Decimal and Fractions
Review Unit
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
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
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 Decimals by Whole Numbers
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.
Flashback: Dividing Whole Numbers
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
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2) 0.435 ÷ 15
Page 5
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?
Try This
1) 10,626 ÷ 21
2) 4905 ÷ 45
3) 2109 ÷ 111
4) 0.91 ÷ 7
5) 0.684 ÷ 9
6) 57.484 ÷ 4
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 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
Simplify Fractions and Equivalent Fractions
Learning Targets
1. I can simplify fractions.
2. I can create equivalent fractions.
Important Terms
 Simplify: To write a fraction or expression in simplest form. To reduce or put in lowest terms.
 Equivalent Fraction: Fractions that name the same amount or part, they are equal.
Examples:
Part A: Simply Fractions
Write the fraction 18/24 in simplest form.
- Method 1: Use a ladder diagram.
- Method 2: Use the Greatest Common Factor
Part B: Equivalent Fractions
-
Create two equivalent fractions for each given faction.
 To do this, multiply or divide both the numerator (top number) and
denominator (bottom number) by the same number.
-
Fill in for the missing number.
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Page 9
Try This:
Write each fraction in simplest form.
1) 6/8
3) 10/35
2) 4/20
4) 12/72
Find two equivalent fractions for each fraction.
1) 2/3
2) 6/8
3) 4/10
4) ¼
Find the missing numbers that make the fractions equivalent.
1) 4/36 = x/18
2) 2/7 = 40/x
3) 70/100 = 7/x
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4) 56/8 = x/2
Page 10
Date
Mixed Numbers and Improper Fractions
Learning Targets
1. I can convert improper fractions into mixed numbers.
2. I can convert mixed numbers into improper fractions.
Important Terms:
1. Numerator: The top number of a fraction and tells how many parts are being used.
2. Denominator: The bottom number of a fraction and tells how many parts make up the whole.
3. Improper Fraction: A fraction where the numerator is greater than or equal to the
denominator. Example: 9/7
4. Proper Fraction: A fraction where the numerator is less than the denominator. Example: ¾
5. Mixed Number: A number made up of a whole number and a fractional part. Example: 3 ½
Examples:
Converting Improper Fractions to Mixed Numbers
 Write 15/2 as a mixed number.
Converting Mixed Numbers to Improper Fractions
 Write 2 1/5 as an improper fraction.
Try This:
Write each improper fraction as a mixed number.
1) 19/5
2) 43/5
3) 108/9
4) 98/11
Write each mixed number as an improper fraction.
5) 9 ¼
6) 4 9/11
7) 18 3/5
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8) 11 4/9
Page 11
Date
Adding & Subtracting Fractions with Unlike Denominators
Learning Targets
1. I can add fractions with unlike denominators.
2. I can subtract fractions with unlike denominators.
Flashback: Adding and Subtracting with Like Denominators
1)
2)
Now we have unlike denominators…
Steps:
 Find a common denominator (find the LCM of the denominators or multiply the denominators).
 Write equivalent fractions using the common denominator.
 Keep the denominator the same.
 Add or subtract the numerators.
 Make sure your answer is in simplest form.
 Don’t forget to ask yourself the following questions before moving on to the next problem. If
you answer YES to either of these questions you MUST fix that before moving on!!!
o Is this an improper fraction?
o Can it be reduced?
Something to Remember
 When the numerator and the denominator are the same number, the fraction is equal to 1.
Examples:
1)
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2)
Page 12
Try This:
1) 10/33 + 4/33
2) 13/18 – 7/18
3) 9/26 + 2/26 – 5/26
4) 3/10 + 1/2
5) 1/6 + 2/9
6) 7/8 + 3/4
7) 2/9 + 1/6 + 1/3
8) 7/8 – 2/3
9) ¾ - 3/5
10) 3/50 – 1/25
11) 2/3 + ¼ + 1/6
12) 5/6 – 2/3 + 7/12
13) Bailey spent 2/3 of his monthly allowance at the movies and 1/5 of it on baseball cards. What
fraction of Bailey’s allowance is left?
14) Carlos has 7 cups of chocolate chips. He used 1 2/3 cups to make a chocolate sauce and 3 1/3 cups
to make cookies. How many cups of chocolate chips does he have now?
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Page 13
Date
Adding & Subtracting Mixed Numbers with Regrouping
Learning Targets
1. I can add mixed numbers.
2. I can subtract mixed numbers.
3. I can subtract mixed numbers using regrouping.
Steps:






Find a common denominator (find the LCM of the denominators or multiply the denominators).
