Multiplying and Dividing with Groups

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What this lesson covers

  • Multiplying means equal groups. You can add them, or set them out in an array.
  • Dividing means sharing equally, or making equal groups.
  • Each multiplication fact gives two division facts.
  • You cannot divide by zero.
Key idea

Multiplying is equal groups

  • 4 × 3 means 4 groups of 3.
  • Add them: 3 + 3 + 3 + 3 = 12.
  • Or set them out in an array: 4 rows of 3. Count 12.
4 × 3 = 12
4 rows of 3
● ● ●
● ● ●
● ● ●
● ● ●
Key idea

Dividing: sharing and grouping

  • Sharing: 12 pāua shells shared between 3 friends. Each friend gets 4.
  • Grouping: 12 eggs in boxes of 6 fill 2 boxes.
  • Taking away: 12 − 6 − 6 = 0. That is 2 lots of 6.
  • We write these as 12 ÷ 3 = 4 and 12 ÷ 6 = 2.
Key idea

Try it: share into groups

Worked example

Facts to know by heart

  • If you know 4 × 8 = 32, you also know 8 × 4 = 32.
  • And you know 32 ÷ 4 = 8 and 32 ÷ 8 = 4.
×12345678910
22468101214161820
336912151821242730
4481216202428323640
55101520253035404550
88162432404856647280
10102030405060708090100
Worked example

Multiplying a two-digit number

  • 2 × 23: split 23 into 20 and 3.
  • 2 × 20 = 40 and 2 × 3 = 6.
  • 40 + 6 = 46.
SumSplit itAnswer
2 × 232 × 20 = 40, 2 × 3 = 646
3 × 143 × 10 = 30, 3 × 4 = 1242
4 × 214 × 20 = 80, 4 × 1 = 484
Key idea

Try it: split the number

Worked example

Dividing with facts you know

  • Ask: what number times the divisor makes the total?
SumFact you knowAnswer
24 ÷ 33 × 8 = 248
32 ÷ 44 × 8 = 328
30 ÷ 55 × 6 = 306
16 ÷ 22 × 8 = 168
Key idea

You cannot divide by zero

  • 12 ÷ 3: share 12 into 3 groups. Each group has 4.
  • 12 ÷ 0: share 12 into 0 groups. There are no groups to put them in.
  • So dividing by zero is impossible. It has no answer.
  • But 0 ÷ 3 = 0. Share nothing out and everyone gets nothing.

Common mistakes

  • 4 × 3 means 4 + 3 = 7.
    4 × 3 means 4 groups of 3, which is 12.
  • 2 × 23 = 26, doing only 2 × 3.
    Multiply the tens too: 2 × 20 = 40, then 40 + 6 = 46.
  • 12 ÷ 0 = 0.
    You cannot share into zero groups, so 12 ÷ 0 has no answer.
  • 24 ÷ 3 = 21, by taking away 3 once.
    Dividing asks how many 3s make 24. 3 × 8 = 24, so the answer is 8.

Your turn

1

4 × 6

2

8 × 5

3

3 × 21

4

32 ÷ 4

5

18 kiwifruit are shared equally between 3 lunchboxes. How many go in each lunchbox?

Show answer

1. 24 2. 40 3. 63 (3 × 20 = 60, 3 × 1 = 3) 4. 8 5. 6 (18 ÷ 3 = 6, because 3 × 6 = 18)

Summary

What to take away

  • Multiplying is equal groups.
  • Dividing is sharing or grouping, and undoes multiplying.
  • Split big numbers into tens and ones to multiply.
  • Nothing can be divided by zero.
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More in Number

Numbers to 1,000: Hundreds, Tens and OnesNotesCounting in Groups, Rounding and EstimatingNotesSkip Counting, Odd and Even NumbersNotesAdding and Subtracting up to 1,000NotesMultiplying and Dividing with GroupsNotesUnit Fractions: One Equal PartNotesComparing Fractions and Finding Equal OnesNotesAdding Fractions and Finding Fractions of NumbersNotesDollars, Cents and Giving ChangeNotes

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