# Understanding Division and Dividing With Decimals

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Understanding Division and Dividing With Decimals

For Learning To Happen:
Remove all other thoughts from your mind. Pay close attention. Try all the examples. Ignore all other distractions. copyright©amberpasillas2010

Understanding Division This block represents 1/100 or 1 square. This flat represents 1 whole. or 100 squares. This rod represents 1/10 or 10 squares. copyright©amberpasillas2010

Understanding Division 0.01 1 hundredth 1.0 0.1 1 whole 1 tenth copyright©amberpasillas2010

How many rods fit into a flat?
Understanding Division Flat 10 How many rods fit into a flat? copyright©amberpasillas2010

How many blocks fit into a flat?
Understanding Division 100 Flat How many blocks fit into a flat? copyright©amberpasillas2010

How many blocks fit into a rod?
Understanding Division 10 rod How many blocks fit into a rod? copyright©amberpasillas2010

Understanding Division What does 36 ÷ 4 really mean? How many 4’s does it take to make 36. Or how many 4’s fit into 36? 9 copyright©amberpasillas2010

Understanding Division What does 50 ÷ 5 really mean? How many 5’s does it take to make 50. Or how many 5’s fit into 50? 10 copyright©amberpasillas2010

Understanding Division What does 1.2 ÷ 0.1 mean? How many one tenths does it take to make whole and 2 tenths? copyright©amberpasillas2010

Understanding Division What does 1.2 ÷ 0.1 mean? How many 0.1’s fit to make 1.2? How many rods are there? How many one tenths fit to make 1.2? 10 1 1 The answer is 12 copyright©amberpasillas2010

Understanding Division What does 1.2 ÷ 0.1 mean? LOOK FOR A PATTERN: 1.2 ÷ 0.1 We get the problem 1 2 ÷ 0 1 If we multiply both sides by 10 BOTH DIVISION PROBLEMS GIVE YOU THE SAME ANSWER! copyright©amberpasillas2010

Understanding Division What does 1.02 ÷ 0.1 mean? How many one tenths does it take to make whole and 2 hundreds? copyright©amberpasillas2010

Understanding Division What does 1.02 ÷ 0.1 mean? How many 0.1’s fit to make 1.02? How many one tenths fit to make 1.02? How many rods fit into 1.02? .1 It takes ten full rods and two-tenths of another 10 .1 The answer is 10.2 copyright©amberpasillas2010

Understanding Division What does 1.02 ÷ 0.01 mean? How many one hundredths does it take to make whole and 2 hundreds? copyright©amberpasillas2010

Understanding Division
What does 1.02 ÷ 0.01 mean? How many 0.01’s fit to make 1.02? How many blocks are there? How many one hundredths fit to make 1.02? 1 100 The answer is 102 1 copyright©amberpasillas2010

Understanding Division What does 1.02 ÷ 0.01 mean? LOOK FOR A PATTERN: 1.02 ÷ 0.01 x 100 = 102 100 x 102 ÷ 01 = 102 Then we get the problem If we multiply both sides by 100 Notice the answer is the SAME for both problems! So to make decimal problems easier multiply your decimals by powers of 10 to work with whole numbers instead of decimals. copyright©amberpasillas2010

Dividing With Decimals There are many ways to write a division problem. There are two symbols , / 24  2 = 12 24 / 2 = 12 copyright©amberpasillas2010

Dividing With Decimals
There are 2 types of division problems involving decimal points: 1.) NO decimal in the divisor Divide  8 2.) YES Decimal in the divisor Divide  0.8 Divisor Dividend copyright©amberpasillas2010

TRICK FOR LONG DIVISION

Dividing With Decimals Divide  3 = 0.27  3 0.09 0.27 copyright©amberpasillas2010

Dividing With Decimals Divisor Dividend Divide  3 Step 1: Write the problem in the long division format 9 . Step 2: Move the decimal point in the dividend straight up into the quotient 0 0 2 7 27 Step 3: Divide as usual TRICK: Dead Monkeys Smell Bad! copyright©amberpasillas2010

Dividing With Decimals Divide  2 = 0.14  2 0.07 0.14 copyright©amberpasillas2010

Dividing With Decimals LOOK FOR A PATTERN When dividing a decimal by a decimal, multiply both numbers by a power of 10 so you can divide by a whole number. To decide which power of 10 to multiply by, look at the denominator. The number of decimal places represents the number of zeros after the 1 in the power of 10. 1.32 0.4 1.32 0.4 10 13.2 4 = = 1 decimal place 1 zero copyright©amberpasillas2010

Dividing With Decimals Divide ÷ 0.22 0.22 )0.352 0.22 has two decimal places so multiply both numbers by 100 to make the divisor a whole number. 1 .6 1 22 )35.2 - 22 Then divide as usual. 1 3 2 2 13 copyright©amberpasillas2010

Dividing With Decimals Dividend  Divisor Step 1: Write the problem in the traditional long division Divide 0.75  0.15 Step 2: Move the decimal point in the divisor to the far right of the divisor . 5 . . Step 3: Move the decimal point the SAME number of places in the dividend 0 0 7 5 75 Step 4: Move the decimal point in the dividend straight up into the quotient Step 5: Divide as usual copyright©amberpasillas2010

Dividing With Decimals Divide 0.45 ÷ 0.25 0.25 has two decimal places so multiply both numbers by 100 to make the divisor a whole number. 0.25 )0.45 1 8 25 )45 Then divide as usual. - 25 2 – 200 copyright©amberpasillas2010

NO decimal point in the divisor. #8
Divisor Dividend Divide  3 Step 1: Write the problem as long division. 9 . Step 2: Move the decimal point in the dividend straight up. 0 0 2 7 27 Step 3: Divide as usual TRICK: Dead Monkeys Smell Bad!

Divide Decimals . #9 Divide 0.42  0.6 . . . . Dividend  Divisor 7
Step 1: Write as long division Yes, decimal point in the divisor. Step 2: Make the divisor a whole number by moving the decimal point to the far right . 7 . . . . Step 3: Inside the dividend move the decimal point the SAME NUMBER of places 0 0 4 2 42 Step 4: Move the decimal point from the dividend straight up Step 5: Divide