Write equivalent fractions using the common denominator.
Keep the denominator the same.
Add or subtract the numerators.
Add or subtract the whole numbers.
Make sure your answer is in simplest form.
 Don’t forget to ask yourself the following questions before moving on to the next problem. If
you answer YES to either of these questions you MUST fix that before moving on!!!
o Is this an improper fraction?
o Can it be reduced?
 Don’t forget to pay special attention for the answers that show up as an improper fraction
within a mixed number. Example: 3 7/6
These must be converted to just a mixed
number. 3 + 1 1/6 = 4 1/6
Examples:
1)
2)
3)
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Page 14
Sometimes you must regroup/borrow before subtracting mixed numbers…
Two Methods
 Method 1: Borrowing
1. Create equivalent mixed numbers with common denominators (same as before).
2. Bring down the denominator (same as before).
3. Borrow one from the whole number in the first mixed number.
4. Rewrite the numerator in the first mixed number. The new numerator is the sum of the
numerator and the denominator.
5. Subtract numerators.
6. Subtract whole numbers.
7. Make sure your answer is in simplest form.
Examples:
1)
2)

Method 2:
1.
2.
3.
4.
5.
Changing to Improper Fractions
Create equivalent mixed numbers with common denominators (same as before).
Change both mixed numbers into improper fractions.
Bring down the denominator.
Subtract the numerators.
Make sure your answer in is simplest form.
Examples:
1) 6 5/12 – 2 7/12
77/12 – 31/12
46/12
3 10/12
3 5/6
change to improper fractions
subtract numerators
change to a mixed number
simplify
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2) 8 – 5 ¾
8/1 – 23/4
32/4 – 23/4
9/4
2¼
change to improper fractions
create like denominators
subtract numerators
change to mixed number
Page 15
Try This:
1) 2 ¾ + 3 ⅚
2) 2 2/3 + 1 ¾
3) 23 ½ + 35 ¼
4) 25 1/7 + 25 2/5
5) 4 7/8 – 2 2/9
6) 10 4/5 – 6 3/10
7) 7 11/12 – 4 2/3
8) 32 4/7 – 14 1/3
9) 28 11/12 – 8 5/9
10) A sea turtle traveled 7 ¾ hours in two days. It traveled 3 ½ hours on the first day. How many hours
did it travel on the second day?
11) Tasha’s cat weighs 15 5/12 lb. Naomi’s cat weighs 11 1/3 lb. Can they bring both of their cats to
the vet in a carrier that can hold up to 27 pounds? Explain.
Try This: Regrouping
1) 10 ½ - 2 5/8
2) 8 – 4 5/6
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3) 2 ½ - 1 ¾
Page 16
Date
Multiplying Fractions and Mixed Numbers
Learning Targets:
1. I can multiply fractions by fractions.
2. I can multiply fractions by whole numbers.
3. I can multiply fractions by mixed numbers.
Important Information
 You DO NOT need common denominators.
 To make any whole number a fraction, put it over 1.
Ex. 8 = 8/1
15 = 15/1
100 = 100/1
 To change any mixed number to a fraction, make it an improper fraction.
Ex. 3 ½ = 7/2
7 ¼ = 29/4
4 ¾ = 19/4
Steps
1. Look for any whole numbers or mixed numbers and make them fractions. (See important
information above if you need help doing this)
2. Look to see if you can simplify before multiplying. Remember you can simplify any numerator
with any denominator as long as they have a common factor.
Ex.
3. Multiply numerators.
4. Multiply denominators.
5. Make sure your answer is in simplest form.
 Don’t forget to ask yourself the following questions before moving on to the next problem. If
you answer YES to either of these questions you MUST fix that before moving on!!!
o Is this an improper fraction?
o Can it be reduced?
Examples:
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Page 17
Try This:
1) ½ ∙ ⅓
2) 4/9 ∙ 3/8
3) 3/10 × 5/6
4) 2 ⅓ × ¾
5) 4 2/5 × 2
6) 3 5/6 × 2 ¾
7) 1 7/8 ∙ 2 ⅓ ∙ 4
8) 2 × 4/5 ∙ 1 2/3
9) 3 5/6 × 9/10 × 4 2/3
10) Dominick lives 1 ¾ miles from his school. If his mother drives him half the way, how far will
Dominick have to walk to school?
11) A nurse gave a patient 3 ½ tablets of a medication. If each tablet contained 1/20 grain of
medication, how much medication did the patient receive?
12) There were 32 passengers on the bus. If 3/8 of them were children, how many of the passengers
were children?
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Page 18