20 minutes, then stopMaths A (practice)Tue 13 October1 / 4
Long division by two digits
Estimate, multiply, subtract. What the remainder means depends on the story
Name Date
How to make the estimateRound the divisor to a multiple of ten and ask "how many of those fit into the number?"
Then multiply, subtract. The remainder you are left with is always smaller than the divisor.
Question 1 is already done for youWork out 236 ÷ 38.
① Round 38 to 40. 236 is about six 40s → estimate 6
② 38 x 6 = 228
③ 236 − 228 = 8 (smaller than 38, so OK)
④ Answer 6 remainder 8 Check 38 x 6 + 8 = 236
Your turn from here
2Work out 365 ÷ 52 in long division. First round 52 to a multiple of ten and make your estimate.
52 → 50. 365 is about seven 50s.
3Work out 782 ÷ 31 in long division. The answer has two digits.
4Work out 645 ÷ 27 in long division, then check it: divisor x quotient + remainder.
If the check is not 645, go back and redo it.
When the estimate is offThe product is bigger than the number being divided → the quotient is too big. Take 1 off.
The remainder is the divisor or more → the quotient is too small. Raise it.
An estimate may miss. Fix it and the answer still comes out right.
5In 170 ÷ 28 you round 28 to 30 and guess 5. Take 28 x 5 away from 170: what is left? Is 5 right? Write the correct quotient and remainder.
If the remainder is 28 or more, the quotient is too small.
6In 150 ÷ 22 you round 22 to 20 and guess 7. What is 22 x 7? Is it bigger than 150? Write the correct quotient and remainder.
If you cannot take it away from 150, the quotient is too big.
What to do with the remainder
7135 pupils go out by bus. One bus holds 42. How many buses are needed?
With 3 buses, some people are left behind.
8There are 300 mandarins. 18 go into each box. How many full boxes of 18 can you make, and how many mandarins are left over?
Count only the boxes that hold exactly 18.
9Someone answered 143 ÷ 26 as "4 remainder 39". 26 x 4 + 39 does make 143. It is still wrong. Say what is wrong and write the correct answer.
Remember: the remainder is smaller than the divisor.
10150 ÷ 24 = 6 remainder 6. Write the answer to each of A to C.
A A car seats 24; 150 people ride. How many cars?
B Boxes of 24 are made from 150 sweets. How many boxes can you make?
C A 150 cm string is cut into 24 cm pieces. How many pieces, and how many cm are left?
Same sum, different answer — the story decides.
11A 4 m 50 cm tape is cut into 35 cm pieces. How many pieces, and how many cm are left?
Use cm first: 4 m 50 cm = 450 cm.
12Find the number in the box: □ ÷ 23 = 15 remainder 8.
□ = divisor x quotient + remainder (the check, used backwards)
13When you divide by 27, the remainder can be anything from 0 up to what? And which number gives quotient 12 with the largest possible remainder when divided by 27?
The largest remainder = divisor − 1