Place Value and the Four Operations
Place Value and the Four Operations is the Year 6 capstone number topic: reading, writing, ordering and rounding whole numbers up to 10,000,000, and choosing and carrying out the correct written or mental method for addition, subtraction, multiplication and division with increasingly large numbers.
Before you start
Make sure you're comfortable with these topics first:
Method
- Read a large number by splitting it into groups of three digits from the right (millions, thousands, ones), saying each group as you would say a number under 1000.
- Identify the value of any digit by naming its column: ones, tens, hundreds, thousands, ten thousands, hundred thousands, or millions.
- To round a number, find the place value column you are rounding to, look at the digit immediately to its right, and round up for 5 or more, or keep the digit the same for less than 5.
- Before calculating, estimate the answer by rounding each number, so you can spot a wildly wrong answer later.
- Choose the most efficient method for the calculation: known facts or mental strategies for small or friendly numbers, and a formal written method (column addition or subtraction with exchanging, long multiplication, short or long division) for larger or less friendly numbers.
- Carry out the written method carefully, lining up digits by place value and showing every exchange or carried digit.
- Check the final answer using the inverse operation (for example, checking a subtraction by adding the answer back to the number subtracted) or by comparing it with your estimate.
Worked example
A wildlife park had 2,847,516 visitors in one year and 3,192,073 visitors the next year. Work out how many more visitors it had in the second year, and use an estimate to check your answer is sensible.
- Estimate first by rounding each number to the nearest 100,000: 2,847,516 rounds to 2,800,000 and 3,192,073 rounds to 3,200,000.
- Estimated difference: 3,200,000 - 2,800,000 = 400,000.
- Set out the exact subtraction in columns, 3,192,073 - 2,847,516, exchanging between columns wherever a digit on top is smaller than the digit being subtracted below it.
- Working through the columns gives 3,192,073 - 2,847,516 = 344,557.
- Check using the inverse operation: 2,847,516 + 344,557 = 3,192,073, which matches the number you started with, so the answer is correct.
- Compare with the estimate: 344,557 is reasonably close to the estimate of 400,000, confirming the answer is sensible.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1Write the number two million, four hundred and six thousand and eighteen in figures.Show answer
Answer: 2,406,018
Q2What is the value of the digit 7 in the number 3,758,204?Show answer
Answer: 700,000 (it is in the hundred thousands column)
Q3Round 5,482,690 to the nearest 10,000.Show answer
Answer: 5,480,000
Q4A factory produced 128,760 tins of paint in March and 96,485 tins in April. Work out the total number of tins produced across both months.Show answer
Answer: 225,245 tins
Q5A theatre group is arranging 3,200 chairs into rows of 24 for a large performance. How many complete rows can they make, and how many chairs will be left over?Show answer
Answer: 133 complete rows, with 8 chairs left over
Q6Work out 2,847 x 36 using long multiplication.Show answer
Answer: 102,492 (2,847 x 30 = 85,410 and 2,847 x 6 = 17,082, then 85,410 + 17,082 = 102,492)
Q7A company had 5,600,000 pounds in the bank. After paying suppliers 1,875,340 pounds, how much money remains in the bank?Show answer
Answer: 3,724,660 pounds
Exam-style questions
Written in the style of a KS2 Maths exam paper, with a full mark scheme.
A cinema sold 48,350 tickets in the summer holidays and 31,725 tickets in the Easter holidays. Work out the total number of tickets sold across both holidays.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 2 available
A shipping company transported 615,384 containers in one year and 583,940 containers the following year. Round each number to the nearest thousand, then use your rounded values to find the approximate difference between the two years.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
A warehouse receives 27 pallets, each holding 486 boxes. After a delivery of 3,150 boxes is sent out to shops, work out how many boxes remain in the warehouse.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the place value and the four operations worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
Next topics
Not quite what you needed?
Tell us what is missing on place value and the four operations, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.