1. Warm Up 28.29 + 13.71 = -18.20 + 9.86 = 7.56 + (-8.27) = 87.51 – 57.49 = -26.38 – (-38.93) =

2. MULTIPLYING AND DIVIDING DECIMALS

3. Rules for Multiplication 1.Line up your numbers with the last digits under each other. 2.Multiply as you would with whole numbers. 3.Add the decimal places in each of the numbers being multiplied. 4.Move the decimal point to the left the TOTAL number of places in the numbers being multiplied.

4. Rules for Multiplication - Example 1.Line up your numbers with the last digits under each other. 1 2. 3 x 6. 1 1 _____________________________________

5. Rules for Multiplication - Example 2.Multiply as you would with whole numbers. 1 2.3 x 6.1 1 _____________________________________ 1 2 3 1 2 3 0 +7 3 8 0 0 ______________________________________ 7 5 1 5 3

6. Rules for Multiplication - Example 3.Add the decimal places in each of the numbers being multiplied. 1 2.3 1 decimal place x 6.1 12 decimal places ______________________________________________________________________________________ 1 2 3 1 2 3 0NEEDS +7 3 8 0 0 ______________________________________ 7 5 1 5 33 decimal places

7. Rules for Multiplication - Example 4.Move the decimal point to the left the TOTAL number of places in the numbers being multiplied. 1 2.3 1 decimal place x 6.1 12 decimal places ______________________________________________________________________________________ 1 2 3 1 2 3 0NEEDS +7 3 8 0 0 ______________________________________ 7 5.1 5 33 decimal places

8. Rules for Multiplication - Example BIG HINT: Check your answer using just whole numbers to make sure your answer is reasonable and the decimal point is in the correct place. 12 x 6 = 72 so 75.153 is reasonable Would 751.53 be reasonable? Would 7.5153 be reasonable? Would 7,515.3 be reasonable?

9. Dividing Decimals Change the divisor to a whole number by moving the decimal to the right. Move the decimal the same number of places in the dividend If you don’t have to move the decimal in the divisor, you don’t move it in the dividend either! Bring the decimal straight up to the quotient Divide Check your solution by multiplying!

10. Dividing Decimals Find the quotient of 12 ÷ 4 Set it up quotient Dividend (in the box) Divisor (out of the box) 3 -12 0 Find the quotient of 156 ÷ 12 1 -12 36 3 -36 0

11. Dividing a whole number by a whole number We are able to divide these numbers because the divisors are whole numbers! 3 -12 0 1 36 3 -36 0 divisor Sometimes, we have to do a little more…………………..

12. Dividing a whole number by a DECIMAL What if the divisor is NOT a whole number?? Example: 156 ÷ 1.2 Set it up The divisor is NOT a whole number! We have to change the divisor to a whole number by moving the decimal to the right (which is the same thing as multiplying by a power of 10) (x 10, x 100, x 1000, etc.)

13. Dividing a whole number by a DECIMAL Example: 156 ÷ 1.2 We have to change the divisor to a whole number by moving the decimal to the right. We had to move the decimal 1 place to the right, to make the divisor a whole number We have to move the decimal the same number of places in the dividend also! (1 place) 0

14. Dividing a whole number by a DECIMAL Bring the decimal straight up to the quotient. 1 -12 36 3 -3 6 00 0 - 0 0 Now, you are ready to divide! Now, CHECK IT by multiplying! 130 X 1.2 2 6 0 +1 3 0 0 1 5 6 0

15. Dividing a DECIMAL by a DECIMAL Bring the decimal straight up to the quotient. 1 -12 36 -3 6 0 3 Now, you are ready to divide! Now, CHECK IT by multiplying! 1.3 X 1.2 2 6 +1 3 0 1 5 6 Find the quotient 1.56 ÷ 1.2

16. Dividing a DECIMAL by a DECIMAL Bring the decimal straight up to the quotient. 1 -12 36 -3 6 0 3 Now, you are ready to divide! Now, CHECK IT by multiplying! 130 X.12 260 +1300 1560 Find the quotient 15.6 ÷.12 0 0 -0 0 0 0