Maths
What is multiplication?
Quick answer
Multiplication is adding equal groups quickly. 4 × 3 means 4 groups of 3 (or 3 groups of 4), which makes 12. The answer is called the product.
In one sentence
Multiplication is a quick way of adding equal groups: 4 × 3 means 4 groups of 3, which makes 12. The answer is called the product.
Explained
Imagine 4 egg cartons (egg boxes in the UK) with 3 eggs in each. You could add 3 + 3 + 3 + 3, or you could say "4 groups of 3" and write 4 × 3 = 12. The × sign is read as "times" or "multiplied by".
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Arrays: order doesn't matter
Arranging things in rows and columns, called an array, shows something useful: 2 rows of 3 is the same as 3 columns of 2. So 2 × 3 = 3 × 2. You can multiply in either order, which halves the number of facts to learn in your times tables.
Handy facts
- × 10: each digit moves one place to the left, so 7 × 10 = 70 and 45 × 10 = 450 (see place value).
- × 1: the number stays the same.
- × 0: the answer is always 0, because no groups means nothing.
Bigger numbers
Split them up. Worked example: 23 × 4.
- 20 × 4 = 80
- 3 × 4 = 12
- 80 + 12 = 92
This is the area model (the grid method in the UK). It leads on to the standard written method, which the UK calls short and long multiplication (see long multiplication).
Multiplication and division undo each other: if 6 × 4 = 24, then 24 ÷ 4 = 6.
Examples
- 3 × 5 = 15 (three groups of five)
- 9 × 0 = 0
- 16 × 5: 10 × 5 = 50 and 6 × 5 = 30, so 80
- 34 × 12, using the area model:
| × | 30 | 4 |
|---|---|---|
| 10 | 300 | 40 |
| 2 | 60 | 8 |
300 + 40 + 60 + 8 = 408.
Common mistakes
- Mixing up × and +, so 3 × 4 becomes 7. This is the most common slip. Fix: say "three groups of four" out loud and picture them.
- Multiplying only the ones and tens straight down, so 23 × 14 becomes 2 × 1 and 3 × 4, giving 212. Fix: use the area model so every part meets every other part.
- Thinking multiplying always makes a number bigger. Not with 0, 1 or fractions: ½ × 8 = 4.
Quick quiz
Multiplication
Check what you know with 4 quick questions.
Question 1 of 4
Which addition is the same as 5 × 3?
Practise it
Try it
- A pack holds 5 juice boxes. How many are in 6 packs?
- What is 14 × 10?
- Use the area model to work out 32 × 3.
Answers: 1) 30. 2) 140. 3) 30 × 3 = 90 and 2 × 3 = 6, so 96.
Multiplication practice
Practise it step by step in a full course: Grade 4 Maths
For grown-ups
Related topics
Times tables
Times tables are lists of the multiplication facts for a number, such as 3 × 1 = 3 up to 3 × 12 = 36. Knowing them by heart speeds up almost all later maths.
Division
Division is sharing into equal groups, or finding how many groups fit. The sign is ÷, so 12 ÷ 3 = 4. The answer is called the quotient.
Addition
Addition is putting amounts together to find a total. The sign is +, and the answer is called the sum or total, so 4 + 3 = 7.
Factors and multiples
Factors are numbers that divide exactly into a number (the factors of 12 are 1, 2, 3, 4, 6 and 12). Multiples are the numbers in its times table (12, 24, 36…).
Arrays
An array is a set of objects arranged in equal rows and columns. 3 rows of 4 dots is an array that shows 3 × 4 = 12, so arrays help children see multiplication.
Long multiplication
Long multiplication multiplies a big number by splitting the second number into ones, tens and hundreds, finding each part, then adding the results together.