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State Board · Class 5 · Mathematics

Lesson 11: Problems on Measurement

5 concepts · 40 practice questions with answers · Free to read

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Length: km, m, cm, mm

From daily life

You walk 500 m to school, a pencil is 15 cm long and the road to the next city is 40 km. We choose a unit that fits the thing we measure.

Simple definition

The units of length are kilometre (km), metre (m), centimetre (cm) and millimetre (mm). 1 km = 1,000 m, 1 m = 100 cm, 1 cm = 10 mm.

Length units from kilometre to millimetre: multiply by 1000, 100 and 10 when moving to the next smaller unit.km× 1,000m× 100cm× 10mmGoing right (to a smaller unit): multiplyGoing left (to a bigger unit): divide

In the figure : Moving to a smaller length unit we multiply by 1000, 100 or 10.

Rule 1: Bigger to smaller: multiply — Multiply by 1000, 100 or 10.

  • Easy : 3 km = 3 × 1,000 = 3,000 m.
  • Medium : 3 km 250 m = 3,000 + 250 = 3,250 m.
  • Exam-type : 2 m 5 cm = 200 + 5 = 205 cm (the 5 cm is not 50).

Rule 2: Smaller to bigger: divide — Divide by 1000, 100 or 10.

  • Easy : 350 cm = 3.5 m.
  • Medium : 6,500 m = 6.5 km and 45 mm = 4.5 cm.
  • Exam-type : Compare 1.2 m, 110 cm, 1 m 15 cm: 120, 110, 115 cm. Order: 110 < 115 < 120.
Live figure

Length: km, m, cm, mm

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Remember

Choose a sensible unit: an ant in mm, a pencil in cm, a room in m, a city distance in km.

Common mistake

Comparing 150 cm and 2 m by looking at 150 > 2. Change both to cm first.

Shortcut

Memory clue: km → m → cm → mm, steps of ×1000, ×100, ×10.

Spot the difference

UnitEqual to
1 km1,000 m
1 m100 cm
1 cm10 mm

Practice questions

Easy
  1. 1Change 3 km to metres.
  2. 2Change 4 m to centimetres.
  3. 3Change 7 cm to millimetres.
Medium
  1. 4Change 6,500 m to km.
  2. 5Change 3 km 250 m to metres.
  3. 6Change 2 m 5 cm to centimetres.
Challenging
  1. 7Arrange from smallest: 1.2 m, 110 cm, 1 m 15 cm.
  2. 8Meena says 150 cm is longer than 2 m because 150 > 2. What is wrong?
Show answers (try them yourself first)
  1. 13,000 m
  2. 2400 cm
  3. 370 mm
  4. 46.5 km
  5. 53,250 m
  6. 6205 cm
  7. 7110 cm, 1 m 15 cm, 1.2 m
  8. 8The units are different. 2 m = 200 cm, so 2 m is longer.

Weight: tonne, quintal, kg, g

From daily life

A shopkeeper weighs sugar in kg, a pinch of salt is in grams, and a truck carries goods in tonnes. Weight has different units for light and heavy things.

Simple definition

1 tonne = 1,000 kg, 1 quintal = 100 kg, 1 kg = 1,000 g. Bigger to smaller: multiply. Smaller to bigger: divide.

Weight units: 1 tonne = 1000 kg, 1 quintal = 100 kg, 1 kg = 1000 g.1 tonne=1,000 kg1 quintal=100 kg1 kg=1,000 g½ kg=500 gBigger → smaller unit: ×

In the figure : Weight units and how they are linked.

Rule 1: Bigger to smaller — Multiply by 1,000 or 100.

  • Easy : 2 kg = 2 × 1,000 = 2,000 g.
  • Medium : 4 quintal = 4 × 100 = 400 kg.
  • Exam-type : 3 kg 250 g = 3,000 + 250 = 3,250 g.

Rule 2: Smaller to bigger — Divide by 1,000 or 100.

  • Easy : 2,500 g = 2 kg 500 g.
  • Medium : 750 kg = 7.5 quintal.
  • Exam-type : A bag holds 25 kg. How many bags make 1 tonne? 1,000 ÷ 25 = 40 bags.
Live figure

Weight: tonne, quintal, kg, g

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Remember

A tonne is a very large weight. 1 tonne = 10 quintals.

Common mistake

Confusing quintal (100 kg) with tonne (1,000 kg).

Shortcut

Memory clue: Kilo = thousand grams; quintal = hundred kilos; tonne = thousand kilos.

