 10 paise
- 6 cm 5 mm + 7 cm 9 mm = 14 cm 4 mm
- 22 m 50 cm + 25 m 75 cm = 48 m 25 cm
- 15 km 740 m + 13 km 950 m = 29 km 690 m
- 25 kg 650 g + 29 kg 770 g = 55 kg 420 g
- 19 l 840 ml + 25 l 250 ml = 45 l 90 ml
2Subtract:
(1) ₹ paise 18 150 19 50− 12 60 6 90
(2) cm mm 23 12 24 2− 3 8 20 4
(3) m cm 19 130 20 30− 17 60 2 70
(4) km m 39 1255 40 255− 17 960 22 295
(5) kg g 34 1150 35 150− 26 470 8 680
(6) l ml 45 1200 46 200− 38 750 7 450
- ₹ 19 and 50 paise − ₹ 12 and 60 paise = ₹ 6 and 90 paise
- 24 cm 2 mm − 3 cm 8 mm = 20 cm 4 mm
- 20 m 30 cm − 17 m 60 cm = 2 m 70 cm
- 40 km 255 m − 17 km 960 m = 22 km 295 m
- 35 kg 150 g − 26 kg 470 g = 8 kg 680 g
- 46 l 200 ml − 38 l 750 ml = 7 l 450 ml
In every subtraction here, 1 bigger unit is borrowed (the green top line). For example, in (4), 1 km = 1000 m is borrowed: 1000 + 255 = 1255 m.
Problem Set 47
1For his birthday, Ajay gave 20 l 450 ml of milk to the children in an Ashramshala and 28 l 800 ml to the children in an orphanage. How much milk did Ajay donate?
l ml 20 450+ 28 800 48 1250 49 250
Ajay donated 49 l 250 ml of milk.
2Under the Rural Cleanliness Mission, college students cleaned 1 km 750 m of a village road that is 2 km 575 m long. How much remained to be cleaned?
km m 1 1575 2 575− 1 750 0 825
825 m of the road remained to be cleaned.
3Babhulgaon used 21,250 litres of treated waste water in the fields. Samvatsar used 31,350 litres of similar water. How much treated waste water was used in all?
21,250 + 31,350 = 52,600
52,600 litres of treated waste water was used in all.
4If half a litre of milk costs 22 rupees, how much will 7 litres cost?
Cost of 1 litre = 2 × 22 = 44 rupees
Cost of 7 litres = 7 × 44 = 308 rupees
7 litres of milk will cost ₹ 308.
5If the speed of a motorcycle is 40 km per hour, how far will it travel in an hour and a quarter?
In 1 hour: 40 km
In a quarter hour: 40 ÷ 4 = 10 km
Total: 40 + 10 = 50 km
It will travel 50 km.
6If a man walks at a speed of 4 kmph, how long will it take him to walk 3 km?
4 km take 1 hour = 60 minutes
1 km takes 60 ÷ 4 = 15 minutes
3 km take 3 × 15 = 45 minutes
He will take 45 minutes (three quarters of an hour).
7If a rickshaw travels at a speed of 30 kmph, how far will it travel in three quarters of an hour?
In a quarter hour: 30 ÷ 4 = 7.5 km = 7 km 500 m
In three quarters of an hour: 3 × 7 km 500 m = 21 km 1500 m = 22 km 500 m
It will travel 22 km 500 m (22.5 km).
8During Cleanliness Week, children collected three quarter kilograms of plastic bags and five and a half kilograms of other garbage. How much garbage did they collect in all?
Three quarter kg = 750 g; five and a half kg = 5 kg 500 g.
750 g + 5 kg 500 g = 5 kg 1250 g = 6 kg 250 g (or 0.75 kg + 5.50 kg = 6.25 kg).
They collected 6 kg 250 g of garbage.
9If one shirt needs 2 m 50 cm of cloth, how much cloth do we need for 5 shirts?
2 m 50 cm × 5 = 10 m 250 cm = 10 m + 2 m 50 cm = 12 m 50 cm.
We need 12 m 50 cm of cloth.
10If a car travels 60 km in an hour, how far will it travel in (1) 2 hours? (2) 15 minutes? (3) half an hour? (4) three and a half hours?
- 2 hours: 2 × 60 = 120 km
- 15 minutes (a quarter hour): 60 ÷ 4 = 15 km
- Half an hour: 60 ÷ 2 = 30 km
- Three and a half hours: 3 × 60 + 30 = 180 + 30 = 210 km
11If one gold bangle is made from 12 grams 250 milligrams of gold, how much gold will be needed to make 8 such bangles? (1000 mg = 1 g)
12 g × 8 = 96 g
250 mg × 8 = 2000 mg = 2 g
Total: 96 g + 2 g = 98 g
98 grams of gold will be needed.
