Dividing a Decimal by a Decimal Dividing a

Dividing a Decimal by a Decimal

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.

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!

Let’s try one together…

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. 1 62 ) 13 2 0 We need to bounce this decimal point until it is all the way to the right of the divisor. Since we bounced the decimal point in the divisor, we have to bounce it the same number of places in the dividend.

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

162 150 ) 1320 Use your fingers to cover the last digit of both the dividend and the divisor. 15 x 2 = 30 If I double that (x 4), 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. ” Now ask yourself: Remember that we are only using the 150 to estimate! “how many times does 15 go into 132? ”

81 162 ) 1320 0 - 1296 24 0 - 16 2 78 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.

8 14 162 150 ) 1320 0 0 - 1296 24 0 - 16 2 78 0 - 64 8 132 I am going 150 again… 162 to x 5 use = 810. 150 isx too 2 = big! 300 Let me Nope! That If I double thatsmaller… (x 4), I have 600. try one If I add another 150 (that would be x 5), 162 thenx. I 4 have 750. I will = 648 that first. I willtry use this one.

8 1 48 162 150 ) 1320 0 - 1296 24 0 - 16 2 78 0 - 64 8 13 2 0 - 12 9 6 I see that my new difference is the same three numbers as in my dividend. I will use 8 again…

8 1 48 162 ) 1320 0 I am rounding to the My division problem seems to hundredths place so I go on and on. I am going to underlined the four. I look at stop. the number to the right of my underline: the 8. Since 8 is Instead, I am going to round my bigger than 4, I will add one to quotient to the hundredths my underlined number. place. 8. 148 8. 15

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.

Let’s Practice…

3. 8 34)1292

5. 1 25)1275

7. 6 003)0228

124 0007)0868