Spot the difference

UnitEqual to
1 kg1,000 g
1 quintal100 kg
1 tonne1,000 kg

Practice questions

Easy
  1. 1Change 2 kg to grams.
  2. 2Change 4 quintal to kg.
  3. 3Change 3 tonne to kg.
Medium
  1. 4Change 2,500 g to kg and g.
  2. 5Change 750 kg to quintal.
  3. 6Change 3 kg 250 g to grams.
Challenging
  1. 7A bag holds 25 kg. How many bags make 1 tonne?
  2. 8A farmer says 20 quintal is 2 tonne. Is he right? Explain.
Show answers (try them yourself first)
  1. 12,000 g
  2. 2400 kg
  3. 33,000 kg
  4. 42 kg 500 g
  5. 57.5 quintal
  6. 63,250 g
  7. 71,000 ÷ 25 = 40 bags
  8. 8Yes. 20 quintal = 20 × 100 = 2,000 kg = 2 tonne.

Capacity: litre and millilitre

From daily life

Milk comes in litres and a spoon of medicine is in millilitres. The amount a container holds is its capacity.

Simple definition

1 litre (L) = 1,000 millilitres (ml). Litre to ml: multiply by 1,000. ml to litre: divide by 1,000.

Four bottles of 250 ml together make 1,000 ml, which is 1 litre.250ml250ml250ml250ml4 bottles of 250 ml4 × 250 = 1,000 ml = 1 litre1 l= 1,000 ml

In the figure : Four 250 ml bottles together make 1,000 ml = 1 litre.

Rule 1: Litre and millilitre — Multiply by 1,000 or divide by 1,000.

  • Easy : 3 L = 3,000 ml and 500 ml = 0.5 L.
  • Medium : 1.2 L = 1,200 ml and 2,500 ml = 2 L 500 ml.
  • Exam-type : 5 bottles of 200 ml = 5 × 200 = 1,000 ml = 1 L.

Rule 2: How many small containers? — Divide the big capacity by the small capacity in the same unit.

  • Easy : 2,000 ml ÷ 250 ml = 8 cups.
  • Medium : 1,500 ml ÷ 400 ml = 3 glasses and 300 ml left.
  • Exam-type : 3 bottles of 1.5 L = 3 × 1.5 = 4.5 L = 4,500 ml.
Live figure

Capacity: litre and millilitre

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Remember

Always write the same unit before you divide.

Common mistake

Writing 0.75 L as 75 ml. It is 750 ml.

Shortcut

Memory clue: Litre = 1,000 ml, like kg = 1,000 g.

Spot the difference

UnitEqual to
1 L1,000 ml
500 ml0.5 L
250 ml0.25 L

Practice questions

Easy
  1. 1Change 3 L to ml.
  2. 2Change 500 ml to litres.
  3. 3Change 1.2 L to ml.
Medium
  1. 4Change 2,500 ml to L and ml.
  2. 5How many 250 ml cups fill a 2 L jug?
  3. 6A 1,500 ml jug fills glasses of 400 ml. How many full glasses and how much is left?
Challenging
  1. 73 bottles of 1.5 L each are bought. How many litres and how many ml is that?
  2. 8Ravi writes 0.75 L = 75 ml. Correct him.
Show answers (try them yourself first)
  1. 13,000 ml
  2. 20.5 L
  3. 31,200 ml
  4. 42 L 500 ml
  5. 52,000 ÷ 250 = 8 cups
  6. 63 glasses and 300 ml left.
  7. 74.5 L = 4,500 ml
  8. 80.75 × 1,000 = 750 ml.

Adding and subtracting measures

From daily life

A tailor adds 2 m 70 cm and 1 m 60 cm of ribbon. He first adds the cm, then the metres. When the cm reach 100, they become a metre.

Simple definition

To add or subtract measures, write the same units in the same column. Work with the smaller unit first. If the smaller unit reaches 100 cm or 1,000 g or 1,000 ml, change it to the bigger unit.

Adding 2 m 70 cm and 1 m 60 cm: 130 cm becomes 1 m 30 cm, giving 4 m 30 cm.2 m 70 cm+ 1 m 60 cm4 m 30 cm70 + 60 = 130 cm130 cm = 1 m 30 cm2 + 1 + 1 = 4 mAdd the small unit first; carry when it passes 100 (or 1,000).

In the figure : 3 m 45 cm + 2 m 80 cm: 125 cm is carried as 1 m 25 cm, so the answer is 6 m 25 cm.

Rule 1: Adding measures — Add the small unit, carry to the bigger unit, then add the bigger unit.

  • Easy : 3 m 45 cm + 2 m 80 cm = 5 m 125 cm = 6 m 25 cm.
  • Medium : 4 kg 600 g + 2 kg 700 g = 6 kg 1,300 g = 7 kg 300 g.
  • Exam-type : 2 km 600 m + 1 km 700 m = 3 km 1,300 m = 4 km 300 m.

Rule 2: Subtracting measures — If the top small unit is smaller, borrow from the bigger unit, or change all to the small unit.

