Multiplication facts: 2, 5 & 10
Theory
Multiplication facts for 2, 5 and 10 are a Year 3 maths skill: multiplying by 2 is the same as doubling, multiplying by 5 means skip counting in fives, and multiplying by 10 means counting in tens. This page shows the facts with arrays and number lines, explains the patterns in the multiples, uses the 10 facts to work out the 5 facts, and shows how to find a missing number. The 2 facts are revised from Year 2 (Level 2 in the Victorian Curriculum). Curriculum: VC2M3A03 / AC9M3A03.
Multiplication is a fast way to count equal groups. The fact \(a \times b\) means \(a\) groups of \(b\). You can find the answer by skip counting — adding the same number again and again.
Times 2 is the same as doubling: \(2 \times 6 = 6 + 6 = 12\). Times 5 means skip count by fives: \(5,\ 10,\ 15,\ 20\). Times 10 means skip count by tens: \(10,\ 20,\ 30,\ 40\).
The 5 facts and the 10 facts are linked, because 5 is half of 10. So \(5 \times 3 = 15\) is half of \(10 \times 3 = 30\). Knowing one helps you find the other.
These facts and patterns are worth learning by heart. Notice how the answer grows as the group size grows.
| \(n\) | \(2 \times n\) | \(5 \times n\) | \(10 \times n\) |
|---|---|---|---|
| 1 | 2 | 5 | 10 |
| 2 | 4 | 10 | 20 |
| 3 | 6 | 15 | 30 |
| 4 | 8 | 20 | 40 |
| 5 | 10 | 25 | 50 |
| 6 | 12 | 30 | 60 |
| 7 | 14 | 35 | 70 |
| 8 | 16 | 40 | 80 |
| 9 | 18 | 45 | 90 |
| 10 | 20 | 50 | 100 |
How to work out a 2, 5 or 10 fact
- Read the fact. The first number is how many groups; the second is how many are in each group.
- Pick a way to count. For times 2, double the number. For times 5, count in fives. For times 10, count in tens.
- Count the groups. Skip count once for each group, then read the number you land on. That is the answer.
Finding a missing number
For \(\square \times 10 = 60\), count in tens until you reach 60: \(10,\ 20,\ 30,\ 40,\ 50,\ 60\). That is 6 jumps, so the missing number is 6. The same idea answers questions like "how many bags of 5 make 25?".
The next multiple
To find the next multiple of 5 after a number, count up to the next number that ends in 0 or 5. The next multiple of 5 after 23 is 25, and the next one after 26 is 30. For 10, count up to the next number ending in 0.
Skip count by fives, seven times.
| \(5,\ 10,\ 15,\ 20,\ 25,\ 30,\ 35\) | ||
| \(5 \times 7\) | \(=\) | \(35\) |
The answer is \(35\).
Double means times 2, so add 9 to itself.
| \(2 \times 9\) | \(=\) | \(9 + 9\) |
| \(2 \times 9\) | \(=\) | \(18\) |
Double \(9\) is \(18\).
| \(5\text{ jumps of }10\) | \(\to\) | \(50\) |
| \(10 \times 5\) | \(=\) | \(50\) |
The jumps land on \(50\).
Because 5 is half of 10, the answer is half of the ten fact.
| \(5 \times 4\) | \(=\) | \(\text{half of }40\) |
| \(5 \times 4\) | \(=\) | \(20\) |
So \(5 \times 4 = 20\).
Common pitfalls
Frequently asked questions
What are the 2, 5 and 10 times tables?
They are the multiplication facts for 2, 5 and 10. Times 2 doubles a number, times 5 counts up in fives, and times 10 counts up in tens. For example \(2 \times 3 = 6\), \(5 \times 3 = 15\) and \(10 \times 3 = 30\).
How do you multiply by 5?
Skip count by fives. For \(5 \times 7\), count \(5, 10, 15, 20, 25, 30, 35\), which is \(35\). Every answer in the 5 facts ends in 0 or 5.
Is multiplying by 2 the same as doubling?
Yes. Multiplying by 2 means adding a number to itself, which is doubling. Double \(9\) is \(9 + 9 = 18\), the same as \(2 \times 9\).
How can I use the 10 facts to work out the 5 facts?
Because 5 is half of 10, the 5 facts are half of the 10 facts. If \(10 \times 4 = 40\), then \(5 \times 4\) is half of \(40\), which is \(20\).
How can you tell if a number is a multiple of 5?
A multiple of 5 always ends in 0 or 5, such as \(35\), \(60\) and \(85\). A multiple of 10 always ends in 0, such as \(60\) and \(90\).
How do you skip count on a number line?
Start at \(0\) and make equal jumps of the same size, counting each jump. Five jumps of \(10\) land on \(50\), which shows \(10 \times 5 = 50\). Count the jumps, not the marks.