Year 6 · Addition, subtraction, multiplication and division
Add and subtract whole numbers
Learn how to calculate with all four operations, using long multiplication and long division, factors, multiples and primes, and the right order for mixed calculations.
Definition
By the end of Year 6 you can use all four operations and choose the best method for the numbers in front of you. Written column methods handle the large numbers: long multiplication and long division are the new ones this year. Knowing your factors, multiples, primes, squares and cubes helps you spot shortcuts, and the order of operations tells you which part of a mixed calculation to work out first.
Why Do I Have to Learn This?
Subtracting tells you what is left, what has changed, and how far apart two numbers are. You use it every time you spend money or count down to something.
Key Rules:
- 1. Add and subtract whole numbers in columns with the place values lined up, or in your head when the numbers allow, and round to estimate so you know roughly what to expect.
Remember:
- •Estimate first, choose the written method the numbers need, then check the answer against your estimate.
Don’t Forget...
- •Leaving out the zero on the tens row of a long multiplication. Multiplying by the 2 in 28 is really multiplying by 20, so without the zero that row is ten times too small and the final total falls far short.
- •Working a mixed calculation from left to right, so 3 + 4 x 5 becomes 35. Multiplication is done before addition, so 4 x 5 = 20 comes first and the correct answer is 3 + 20 = 23.
- •Mixing up factors and multiples. The factors of 12 divide into it, so 1, 2, 3, 4, 6 and 12; the multiples of 12 come from its times table, so 12, 24, 36 and onwards, and only 12 itself is both.
Difference
The result of a subtraction, a − b: how far apart two numbers are.
The difference between 10 and 6 is 4.
Worked Example:
A stadium has 2739 seats in each block and there are 28 blocks. How many seats are there altogether?
Estimate first: 2739 is close to 3000 and 28 is close to 30, so the answer should be a little under 90000.
Multiply by the ones digit: 2739 x 8 = 21912.
Multiply by the tens digit: write a zero in the ones column, then 2739 x 2 tens gives 54780.
Add the two rows: 21912 + 54780 = 76692.
Check against the estimate: 76692 sits just under 90000, which fits because both numbers were rounded up.
Answer: 76692 seats
Why It Works:
Long multiplication works because 28 lots of a number is 20 lots plus 8 lots, so the two rows are the two parts of one product. Long division runs the same idea in reverse, sharing out the thousands, then hundreds, then tens, then ones, and carrying anything left over into the next column. Place value makes both methods safe, because every carried amount is worth exactly ten of the column to its right.
Another Example:
A charity has £8532 to share equally between 12 local schools. How much money does each school receive?
Divide 85 by 12: 12 x 7 = 84, so write 7 and carry the remainder 1.
Bring down the 3 to make 13: 12 goes in once with remainder 1.
Bring down the 2 to make 12: 12 goes in exactly once, so nothing is left over.
Check with the inverse: 711 x 12 = 8532.
Answer: £711 each
Animated Example:
Free Add and subtract whole numbers Worksheet
Download free worksheets and practise today.
Every download has a fresh set of questions.
Before this: Addition and subtraction (Year 5) · Next: Four operations (Year 7)
Let’s Practise the Concept
Step 1 of 3
Jump along the line
Start at 6 and jump on 49. Tap where you land.
Tap the line where 6 + 49 belongs.