Year 5 · Short Division and Remainders · Summary

Year 5 Short Division and Remainders: summary and key words

Part of the Year 5 short division and remainders chapter. Chapter overview · whole chapter on one page

Chapter summary

Skill	Method
Divide by 10, 100, 1,000	Every digit moves 1, 2 or 3 places to the RIGHT. Fill empty places with zeros. The decimal point does not move: 4.7 ÷ 10 = 0.47 and 35 ÷ 1,000 = 0.035.
Known facts and zeros	Use 42 ÷ 6 = 7 to get 4,200 ÷ 6 = 700 and 4,200 ÷ 60 = 70. Take the same number of zeros off both, then put back what is left.
Inverse and fact families	7 × 80 = 560 gives 560 ÷ 7 = 80 and 560 ÷ 80 = 7. The product is the number you divide.
Mental strategies	÷ 2 halve; ÷ 4 halve twice; ÷ 8 halve three times; ÷ 5 double then ÷ 10; ÷ 20 ÷ 10 then halve; ÷ 25 double twice then ÷ 100; split the divisor into factors; chunking.
Short division (bus stop)	Start on the left. Divide each digit plus any carry. Write the answer above. Exchange the remainder for the next place and carry it. Write 0 when a digit is too small. Check: answer × divisor (+ remainder).
Remainders	The remainder is smaller than the divisor. Round UP for “how many needed”, round DOWN for “how many full”, use the remainder for “how many left over”. 7 ÷ 2 = 3 r 1 = 3½ = 3.5.
Estimating and checking	Round to a number the divisor goes into easily. Multiply back to check.
Sharing, grouping, scaling	Sharing: you know the number of groups. Grouping: you know the size of each group. “A fifth as long”: ÷ 5. “How many times as long”: longer ÷ shorter.
Rates	“Per” means divide: 392 km in 7 hours is 56 km per hour. Price of one = total ÷ number. Divide both amounts by the same number to scale down.
Order of operations	Brackets first, then × and ÷ (left to right), then + and − (left to right): 24 + 36 ÷ 4 = 33.
The equals sign	It means “is the same value as”. Work out the side you can, then use an inverse operation to find the missing number: 56 ÷ 7 = 4 × [2].
Reasoning	Spot the mistake by doing it yourself. “Prove it” needs working and a sentence. One counter-example breaks “always”. Puzzles: list the possibilities and cross out.

Can you…?

I can divide whole numbers and decimals by 10, 100 and 1,000 by moving the digits to the right.
I can use known facts, place value and the inverse of multiplication to divide in my head.
I can halve, and use halving, doubling and factors to divide by 4, 5, 8, 20 and 25.
I can divide a number with up to 4 digits by a one-digit number using short division.
I can exchange remainders across place values and write a 0 in the answer when I need to.
I can decide whether to round a remainder up or down, use it as the answer, or write it as a fraction or decimal.
I can estimate and check a division by multiplying back.
I can solve sharing, grouping, scaling and rate problems.
I can use the order of operations and understand the equals sign.
I can solve multi-step problems with bar models and explain my reasoning.

Key terms

Divide: To split an amount into equal parts or groups. Division is the inverse of multiplication.
Divisor: The number you divide by. In 56 ÷ 7 the divisor is 7.
Quotient: The answer to a division. In 56 ÷ 7 = 8 the quotient is 8.
Remainder: The amount left over when a number does not divide exactly, written r. 47 ÷ 5 = 9 r 2.
Short division: A written method for dividing by a one-digit number, also called the bus stop method.
Exchange: To swap one place value for ten of the next smaller one, such as 1 hundred for 10 tens.
Place holder: A zero that keeps the other digits in the right columns, such as the 0 in 1,014.
Inverse: The opposite operation. Multiplying and dividing are inverses of each other.
Fact family: A set of multiplication and division facts that use the same three numbers.
Halve: To divide by 2.
Factor: A whole number that divides exactly into another number.
Sharing: Splitting an amount into a known number of equal groups to find the size of each group.
Grouping: Finding how many groups of a given size can be made.
Rate: A comparison of two amounts, such as £12 for 4 pens or 60 km each hour.
Per: A word that means “for each”. It shows a division, such as 56 km per hour.
Scaling: Making an amount bigger or smaller, such as “a fifth as long”.
Estimate: An answer that is close, found by rounding. Written with ≈.
Order of operations: The rules for which part of a calculation to do first: brackets, then × and ÷, then + and −.
Brackets: Symbols ( ) that show which part of a calculation to do first.
Equals sign: The symbol = which means “is the same value as”. Both sides must balance.
Counter-example: One example that shows a statement is false.