Simplifying multiplication and division using multiples of 10 | Maths

Starter quiz

Select all the calculations which have a negative answer.
- $(-37)\times92$ ✓
- $(-37)\times(-92)$
- $(-92)\times37$ ✓
- $(-92)\times(-37)$
Work out: $(-4)\times(-6)=$ ______
- '24' ✓
Match each multiplication to the correct product.
- $3\times(-8)$
  
  ⇔
  
  $(-24)$ ✓
- $(-6)\times2$
  
  ⇔
  
  $(-12)$ ✓
- $(-6)\times(-6)$
  
  ⇔
  
  $36$ ✓
- $(-6)\times(-4)$
  
  ⇔
  
  $24$ ✓
- $(-6)\times6$
  
  ⇔
  
  $(-36)$ ✓
- $(-6)\times(-2)$
  
  ⇔
  
  $12$ ✓
Work out: $(-35)\div(-7)=$ ______
- '5' ✓
Select all the correct statements.
- $4\times(-5)\times(-2)=(-40)$
- $(-4)\times5\times(-2)=40$ ✓
- $4\times(-5)\times2=(-40)$ ✓
- $(-4)\times(-5)\times2=(-40)$
- $(-4)\times(-5)\times(-2)=(-40)$ ✓
Work out: $(-100)\div5\div(-2)\div(-5)=$ ______
- '(-2)' ✓

÷ 10 and × 10 are ______ of each other.
- 'inverses' ✓
Complete the statement. Dividing by 10 is equivalent to multiplying by ______.
- '0.1' ✓
Given that the product of 3 and 5 is 15, complete the statement. The product of 0.003 and 500 is __________ 15.
- less than ✓
- equal to
- greater than
Which of the following calculations have the decimal point in the correct place?
- 3.5 × 11.8 = 41.3 ✓
- 35 × 1.18 = 4.13
- 0.35 × 1.18 = 4.13
- 3.5 × 1.18 = 4.13 ✓
Use the multiples of $10^n$ to work out $40\;000 \times 0.002=$ ______
- '80' ✓
Use the multiples of $10^n$ to work out $480\;000 \div 1600 =$ ______
- '300' ✓

Factorising multiples of 10 can scale the calculation to easier values.
It is important to consider place value so answers are scaled back correctly when multiplying.
Factorising multiples of 10 is one of the multiplication and division strategies.

That 0.0004 is one thousand times smaller than 4 as there are three zeros after the decimal point.

The use of a place value or Gattegno chart is invaluable here to highlight this misconception . The 4 is in the 10 thousandths column.

Product - A product is the result of two or more numbers multiplied together.
Partitioning - Partitioning is the act of splitting an object or value down into smaller parts.