Download Unit 1a -Decimals

Unit 1a – Decimals –
Class Notes
Date
Adding and Subtracting Decimals
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
2) 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
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
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.
Steps
1) Divide
2) Multiply
3) Subtract
4) Check
5) Bring down
6) Repeat, as needed

Way to remember these steps:
o Does McDonald’s Sell CheeseBurgers?
Example
Try This
1) 945 ÷ 4
2) 10,626 ÷ 21
3) 331 ÷ 84
4) 96,446 ÷ 26
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Page 5
Date
Dividing Decimals by Whole Numbers
Learning Target: I can divide decimals by whole numbers.
Steps
1)
2)
3)
4)
5)
6)
7)
Place the decimal point in the quotient (answer) directly about where it appears in the dividend.
Divide
Multiply
Subtract
Check
Bring down
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 scultpute using balloons, strips of paper and paint. The
materials cost $11.61. If they share the cost equally, how much should each person pay?
Try This
1) 0.91 ÷ 7
2) 0.684 ÷ 9
3) 57.484 ÷ 4
4) 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 6
Date
Dividing Decimals by Decimals
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.
Examples
Try This
1) 51.2 ÷ 0.24
2) 10.875 ÷ 1.2
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3) 18.4 ÷ 2.3
Page 7
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 8
Date
Greatest Common Factor (GCF)
Learning Target: I can find the greatest common factor of two numbers.
Key Terms


Factor: A number that is multiplied by a number to get a product. For example, the factors of 6
are 1, 2, 3 and 6.
Greatest Common Factor: The largest common factor of two or more numbers. This is
sometimes referred to as the GCF.
Methods
1. List the factors.
2. Use a Ladder Diagram
Examples
1) Find the GFC of 16 and 24.
Method 1: List the factors
2) Find the GFC of 12 and 18.
Method 2: Use a Ladder Diagram
3) There are 12 boys and 18 girls in Mr. Smith’s science class. The students must form lab groups. Each
group must have the same number of boys and the same number of girls. What is the greatest number
of groups Mr. Smith can make it every student must be in a group?
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
The GCF of 12 and 18 is 6, so Mr. Smith students can create 6 lab groups.
Try This
Write the GCF of each set of numbers using Method 1.
1) 10 and 35
2) 28 and 70
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3) 36 and 72
Page 9
Write the GCF of each set of numbers using Method 2.
4) 60 and 84
5) 45 and 75
6) 42 and 56
Write the GCF of each set of numbers using either method.
7) 66 and 88
8) 14 and 17
9) 28 and 42
Solve the following word problems.
10) The local recreation center held a scavenger hunt. There were 15 boys and 9 girls at the event. The
group was divided into the greatest number of teams possible with the same number of boys and each
team and the same number of girls on each team. How many teams were made if each person was on a
team?
11) Ms. Kline makes balloon arrangements. She has 32 blue balloons and 24 yellow balloons. Each
arrangement must have the same number of each color. What is the greatest number of arrangements
that Ms. Kline can make if every balloon is used?
12) Peter has 18 oranges and 27 pears. He wants to make fruit baskets with the same number of each
fruit in each basket. What is the greatest number of fruit baskets he can make?
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Page 10
Date
Least Common Multiple (LCM)
Learning Target: I can find the least common multiple of two numbers.
Key Terms


Least Common Multiple: The smallest number, other than zero, that is a multiple of two or
more numbers. Also referred to as the LCM.
Multiple: The product of any number and a whole number is a multiple of that number. For
example, multiples of 2 include 2, 4, 6, 8, 10, 12, 14, 16, 18, 20….
Methods
1. List the Multiples.
2. Use a Ladder Diagram
Examples
Find the LCM of 5 and 6.
Method 1: List the multiples
Find the LCM of 8 and 12
Method 2: Use a ladder diagram.
5: 5, 10, 15, 20, 25, 30, 35, 40, 45…
6: 6, 12, 18, 24, 30, 36, 42, 48, 54…
LCM: 30
Try This
Write the LCM of each set of numbers using Method 1.
1) 6 and 20
2) 5 and 8
3) 10 and 15
Write the LCM of each set of numbers using Method 2.
4) 6 and 7
5) 22 and 55
6) 14 and 6
Write the LCM of each set of numbers using either method.
7) 21 and 63
8) 6 and 16
9) 28 and 10
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Page 11
Solve the following word problems.
10) Two students are stacking blocks, one on top of the other. Reece’s blocks are 5 cm high and
Maddy’s blocks are 8 cm high. How tall will their stacks be when they are the same height for the first
time?
11) During a promotion, a music store gives a free CD to every fifteenth customer and a free DVD to
every fortieth customer. Which customer will be the first to get both gifts?
12) Pencils are sold in packs of 12 and erasers are sold in packs of 9. Mr. Jones wants to give each of 36
students a pencil and an eraser. What is the least number of packs he should buy so that there are no
left overs?
13) Tony wants to make 36 party bags. Glitter pens come in packs of 6. Stickers come in sheets of 4,
and balls come in packs of 3. What is the least number of each package he should buy to have 1 of each
item in every party bag, and no supplies left over?
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Page 12