Warm Up

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Warm Up
Problem of the Day
Lesson Presentation
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Warm Up Add or subtract.
2 5
3 5
1.
1
7 12
11 12
2.
3 2
3. 6.5 1.2
5.3
4. 3.4 0.9
2.5
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Problem of the Day The least common multiples of
6 and a number is 24. What is the other number?
8
4
Learn to add and subtract fractions with unlike
denominators.
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North Dome trail in Yosemite National Park is 5
miles to the summit. Two hikers walk 2 miles
before taking a break. They then hike another 1
miles before taking a second break. How many more
miles do they have to hike before reaching the
summit?



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To solve this problem, add and subtract rational
numbers with unlike denominators. First find a
common denominator using one of the following
methods
Method 1 Find a common denominator by
multiplying one denominator by the other
denominator.
Method 2 Find the least common denominator (LCD).
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Additional Example 1A Adding and Subtracting
Fractions with Unlike Denominators
Add or Subtract. Method 1
Find a common denominator 8(7)56.
2 7
1 8
A.

Multiply by fractions equal to 1.
Rewrite with a common denominator. Simplify
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Additional Example 1B Adding and Subtracting
Fractions with Unlike Denominators
Add or Subtract. Method 2
Write as improper fractions.
1 6
5 8
1
1
B.
List the multiples of each denominator and find
the LCD
Multiply by fractions equal to 1.
Rewrite with a common denominator.
Simplify.
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Check It Out Example 1A
Add or Subtract. Method 1
Find a common denominator 3(8)24.
5 8
1 3

A.

Multiply by fractions equal to 1.
Rewrite with a common denominator.
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Check It Out Example 1B
Add or Subtract. Method 2
Write as an improper fraction.
1 6
3 4
2

B.
List the multiples of each denominator and find
the LCD
Multiply by fractions equal to 1.
Rewrite with a common denominator.
Simplify.
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Additional Example 2 Evaluating Expressions with
Rational Numbers
4 5
5 6
Evaluate t for t .
Multiply by fractions equal to 1.
Rewrite with a common denominator 6(5) 30.
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Check It Out Example 2
Multiply by fractions equal to 1.
Rewrite with lowest common denominator (36).
Simplify.
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Additional Example 3 Consumer Application
Two dancers are making necklaces from ribbon for
their costumes. They need pieces measuring 13
inches and 12 inches. How much ribbon will be
left over after the pieces are cut from a 36-inch
length?
Subtract both amounts from 36 to find the amount
of ribbon left.
Write as improper fractions. The LCD is 8.
Rewrite with a common denominator.
Simplify.
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Check It Out Example 3
Fred and Jose are building a tree house. They
need to cut a 6 foot piece of wood and a 4
foot piece of wood from a 12 foot board. How
much of the board will be left?
Subtract both amounts from 12 to find the amount
of board left.
Write as improper fractions. The LCD is 12.
Rewrite with a common denominator.
Simplify.
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Lesson Quiz
Add or subtract.
5 14
1 7
1.

12
2 3

2.
8
1
3 5
2 3
3.
2

38
9 16
4. Evaluate n for n .
1
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Robert is 5 feet 6 inches tall. Judy is 5 feet
3 inches tall. How much taller is Robert than
Judy?
5.
3 4