1 · Two questions, one operation
Sharing: 24 pencils shared by 4 kids. How many each? 24 ÷ 4 = 6.
Grouping: 24 pencils, 4 in each box. How many boxes? 24 ÷ 4 = 6. Both questions use the same division.
2 · Division undoes multiplication
72 ÷ 8: ask "8 times what is 72?" 8 × 9 = 72, so 72 ÷ 8 = 9. Each division fact comes from a multiplication fact you already know.
The fact family for 8, 9, 72: 8 × 9, 9 × 8, 72 ÷ 8, 72 ÷ 9.
3 · Dividing by 10 and 100
÷ 10 takes a zero off the end: 340 ÷ 10 = 34. ÷ 100 takes two: 3,400 ÷ 100 = 34.
Multiples of ten: 120 ÷ 40 is "12 tens ÷ 4 tens" = 3.
4 · Remainders
30 ÷ 7: 7 × 4 = 28 fits, 7 × 5 = 35 is too big. So 4 groups, and 30 − 28 = 2 left over. We write 4 R2.
The remainder is always smaller than the divisor. If it is not, you can make another group.
5 · Long division: two digits
84 ÷ 6. Divide the tens: 8 ÷ 6 goes 1 time (write 1 on top), 1 × 6 = 6, 8 − 6 = 2. Bring down the 4: 24.
Divide: 24 ÷ 6 = 4 (write 4 on top), 4 × 6 = 24, 24 − 24 = 0. Answer 14, no remainder.
6 · Long division: three digits
136 ÷ 8. 1 ÷ 8 does not go, so use 13: 13 ÷ 8 = 1, 1 × 8 = 8, 13 − 8 = 5. Bring down the 6: 56.
56 ÷ 8 = 7, 7 × 8 = 56, 56 − 56 = 0. Answer 17.
7 · Long division with a remainder
94 ÷ 9. 9 ÷ 9 = 1, 1 × 9 = 9, 9 − 9 = 0. Bring down 4: 4 ÷ 9 does not go, write 0 on top. Remainder 4.
Answer: 10 R4. Check: 10 × 9 + 4 = 94.
8 · Check by multiplying back
Quotient × divisor + remainder should give the number you started with. 136 ÷ 8 = 17: check 17 × 8 = 136 ✓.
30 ÷ 7 = 4 R2: check 4 × 7 + 2 = 30 ✓. Check your answer this way on a test. It only takes a few seconds.
9 · "How many are left over?"
"72 eggs are packed into boxes of 7. How many eggs are left over?" The question wants the remainder: 72 ÷ 7 = 10 R2. Answer: 2 eggs.
Read the question twice to see whether it wants the quotient or the remainder.
10 · "How many buses?" Round up
"118 children go on a trip. Each bus holds 9. What is the least number of buses?" 118 ÷ 9 = 13 R1. 13 buses leave 1 child behind, so you need 14.
When a remainder means "someone is left out," add one more group.
11 · Sharing money and measures
"$150 for tickets at $25 each. How many tickets?" 150 ÷ 25 = 6. Count by 25s: 25, 50, 75, 100, 125, 150.
"A 6 m wall, tiles 40 cm wide." Change to the same unit: 600 cm ÷ 40 = 15 tiles.
12 · Two steps with division
"200 stickers shared by 8 children, then each child gives away 5." 200 ÷ 8 = 25 each, then 25 − 5 = 20.
Write the first answer down before the second step.
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