  • Easy : 6 m − 2 m 40 cm = 600 − 240 = 360 cm = 3 m 60 cm.
  • Medium : 3 kg 200 g − 1 kg 500 g = 3,200 − 1,500 = 1,700 g = 1 kg 700 g.
  • Exam-type : 7 m 20 cm − 3 m 85 cm = 720 − 385 = 335 cm = 3 m 35 cm.
Remember

Add and subtract the small unit first, in its own column.

Common mistake

Writing 5 m 125 cm as the final answer. 125 cm is more than 1 m; carry it.

Shortcut

Memory clue: Small unit first, carry at 100 or 1,000.

Spot the difference

StepWhat to do
1Write units in columns
2Work on the small unit
3Carry or borrow, then big unit

Practice questions

Easy
  1. 1Add: 3 m 45 cm + 2 m 80 cm.
  2. 2Add: 4 kg 600 g + 2 kg 700 g.
  3. 3Add: 5 L 300 ml + 2 L 450 ml.
Medium
  1. 4Subtract: 6 m − 2 m 40 cm.
  2. 5Subtract: 3 kg 200 g − 1 kg 500 g.
  3. 6Subtract: 5 L − 1 L 250 ml.
Challenging
  1. 7Add: 2 km 600 m + 1 km 700 m.
  2. 8Subtract 7 m 20 cm − 3 m 85 cm and check by adding.
Show answers (try them yourself first)
  1. 16 m 25 cm
  2. 27 kg 300 g
  3. 37 L 750 ml
  4. 43 m 60 cm
  5. 51 kg 700 g
  6. 63 L 750 ml
  7. 74 km 300 m
  8. 83 m 35 cm. Check: 3 m 35 cm + 3 m 85 cm = 7 m 20 cm.

Word problems on measures

From daily life

A tailor needs 1 m 50 cm of cloth for one shirt and wants to stitch 3 shirts. How much cloth should he buy? This is a word problem on measures.

Simple definition

Steps: (1) read and find what is given and what is asked, (2) make all units the same, (3) choose the operation, (4) solve, (5) check if the answer is sensible.

A 24 m rope divided into eight 3 m pieces: 24 divided by 3 is 8.A rope of 24 m cut into 3 m pieces3 m3 m3 m3 m3 m3 m3 m3 m24 m24 ÷ 3 = 8 piecesCheck: 8 × 3 = 24

In the figure : A 30 m rope cut into 5 m pieces gives 30 ÷ 5 = 6 pieces.

Rule 1: Equal groups — Equal groups together: multiply. Sharing or cutting into equal pieces: divide.

  • Easy : 5 packets of 2 kg = 5 × 2 = 10 kg.
  • Medium : 3 shirts of 1 m 50 cm = 3 × 150 = 450 cm = 4 m 50 cm.
  • Exam-type : 30 m rope ÷ 5 m = 6 pieces.

Rule 2: Price and speed — Rate × quantity = total.

  • Easy : ₹ 36 per kg × 4 kg = ₹ 144.
  • Medium : 12 km per litre × 5 litres = 60 km.
  • Exam-type : 5 kg sugar − 1 kg 750 g used = 5,000 − 1,750 = 3,250 g = 3 kg 250 g left.
Remember

Finish by asking: is the answer sensible? A shirt cannot need 50 m of cloth.

Common mistake

Mixing units, like adding 2 kg and 500 g as 502. Change to g or kg first.

Shortcut

Memory clue: Read – same unit – sign – solve – sense check.

Spot the difference

Problem typeUse
Equal groups×
Cutting into pieces÷
Rate and total×

Practice questions

Easy
  1. 15 packets of 2 kg each. How many kg in all?
  2. 2A 30 m rope is cut into 5 m pieces. How many pieces?
  3. 3Sugar costs ₹ 36 per kg. Find the cost of 4 kg.
Medium
  1. 4A scooter runs 12 km on 1 litre. How far on 5 litres?
  2. 5A tailor needs 1 m 50 cm for one shirt. How much cloth for 3 shirts?
  3. 6A jug of 2 L fills glasses of 250 ml. How many glasses?
Challenging
  1. 75 kg sugar is bought and 1 kg 750 g is used. How much is left?
  2. 8A tank holds 5 L 500 ml. Eight glasses of 250 ml are taken out. How much water is left?
Show answers (try them yourself first)
  1. 110 kg
  2. 230 ÷ 5 = 6
  3. 3₹ 144
  4. 460 km
  5. 54 m 50 cm
  6. 62,000 ÷ 250 = 8
  7. 73 kg 250 g
  8. 88 × 250 = 2,000 ml = 2 L. Left: 5 L 500 ml − 2 L = 3 L 500 ml.