DIVISION 10 ÷ 2 = 5 Quotient LET’S LEARN Dividend Divisor LET’S LEARN Division is an operation in which the result indicates how many groups have been separated. The numbers that are divided have special names. Look at the illustration above. Division can be written horizontally or vertically. Long division needs to be written vertically, though.

10 ÷ 2 = 5 THE DIVIDEND TELLS US HOW MUCH OF AN OBJECT WE HAVE. THE DIVISOR TELLS US HOW MANY GROUPS WE’LL BE DIVIDING INTO. THE QUOTIENT IS THE CUANTITY THAT REMAINS IN ONLY ONE GROUP.

We say , “Four divided by two”. HORIZONTALLY 4 ÷ 2 We say , “Four divided by two”. This means that the FOUR is separated INTO TWO GROUPS. The result is the amount contained in ONE GROUP. 4 Stars 2 Groups

Now we place the same amount of stars in each group. 4 ÷ 2 Now we place the same amount of stars in each group.

We continue placing the same amount of stars in each group. 4 ÷ 2 We continue placing the same amount of stars in each group. 1 1

4 ÷ 2 4 ÷ 2 = 2 The result is the amount contained in only one group. Therefore, the result is 2. 4 ÷ 2 = 2 1 2 1 2

We say , “Nine divided by three”. HORIZONTALLY 9 ÷ 3 We say , “Nine divided by three”. This means that the NINE is separated INTO THREE GROUPS. The result is the amount contained in ONE GROUP. 9 Cubes 3 Groups

Now we place the same amount of cubes in each group. 9 ÷ 3 Now we place the same amount of cubes in each group.

We continue placing the same amount of cubes in each group. 9 ÷ 3 We continue placing the same amount of cubes in each group. 1 1 1

We continue placing the same amount of cubes in each group. 9 ÷ 3 We continue placing the same amount of cubes in each group. 1 2 1 2 1 2

9 ÷ 3 9 ÷ 3 = 3 The result is the amount contained in only one group. Therefore, the result is 3. 9 ÷ 3 = 3 1 2 3 1 2 3 1 2 3

PRACTICE Find the quotient. 10 ÷ 5 = 12 ÷ 4 = 18 ÷ 6 =

ANSWER 10 ÷ 5 = 2 12 ÷ 4 = 3 18 ÷ 6 = 3

PRACTICE Find the quotient. 15 ÷ 3 = 16 ÷ 4 = 14 ÷ 2 =

ANSWER 15 ÷ 3 = 5 16 ÷ 4 = 4 14 ÷ 2 = 7

0 ÷ 3 = 0 DIVIDING WITH ZERO 20 ÷ 0 = NOT POSSIBLE Zero can be divided by any number. The quotient (result) is ALWAYS zero. NO NUMER can be divided by ZERO. This means you will be dividing the number into zero groups. It isn’t possible! 20 ÷ 0 = NOT POSSIBLE

THE SMALLEST WHOLE NUMBER WE CAN DIVIDE BY IS 1. 5 ÷ 1 = FIVE DIVIDED BY ONE 5 ÷ 0 = FIVE DIVIDED BY ZERO Observe that there is 1 group where 5 objects can be placed. 5 ÷ 1 = 5 Observe that there is no group to place five objects in. ? 5 ÷ 0 = NOT POSSIBLE

PRACTICE Find the quotient. 8 ÷ 2 = 0 ÷ 4 = 14 ÷ 0 =

ANSWER 8 ÷ 2 = 4 0 ÷ 4 = 0 14 ÷ 0 = NOT POSSIBLE

10 ÷ 2 24 8 DIVISION CAN BE WRITTEN IN 3 FORMS. DIVISOR DIVIDEND

LET’S LEARN Long division is written vertically. We go through a repetitive process of dividing, multiplying, subtracting, and comparing. Find the quotient. 496 ÷ 8 = 1st STEP Place the dividend inside the division box. The divisor is always placed outside. 8 4 9 6

2nd STEP 8 4 9 6 Now we see if the 8 fits into the first digit, the 4. Since 8 does not fit into four, we place a zero on top of it. 3rd STEP We move on to the next digit combining it with the previous number. Here we see that 8 does fit into 49. 8 4 9 6

6 8 4 9 - 4 1 We begin the repetitive process: 1. Divide: 49 ÷ 8 = 6 2. Multiply : 6 X 8 = 48 3. Subtract: 49 – 48 = 1 4. Compare: 1 < 8 (THIS STEP IS IMPORTANT BECAUSE THE RESULT OF THE SUBTRACTION, THE DIFFERENCE, HAS TO BE LESS THAN THE DIVISOR.)

Then we bring down the next digit and continue the repetitive process. Quotient 6 2 8 4 9 - 4 1 - 1 Remainder Then we bring down the next digit and continue the repetitive process. 1. Divide: 16 ÷ 8 = 2 2. Multiply: 2X 8 = 16 3. Subtract: 16 – 16 = 0 4. Compare: 0 < 8 That is, 496 ÷ 8 = 62 The result can be checked by doing the inverse operations. (Inverse means backward.)

CHECK 1. Multiply the quotient and divisor. 6 2 8 4 9 - 4 1 - 1 1 6 2 x 8 4 9 + 2. Add the remainder. Since the result of the check is 496 (the original dividend), we know our quotient is correct.

LET’S REVIEW Find the quotient. 581 ÷ 3 = 1st STEP Place the dividend inside the division box. 3 5 8 1

2nd STEP 1 3 5 8 - 3 2 Begin the repetitive process: 1. Divide: 5 ÷ 3 = 1 2. Multiply : 1 X 3 = 3 3. Subtract: 5 – 3 = 2 4. Compare: 2< 3

3rd STEP 1 9 3 5 8 - 3 2 - 2 7 Bring down the 8. Continue the repetitive process: 1. Divide: 28 ÷ 3 = 9 2. Multiply : 9 X 3 = 27 3. Subtract: 28 – 27 = 1 4. Compare: 1< 3

4th STEP 1 9 3 5 8 - 3 2 - 2 7 - Bring down the 1. Again, we continue the repetitive process: 1. Divide: 11 ÷ 3 = 3 2. Multiply : 3X 3 = 9 3. Subtract: 11– 9 = 2 4. Compare: 2< 3 Remainder

CHECK 1 9 3 5 8 - 3 2 - 2 7 - 1. Multiply the quotient and divisor. 2 1 9 3 X 5 7 + 8 1 2. Add the remainder. The final answer is 193 R 2.

PRACTICE Find the quotient. 9 1 4 5 2 4 5 8 7 9 2 3

ANSWER 1 6 R1 9 4 5 2 9 4 5 8 1 3 R6 7 9 2

NOW WE ARE READY TO PRACTICE AND ENJOY DIVIDING!