12How many pouches of 20 g cloves each can be made from 1 kg 240 g of cloves?
1 kg 240 g = 1000 g + 240 g = 1240 g. 1240 ÷ 20 = 62.
62 pouches can be made.
Advertisement
13Seema’s mother bought 2 m 70 cm of cloth for a kurta and 2 m 40 cm for a shirt. How much cloth did she buy in all?
m cm 2 70+ 2 40 4 110 5 10
She bought 5 m 10 cm of cloth in all.
14A water tank holds 125 l of water. If 97 l 500 ml of the water is used, how much water remains in the tank?
l ml 124 1000 125 0− 97 500 27 500
27 l 500 ml of water remains in the tank.
15Harminder bought 57 kg 500 g of wheat from one shop and 36 kg 800 g of wheat from another shop. How much wheat did he buy altogether?
kg g 57 500+ 36 800 93 1300 94 300
He bought 94 kg 300 g of wheat altogether.
16Renu took part in a 100 m race. She tripped and fell after running 80 m 50 cm. How much distance did she have left to run?
m cm 99 100 100 0− 80 50 19 50
She had 19 m 50 cm left to run.
17A sack had 40 kg 300 grams of vegetables. There were 17 kg 700 g potatoes, 13 kg 400 g cabbage and the rest were onions. What was the weight of the onions?
Potatoes + cabbage kg g 17 700+ 13 400 30 1100 31 100
Onions kg g 40 300− 31 100 9 200
The weight of the onions was 9 kg 200 g.
18One day, Gurminder Singh walked 3 km 750 m and Parminder Singh walked 2 km 825 m. Who walked farther and by how much?
km m 2 1750 3 750− 2 825 0 925
Gurminder Singh walked farther, by 925 m.
19Suresh bought 3 kg 250 g of tomatoes, 2 kg 500 g of peas and 1 kg 750 g of cauliflower. How much was the total weight of the vegetables he bought?
kg g 3 250+ 2 500+ 1 750 6 1500 7 500
The total weight was 7 kg 500 g.
20Jalgaon, Bhusawal, Akola, Amravati and Nagpur lie serially on a certain route. Distances from Akola: Amravati 95 km, Bhusawal 154 km, Nagpur 249 km, Jalgaon 181 km. Use them to make word problems and solve the problems.
On the route the order is Jalgaon – Bhusawal – Akola – Amravati – Nagpur. So Jalgaon and Bhusawal are on one side of Akola, and Amravati and Nagpur are on the other.
Problem 1: How far is Bhusawal from Jalgaon?
Jalgaon to Akola − Bhusawal to Akola = 181 − 154 = 27 km.
Problem 2: How far is Nagpur from Amravati?
249 − 95 = 154 km.
Problem 3: A bus goes from Bhusawal to Amravati through Akola. How far does it travel?
154 + 95 = 249 km.
Problem 4: How long is the whole route from Jalgaon to Nagpur?
181 + 249 = 430 km.
Students may frame other problems; the key idea is to add distances on opposite sides of Akola and subtract distances on the same side.
21Complete the following table and prepare the total bill.
| Foodstuff | Weight (kg) | Rate (₹ per kg) | Cost (₹) |
|---|
| Sugar | 2.5 | 32 | 80 (2.5 × 32) |
| Rice | 4.0 | 35 | 140 (4.0 × 35) |
| Chana Dal | 1.5 | 60 | 90 (1.5 × 60) |
| Toor Dal | 3.0 | 70 | 210 (3.0 × 70) |
| Wheat | 7.0 | 21 | 147 (7.0 × 21) |
| Oil | 1.5 | 110 | 165 (1.5 × 110) |
| Total | ₹ 832 |
The total bill is ₹ 832.
For half kilograms: 2.5 kg × 32 = (2 × 32) + (half of 32) = 64 + 16 = 80. Similarly, 1.5 kg × 60 = 60 + 30 = 90 and 1.5 kg × 110 = 110 + 55 = 165.
Activity
APotato vadas, a shadow stick and a pen refill.
- Potato vadas (approximate, for 1 kg potatoes): about 250 g gram flour (besan), 4–5 green chillies, a small piece of ginger, 8–10 garlic cloves, a handful of coriander leaves, mustard seeds, turmeric, salt, and about 500 ml oil for frying. This makes roughly 20–25 vadas. Costs depend on local prices; find them and add them up.
- Shadow stick: of the four times, the shadow is shortest at 12:00 noon, when the sun is highest in the sky. It is longest at 5:00 in the evening, when the sun is lowest. At 9:00 am and 3:00 pm the shadow falls in opposite directions.
- Pen refill: a common ballpoint refill is about 13 cm to 14 cm long. Measure your own with a ruler.
These are practical activities; actual measurements and costs will vary.
