Transcript 2 - s3.amazonaws.com

5.3
Adding and Subtracting Unlike Fractions
Skill Check
Lesson Presentation
Lesson Quiz
5.3
Adding and Subtracting Unlike Fractions
Skill Check
Write the mixed number as an improper fraction.
1.
2.
3.
4.
5.3
Adding and Subtracting Unlike Fractions
Hiking You are hiking
between two campsites in the
Chesapeake and Ohio Canal
National Historic Park. The
distance between the
1
campsites is 10 miles. You
5
have already hiked 5 3
4
miles. How many more miles
do you have to hike?
5.3
Adding and Subtracting Unlike Fractions
To add or subtract fractions with different denominators, begin by using the
LCD of the fractions to write equivalent fractions that have the same
denominator.
5.3
Adding and Subtracting Unlike Fractions
EXAMPLE
1
Adding and Subtracting Fractions
5
1
5
4
+
=
+
12
3
12
12
5+4
= 12
=
9
12
3
= 4
Write
1
using LCD.
3
Write sum of numerators over denominator.
Add.
Simplify.
5.3
Adding and Subtracting Unlike Fractions
EXAMPLE
5
1
Adding and Subtracting Fractions
7
–15
14
– 6 – 9 = 18 – 18
Write fractions using LCD.
= –15 – 14
Write difference of numerators over denominator.
= –29
Subtract.
18
18
11
= –1 18
Write fraction as a mixed number.
5.3
EXAMPLE
–4
Adding and Subtracting Unlike Fractions
2
Adding Mixed Numbers
2
6
–22
–28
+
+
=
–2
5
11
5
11
Write mixed numbers as improper fractions.
=
–242
–140
+
55
55
Write fractions using LCD.
=
–242 + (–140)
55
Write sum of numerators over denominator.
=
–382
52
=
–6
55
55
Add. Then write fraction as a mixed number.
5.3
Adding and Subtracting Unlike Fractions
EXAMPLE
3
Subtracting Mixed Numbers
You are hiking between two campsites in the Chesapeake and
Ohio Canal National Historic Park. The distance between the
1
3
campsites is
You have already hiked
miles.
10miles.
5
5
4
How many more miles do you have to hike?
SOLUTION
10
To find the remaining distance, subtract.
1
3
51
23
–
–
5
=
5
4
5
4
Write mixed numbers as
improper fractions.
=
204 115
– 20
20
Write fractions using LCD.
=
204 – 115
20
Write difference of numerators over denominator.
5.3
EXAMPLE
Adding and Subtracting Unlike Fractions
3
Subtracting Mixed Numbers
You are hiking between two campsites in the Chesapeake and
Ohio Canal National Historic Park. The distance between the
1
3
campsites is
You have already hiked
miles.
10miles.
5
5
4
How many more miles do you have to hike?
SOLUTION
To find the remaining distance, subtract.
=
204 – 115
20
89
9
= 20 = 4 20
ANSWER
Subtract. Then write fraction as a mixed number.
9
1
You need to hike 4 20 miles, or about 4 2 miles.
5.3
Adding and Subtracting Unlike Fractions
EXAMPLE
4
Simplifying an Expression
a
a
Simplify the expression 2 – 6 .
a
a
–
2
6
a
3
a
= 2•3 – 6
3a
a
= 6 – 6
=
3a – a
6
2a
= 6
a
Write 2 using LCD.
Multiply.
Write difference of numerators over denominator.
Subtract.
1
2a
= 6
3
a
= 3
Divide out common factor.
Simplify.
5.3
Adding and Subtracting Unlike Fractions
Lesson Quiz
Find the sum or difference.
1.
2.
3.
4.
6. Challenge Find a value of y so that the sum
is equal to 2. 2