Download Unit 1B – The Number System – Fraction Operations

Unit 1B – The Number System – Fraction Operations
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 GCF (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 1
Unit 1B – The Number System – Fraction Operations
Try This:
Write each fraction in simplest form.
1) 6/8
2) 4/20
3) 10/35
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
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Unit 1B – The Number System – Fraction Operations
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
8) 11 4/9
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Page 3
Unit 1B – The Number System – Fraction Operations
Date
Adding & Subtracting Fractions with Like Denominators
Learning Targets
1. I can add fractions with like denominators.
2. I can subtract fractions with like denominators.
Steps




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?
Things to Remember
 When the numerator and the denominator are the same number, the fraction is equal to 1.
Examples:
1)
2)
3)
Try This:
1) 10/33 + 4/33
2) 26/75 + 24/75
3) 100/999 + 899/999
4) 11/24 + 1/24 + 5/24
5) 13/18 – 7/8
6) 14/15 – 9/15
7) 16/21 – 6/21
8) 9/26 + 2/26 – 5/26
9) 13 1/25 + 2 5/25
10) 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 4
Unit 1B – The Number System – Fraction Operations
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.
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?
Examples:
1)
2)
Try This:
1) 3/10 + 1/2
2) 1/6 + 2/9
3) 7/8 + 3/4
4) 2/9 + 1/6 + 1/3
5) 7/8 – 2/3
6) ¾ - 3/5
7) 3/50 – 1/25
8) 2/3 + ¼ + 1/6
9) 5/6 – 2/3 + 7/12
10) 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?
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Page 5
Unit 1B – The Number System – Fraction Operations
Date
Adding & Subtracting Mixed Numbers
Learning Targets
1. I can add mixed numbers.
2. I can subtract mixed numbers.
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 6
Unit 1B – The Number System – Fraction Operations
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 miles 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.
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Page 7
Unit 1B – The Number System – Fraction Operations
Date
Subtracting Mixed Numbers Requiring Regrouping
Learning Target: I can subtract mixed numbers that require regrouping.
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.
6.
Examples:
1) 6 5/12 – 2 7/12
77/12 – 31/12
46/12
3 10/12
3 5/6
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.
Subtract whole numbers.
Make sure your answer in is simplest form.
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 8
Unit 1B – The Number System – Fraction Operations
Try This:
Use the borrowing method for the following problems.
1) 10 ½ - 2 5/8
2) 8 – 4 5/6
3) 2 ½ - 1 ¾
Change to improper fractions before subtracting for the following problems.
4) 10 ½ - 2 5/8
5) 8 – 4 5/6
6) 2 ½ - 1 ¾
Solve using either method.
7) 7 4/7 – 3 6/7
9) 7 4/11 – 2 8/11 – 10/11
8) 13 – 4 2/11
10) 8 1/3 – 5 8/9 + 8 ½
11) The average person in the United States eats 270 1/16 pounds of meat each year. The average person in Australia
eats 238 ½ pounds. How much more do Americans eat a year that people in Australia?
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Page 9
Unit 1B – The Number System – Fraction Operations
Date
Multiplying Fractions by Fractions
Learning Target: I can multiply fractions.
Important Information
 You DO NOT need common denominators.
Steps
1. 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.
Example:
2.
3.
4.

Multiply numerators.
Multiply denominators.
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:
1)
2)
Try This:
1) ½ ∙ ⅓
2) 4/9 ∙ 3/8
3) 3/10 × 5/6
4) 2/11 × 2/3 × 2/7
5) 5/12 ∙ 9/10
6) 2/5 × 2/7 ∙ 5/8
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Page 10
Unit 1B – The Number System – Fraction Operations
Date
Multiplying Fractions by Whole Numbers & Mixed Numbers
Learning Targets:
1. I can multiply fractions by whole numbers.
2. 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:
1)
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2)
Page 11
Unit 1B – The Number System – Fraction Operations
Try This:
1) ⅓∙ 1 ½
2) 5 ∙ 3 2/11
3) 1 ¼ ∙ 1 ⅓
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 12
Unit 1B – The Number System – Fraction Operations
Date
Dividing Fractions by Fractions
Learning Target: I can divide fractions.
Important Term:
 Reciprocal: One of two numbers whose product is one. For example, 2/3 and 3/2 are reciprocals.
Important Information
 You DO NOT need common denominators.
 To find the reciprocal of a fraction, flip it.
Ex. ¾ is 4/3
2/9 = 9/2
1/10 = 10/1
Steps
1. Multiply by the reciprocal.
a. Change the division sign to a multiplication sign.
b. “Flip” the fraction that comes after it.
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.
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?
Example:
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Page 13
Unit 1B – The Number System – Fraction Operations
Try This:
1) 2/3 ÷ 1/6
2) 5/8 ÷ 3/4
3) 9/10 ÷ 2/5
4) 9/16 ÷ 7/12
5) 11/12 ÷ 5/6
6) 11/15 ÷ 3/5
7) 7/8 ÷ 3/4
8) 5/6 ÷ 2/9
9) 7/8 ÷ 1/6
10) Julia has ¾ of a yard of felt. How many puppets can she make if she uses ¼ of a yard of felt for each puppet?
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Page 14
Unit 1B – The Number System – Fraction Operations
Date
Dividing Fractions by Whole Numbers & Mixed Numbers
Learning Targets:
 I can divide fractions by whole numbers.
 I can divide fractions by mixed numbers.
Important Information
 You DO NOT need common denominators.
 To find the reciprocal of a fraction, flip it. The reciprocal of…
Ex. ¾ is 4/3
2/9 is 9/2
1/10 is 10/1
 To find the reciprocal of a whole number or mixed number, make it a fraction first then flip it.
Ex. 8 = 8/1 is 1/8
2 ½ = 5/2 is 2/5
Steps
1. Look for any whole number of mixed numbers and make them fractions.
2. Multiply by the reciprocal.
a. Change the division sign to a multiplication sign.
b. “Flip” the fraction that comes after it.
3. 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.
4. Multiply numerators.
5. Multiply denominators.
6. 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:
1)
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2)
Page 15
Unit 1B – The Number System – Fraction Operations
Try This:
1) 9/16 ÷ 6
2) 12 ÷ 2 ¼
3) 7 ÷ 1 ¾
4) 1 3/7 ÷ 7/12
5) 15/16 ÷ 1 5/6
6) 3 3/11 ÷ 1 4/5
7) 1 ½ ÷ ¾ ∙ ⅖
8) 2 ¾ ÷ 1⅔ ÷ 5
9) 11/12 ∙ 9/10 ÷ 1 ¼
10) A washing machine holds 36 gallons of water. It fills at a rate of 8 ⅖ gallons a minute. How long does the machine
take to fill with water?
11) A roll contains 80 ½ feet of ribbon. It takes 3 ⅚ feet of ribbon to make a bow. How many bows can be made?
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Page 16
Unit 1B – The Number System – Fraction Operations
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Page 17