Dividing a Decimal by a Decimal

1. Dividing a Decimal by a Decimal

2. Dividing a Decimal by a Decimal • We NEVER want a decimal in the divisor. • If you have a decimal in the divisor, you need to bump it over until it is all the way over to the right of the number. • Move it the same number of places in the dividend.

3. Remember… no remainders! • If you solve a problem and you see a remainder at the end, you are NOT done! • Add a decimal and a zero • If you already have a decimal point, just add a zero • Do not put 2 decimal points in one problem!

4. Let’s try one together…

5. We cannot have a decimal point in the divisor! Let’s fix it! We bounced more places than there were numbers. This blank represents the extra spot we bounced. Turn it into a zero. ) 13 2 0 1 62 Since we bounced the decimal point in the divisor, we have to bounce it the same number of places in the dividend. We need to bounce this decimal point until it is all the way to the right of the divisor.

6. ) 1320 162 150 Does 150 go into 132? Is this divisor, 162, closest to 100? 150? or 200? After you have bounced the decimal point in both the divisor and the dividend, you can eliminate the new decimal point in the divisor. 162 is closest to 150. I am going to use 150 to estimate how many times 162 will go into my dividend. No, 150 is too big. I need to use one more digit of the dividend then. Instead of 132, I will use 1320. When you do long division, it is easiest to solve the problem when you estimate using your divisor.

7. ) 1320 162 150 15 x 2 = 30 If I double that (x4), that would be 60. If I double that (x 8) would be 120. If I add 15 more to 120, I would have more than 132, so I should stop at “times 8.” Use your fingers to cover over the last digit of both the dividend and the divisor. Now ask yourself: “how many times does 15 go into 132?” Remember that we are only using the 150 to estimate!

8. 8 1 ) 1320 162 0 - 1296 24 0 - 16 2 I know that 162 x 2 is greater than 300. That is too big! Instead, I will use 1 as the next number in my quotient. 78

9. 8 1 4 ) 1320 I am going to use 150 again… 150 x 2 = 300 If I double that (x 4), I have 600. If I add another 150 (that would be x5), then I have 750. I will try that first. 162 x 5 = 810. Nope! That is too big! Let me try one smaller… 162 x 4 = 648 I will use this one. 162 0 0 150 - 1296 24 0 - 16 2 78 0 - 64 8 132

10. 8 1 4 ) 1320 8 162 0 0 0 150 I see that my new difference is the same three numbers as in my dividend. I will use 8 again… - 1296 24 0 - 16 2 78 0 - 64 8 13 2 0 - 12 9 6 2 4

11. 8 1 4 ) 1320 8 162 0 0 0 I am rounding to the hundredths place so I underlined the four. I look at the number to the right of my underline: the 8. Since 8 is bigger than 4, I will add one to my underlined number. My division problem seems to go on and on. I am going to stop. Instead, I am going to round my quotient to the hundredths place. 8.148 8.15

12. Things to remember… • You can never have a decimal point outside the division sign • Bounce the outside decimal all the way to the right • Count up the number of places you bounced • Bounce the inside decimal as many times as you did the outside. • If you do not have a decimal point, add one to the end of the number • If you do not have enough places, then add zeros to the end of a decimal to make more places • After the decimal point has been bounced in both places, divide as usual.

13. Let’s Practice…

14. ) 1 2 9 2 3.8 3 4

15. ) 1 2 7 5 5.1 2 5

16. ) 0 2 2 8 7. 6 0 0 3

17. ) 0 8 6 8 1 2 4 0 0 0 7