The relationship between multiplying by 0.1 and dividing by 10 | Maths

Starter quiz

There are ______ millimetres in one centimetre.
- '10' ✓
Match the equation to its answer
- 1.2 × 10 =
  
  ⇔
  
  12 ✓
- 10 × 10 =
  
  ⇔
  
  100 ✓
- 4 × 10 =
  
  ⇔
  
  40 ✓
- 4.7 × 10 =
  
  ⇔
  
  47 ✓
- 35 × 10 =
  
  ⇔
  
  350 ✓
- 3.5 × 10 =
  
  ⇔
  
  35 ✓
Match the expression to its answer.
- 10 ÷ 10
  
  ⇔
  
  1 ✓
- 30 ÷ 10
  
  ⇔
  
  3 ✓
- 90 ÷ 10
  
  ⇔
  
  9 ✓
- 25 ÷ 10
  
  ⇔
  
  2.5 ✓
- 3 ÷ 10
  
  ⇔
  
  0.3 ✓
If 3,490 is divided by 10, which digit would be in the ones place after the division?
- 3
- 4
- 9 ✓
- 0
Lucas has 350 marbles. He packs them equally into ten bags. How many marbles are in each bag? ______ marbles.
- '35' ✓
Sofia has 54 cm of ribbon. She cuts it into 10 equal pieces. What is the length of each piece? ______ cm
- '5.4' ✓

Exit quiz

One tenth of 30 kg = ______ kg
- '3' ✓
One tenth of 6 ml = ______ ml
- '0.6' ✓
One tenth of 1.6 m = ______ m
- '0.16' ✓
Match the equation to its answer.
- 600 × 0.1 =
  
  ⇔
  
  60 ✓
- 60 × 0.1 =
  
  ⇔
  
  6 ✓
- 6 × 0.1 =
  
  ⇔
  
  0.6 ✓
- 0.6 × 0.1 =
  
  ⇔
  
  0.06 ✓
- 0.06 × 0.1 =
  
  ⇔
  
  0.006 ✓
The mass of an apple is 210 g. Lucas eats one-tenth of the apple. What is the mass of the apple he has eaten? ______ g
- '21' ✓
Lucas measures the length of a stick to be 18 cm. The length of a twig is one-tenth times this. What is the length of the twig in cm? ______ cm
- '1.8' ✓

Worksheet

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Presentation

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Lesson Details

Key learning points

0.1 can be represented as the fraction 1/10
Multiplying by 0.1 is the same as multiplying by 1/10
Multiplying by 1/10 is the same as dividing by 10
Multiplying by 0.1 is the same as dividing by 10

Common misconception

Children may struggle to make the connection between multiplying by 0.1 and dividing by ten.

When we multiply by 0.1, it is the same as multiplying by one-tenth. When we multiply by a unit fraction, we can divide by the denominator - in this case, 10.

Keywords

Unit fraction - A unit fraction is any fraction with a numerator of one.
Tenth - A tenth is one part in ten equal parts.