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Number Sense and Numeration

Number Sense and Numeration. Dividing Three Digit Numbers by One Digit Numbers . Important information about Dividing. When we divide numbers to find an answer, the answer is called a “ quotient ”

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Number Sense and Numeration

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  1. Number Sense and Numeration Dividing Three Digit Numbers by One Digit Numbers

  2. Important information about Dividing • When we divide numbers to find an answer, the answer is called a “quotient” • This is important to remember because it is different than adding (where the answer is called a “sum”), different than subtracting (where the answer is called the “difference”), and different than multiplying (where the answer is called the “product”) • When we divide numbers that are larger than one digit, we break down the question to make it easier to solve by using “number facts”

  3. How this is Related to Multiplication... • It is still very important to know your multiplication tables at this point in your Math careers, because division is just the backwards version of multiplication • Please take a look at your multiplication table before you complete your work, just for review (you will see why in this PowerPoint)...

  4. What is Division? • We know that when we multiply numbers, we are making them larger, but what happens when we divide numbers? • When we divide, we are trying to split something into equally numbered groups

  5. For Example (an easy one): • Take these 16 apples: • Dividing these 16 apples into 4 equal groups gives you 4 groups of 4 apples • This tells us that 16 4 = 4 • This is dividing a two digit number by a one digit number

  6. Now, let’s look at dividing three digit numbers (dividends) by one digit numbers (divisors) • Today you will learn how to divide a three-digit dividend by a one-digit divisor, to get a quotient without a remainder and with a remainder • Let’s review these terms…

  7. The Parts of a Division Problem • The dividend is the number you are dividing • The divisor is the number you are dividing by • The quotient is the evenly divided result (the answer) • The remainder is what is left over that cannot be evenly divided (sometimes this is not there) • We can write a division problem two different ways: • The first uses the “obelus”( ), which is what we know as the division sign • The second uses the “division bracket” ( )

  8. 136 is the dividend 27 is the quotient 5 is the divisor 1 is the remainder When we write the problem like this:1365= 27, R 1

  9. 1 is the remainder R1 27 5, the divisor, moves to here 27, the quotient,stays here 5 136 136, the dividend, moves here When we write the problem like this:

  10. The 4 Steps to Solving a Division Problem • 1) Find • 2) Multiply • 3) Subtract • 4) Bring down

  11. Find • Start by looking at the first number in the dividend (the number you are dividing) • For example, in 645, the first number is 6 • Find how many times the divisor (the number we’re dividing the dividend by) fits into that number without going higher than the number • For example, if our divisor was 5, then it would only fit into 6 once • Use your knowledge of number facts, or a multiplication table to help you with this

  12. 1 5 675 “Find” – Using a Multiplication Table 1 5 • In the5’s, the number closest to6, but not more than6, is5 • The other factor is 1 • Put a 1above the 6

  13. 1 5 5 675 Multiply • You found 1,multiply it times the divisor, 5 • 1times 5equals 5 • 1X 5= 5 • Put a 5under the 6

  14. 1 5 5 675 Subtract • You got a 5 when you multiplied • Subtract5from 6 – 1 • 6–5= 1 • ***The difference must be smaller than the divisor!!! Otherwise your divisor will fit more times than you have shown and you have to go back and figure it out before moving on***

  15. 1 5 5 675 – 1 Bring down • Bring down the next number in the dividend 7 • The new number you have is 17 • Now start over again with Find for the tens place

  16. 1 6 5 675 – 1 – 7 Now, let’s do the second step 3 • Find: 15is the closest multiple, the other factor you found is 3 • Multiply: 3X 5= 15, put a 15under the 17 15 • Subtract: subtract 15from 1717- 15= 2 5 2 • Bring down: bring down the 5

  17. 3 1 5 5 675 – 1 – – 15 7 5 2 Now, let’s do the last step 5 R=0 • Find: 25is the closest multiple, the other factor is 5 • Multiply: 5X 5 = 25, put 25under the 25 • Subtract: subtract 25from 2525- 25= 0 25 • Bring down: nothing’s left, you’re done! 0

  18. – 4 865 Now, let’s practice! 2 2 • Find: the closest multiple is 8, the other factor is 2 6 4 8 8 • Multiply: multiply 2x4=8 0 6 • Subtract: subtract 8-8=0 • Bring down: bring down the 6

  19. 2 6 8 4 86 – 0 – 6 Now, let’s do the second step 1 • Find: the closest multiple is 4, the other factor is 1 5 • Multiply: multiply 4x1=4 4 • Subtract: subtract 6-4=2 5 2 • Bring down: bring down the 4

  20. 1 2 6 8 4 865 – 0 – – 4 6 5 2 Now, let’s do the last step 6 R=1 • Find: the closest multiple is 24, the other factor is 6 • Multiply: multiply 6x4=24 • Subtract: subtract 24-24=0 24 • Bring down: nothing’s left, you’re done! You’re left with a remainder of 1. 1

  21. On Your Own • Please complete the handout titled “Division (1)” • Don’t forget to review your multiplication tables

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