Before this page: know how to multiply and divide by powers of ten, and know basic multiplication and division facts.
One fact, related calculations
Knowing 43 × 26 = 1,118 saves us doing several other multiplications. If one factor becomes ten times smaller and the other stays the same, the product becomes ten times smaller too.
For 4.3 × 26, compare each value with the given calculation:
- The first factor 43 → 4.3 Divided by 10.
- The second factor 26 → 26 Unchanged.
- The product 1,118 → 111.8 Divided by 10 as well.
Changing the factors
Write each change beside the number it affects, ÷ 10 beside 43 → 4.3 and unchanged beside 26, so the product's change is read off before its decimal point is placed.
A tenth of a tenth is a hundredth, so ÷ 10 on both factors is ÷ 100 on the product: 1,118 → 11.18.
product change = first-factor change × second-factor change
An unchanged factor contributes ×1.
Reversing a multiplication
Every multiplication fact gives two division facts. From 43 × 26 = 1,118 come:
To find a quotient, form the related multiplication fact first, then read it backwards:
Same product, smaller divisor
4.3 × 260 = 1,118
4.3 is one tenth of 43. To keep the product at 1,118, the other factor must be ten times 26.
1,118 ÷ 4.3 = 260
Product and divisor both smaller
43 × 2.6 = 111.8
2.6 is one tenth of 26 and 111.8 is one tenth of 1,118, so the other factor stays 43.
111.8 ÷ 2.6 = 43
Finding a missing value
Use multiplication to undo division, and division to undo multiplication. Then compare the numbers with the given fact, 43 × 26 = 1,118. For example, 4.3 is one tenth of 43, while 260 is ten times 26.
Find the missing dividend in ? ÷ 4.3 = 260
Missing dividend
Identify the missing dividend
The divisor is 4.3 and the quotient is 260.
Find the missing factor in ? × 2.6 = 11.18
Missing factor
Identify the missing factor
The product is 11.18 and the known factor is 2.6.
Explore related calculations
Whichever two are scaled, the third is fixed by them:
Given 43 × 26 = 1,118
430 × 26 = 11,180
The first factor is multiplied by 10 and the second factor is unchanged, so the product is multiplied by 10.
Key points
- Track what happens to each factor; combine the scale changes to find the product.
- Division reverses multiplication, so one product fact also gives two division facts.
- Undo the stated operation to find a missing value.