Division as repeated subtraction

Remember how MULTIPLICATION is repeated addition: 5 × 4 = 4 + 4 + 4 + 4 + 4 = 20. Let's draw one group of four... Draw another group of four to the picture. And another group. And another group. And yet one more group. | | | | You drew or added __ groups of four.

Let's reverse the process.  You start out with 20 sticks. Make one group of four.  In your mind, "move it away" from the picture. Form another group of four.  Again, "move it away" in your mind, or subtract it from the picture.  Keep forming groups of four till you have none left. How many groups did you make?  ___  | | | | | | | | | | | | | | | | | | | |  20 − 4 − 4 − 4 − 4 − 4 = 0 This is repeated subtraction.  You subtract 4 repeatedly, or many times, till you hit zero.  Each subtraction is forming a group of 4.  How many groups did you form?  How many times did you subtract?  That is the answer to the division problem 20 ÷ 4.

Try it yourself: Separate groups, but in your mind 'move them away' or subtract.

42 ÷ 3

| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | 42 ÷ 14

DIVISION is repeated subtraction: 20 ÷ 4 = ?? 20 − 4 − 4 − 4 − 4 − 4 = 0.I subtracted 4 five times, so 20 ÷ 4 = 5. 84 ÷ 21 = ?? 84 − 21 1 63 − 21 1 42 − 21 1 21 − 21 1 0 4 I subtracted 21 four times,  so 84 ÷ 21 = 4

Often, it is handier to actually add instead of subtract: Since 13 + 13 = 26, 13 goes to 26 two times. So 26 ÷ 13 = 2 Since 21 + 21 + 21 + 21 = 84, 21 goes to 84 four times. So 84 ÷ 21 = 4

Example problems

1.  Write a multiplication sentence AND a division sentence that fits the addition/subtraction facts.

5 + 5 + 5 = 15 15 − 5 − 5 − 5 = 0 __ ÷ __ = __ __ ÷ __ = __	12 + 12 + 12 + 12 = 48 48 − 12 − 12 − 12 − 12 = 0 __ ÷ __ = __ __ ÷ __ = __
23 + 23 + 23 = __ __ − 23 − 23 − 23 = 0 __ ÷ __ = __ __ ÷ __ = __	40 + 40 = __ __ − 40− 40 = 0 __ ÷ __ = __ __ ÷ __ = __

2.  Write a subtraction sentence for each division sentence.

45 ÷ 15 = __ 45 −

32 ÷ 8 = __ 32 −