Unit 1a Decimals
Class Notes
Date
Adding and Subtracting Decimals
Common Core Standard: 6.NS.B.3 Fluently add, subtract, multiply and divide multi-digit decimals using
the standard algorithm for each operation.
Learning Targets
1. I can add decimals.
2. I can subtract decimals.
Steps
1.
2.
3.
4.
5.
Write the problem vertically, lining up the decimals.
Fill in any empty spaces with zeros (0).
Add or subtract from right and left to get your answer.
Bring the decimal straight down.
Simplify by erasing any unnecessary zeros. These are the zeros that appear at the very end of
the answer, to the right of the decimal.
Examples
1) 9.8 + 9.7 + 9.425 +9.85
2) 10 – 9.85
3) Logan wants to buy a new bike that costs $135.00. He started with $14.83 in his savings account.
Last week, he deposited $15.35 into his account. Today, he deposited $32.40. How much more
money does he need to buy the bike?
Solution
Determine the total amount of money Logan has by adding.
14.83
15.35
+ 32.40
$62.58
Determine how much more Logan needs by subtracting what he has from the total cost.
135.00
- 62.58
$72.42
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Page 1
Try This
1) 8.3 + 2.7
2) 9.7 – 4
3) 13.009 + 12.83
4) 7.435 – 3.0042
5) 0.0679 + 3.75
6) 9.67 – 0.635
7) 7.03 + 33.8 + 12.006
8) 5.35 – 4.7612
9) Brad works afterschool at a local grocery store. How much did he earn in all for the month of
October?
10) The highest career batting average ever achieved by a professional baseball player is 0.366. Bill
Bergen finished with a career 0.170 average. How much lower is Bergen’s career average that the
highest career average?
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Page 2
Date
Multiplying Decimals
Common Core Standard: 6.NS.B.3 Fluently add, subtract, multiply and divide multi-digit decimals using
the standard algorithm for each operation.
Learning Target
I can multiply decimals using the standard algorithm.
Important Information

There are three ways to show multiplication
 4×2
traditional symbol (this symbol disappears in Algebra)
 4(2)
parentheses around one or both numbers
 4•2
dot in the middle of two numbers, not to be confused with a decimal
Steps
1. Line up the digits to the right, ignore the decimals for now. DO NOT LINE UP THE DECIMALS!
2. Starting at the far right side, multiply the ones digit on the bottom row by each number of the
top row.
3. Place a zero as a place holder in the second line of your answer in the ones column.
4. Multiply the tens digit by each number in the top row.
5. Continue to use a zero as a place holder and multiply until there are no numbers left.
6. Add each of your columns up.
7. Count up all the decimal places from both numbers that you multiplied and place that many
decimals in your final answer.
8. Simplify by erasing any unnecessary zeros. These are the zeros that appear at the very end of
the answer, to the right of the decimal.
Examples
1) 3.062 × 5
2) 3.25 × 4.8
3) Apples are on sale for $0.49 per pound. What is the price for 6 pounds of apples?
0.49
× 6
$2.94
2 decimal places
+ 0 decimal places
2 decimal places
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Page 3
Try This
1) 0.06 × 1.02
2) 0.66 • 2.52
3) 1.4(0.21)
4) 12.6 • 2.1
5) 0.005 × 0.003
6) 6.017(2)
7) (1.54)(3.05)(2.6)
8) 0.2 • 0.94 • 1.3
9) Jill walks her dog every morning. If she walks 0.37 kilometers each morning, how many kilometers
did she walk during the month of January?
10) A deli charges $4.56 for a pound of turkey. If Tim wants 3.8 pounds, how much will it cost him?
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Page 4
Date
Dividing Whole Numbers
Common Core Standard: 6.NS.B.2 Fluently divide multi-digit numbers using the standard algorithm.
Learning Target: I can divide whole numbers.
Important Information
 Parts to a Division Problem
 Dividend ÷ Divisor = Quotient
 Dividend: The number being divided. It goes on the inside of the house when working
the problem out.
 Divisor: The number you are dividing by. It goes on the outside of the house.
 Quotient: The answer to a division problem. It goes on top of the house.
Dividing Whole Numbers
Try This
1) 826 ÷ 4
2) 6312 ÷ 9
3) 5989 ÷ 5
4) There are 34 students in Mrs. Jones 4th grade class. The end of the year party is going to cost $578. If
the students plan to equally pay for the party, how much will it cost each of them?
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Page 5
Dividing with Zeros in the Quotient
Try This
1) 10,626 ÷ 21
2) 4905 ÷ 45
3) 6018 ÷ 6
4) A roller coaster at King’s Island can allow 28 people to ride at one time, how many trips will the
coaster have to make so that 5796 people will have the opportunity to ride?
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Page 6
Date
Dividing Decimals by Whole Numbers
Common Core Standard: 6.NS.B.3 Fluently add, subtract, multiply and divide multi-digit decimals using
the standard algorithm for each operation.
Learning Target: I can divide decimals by whole numbers.
Important Information
 Parts to a Division Problem
 Dividend ÷ Divisor = Quotient
 Dividend: The number being divided. It goes on the inside of the house when working
the problem out.
 Divisor: The number you are dividing by. It goes on the outside of the house.
 Quotient: The answer to a division problem. It goes on top of the house.
Now the dividend becomes a decimal…
Steps
1) Place the decimal point in the quotient (answer) directly about where it appears in the dividend.
2) Divide
3) Multiply
4) Subtract
5) Check
6) Bring down
7) Repeat steps 2-7, as needed
Examples
1) 2.52 ÷ 3
2) 0.435 ÷ 15
3) Ethan and two of his friend are making a sculpture using balloons, strips of paper and paint. The
materials cost $11.61. If they share the cost equally, how much should each person pay?
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Page 7
Try This
1) 0.91 ÷ 7
2) 0.684 ÷ 9
3) 57.484 ÷ 4
4) 4.08 ÷ 24
5) 16.95 ÷ 20
6) 0.564 ÷ 12
7) The tennis team is having three tennis rackets restrung. The total cost is $54.75. What is the average
cost per racket?
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Page 8
Date
Dividing Decimals by Decimals
Common Core Standard: 6.NS.B.3 Fluently add, subtract, multiply and divide multi-digit decimals using
the standard algorithm for each operation.
Learning Target: I can divide decimals by decimals.
Steps
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
Move the decimal in the divisor to the very end, make it a whole number.
Count how many places it had to be moved.
Move the decimal in the dividend the same number of spots. Ignore the old decimal.
Place the decimal point in the quotient (answer) directly about where it appears in the dividend.
Divide
Multiply
Subtract
Check
Bring down
Repeat steps 5-10, as needed until it either terminates (ends) or becomes a repeating decimal.
You may need to add additional zeros (0) before one of these two things happen.
11)
Examples
C. Jon wants to buy a new bike that costs $129.79. He gets $11.25 in allowance each week. How many
weeks will it take him to save up enough money to buy the bike?
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Page 9
Try This
1) 51.2 ÷ 0.24
2) 10.875 ÷ 1.2
3) 18.4 ÷ 2.3
4) 12.586 ÷ 0.35
5) 50.9 ÷ 4.5
6) 8.43 ÷ 0.12
7) Kyle’s family drove 329.44 miles. Kyle calculates that the car averages 28.4 miles per gallon of gas.
How many gallons of gas did the car use?
8) Jan spends $5.98 on ribbon. Ribbon costs $0.92 per meter. How many meters of ribbon does Jen
buy?
9) Anna is saving $6.36 a week to buy a computer game that costs $57.15. How many weeks will she
have to save to buy the game?
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Page 10
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Page 11