3-5 Adding and Subtracting Fractions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem...

3-5 Adding and Subtracting Fractions

Warm UpWarm Up

Lesson PresentationLesson Presentation

Problem of the DayProblem of the Day

Lesson QuizzesLesson Quizzes


Warm UpFind the LCM for each set of numbers.

1. 8 and 12

2. 12 and 18

3. 10 and 12

4. 12 and 24

24

36

60

24


Problem of the Day

Let A through l represent digits of a number. Replace the letters A through l with the digits 1 through 9, respectively, and verify that the statement is true.

( ECD) +

ABl + G

FH= 1( ) ( )

534

912

768

+ + = 60 + 306 + 42408

= 1


Learn to add and subtract fractions.


From January 1 to March 14 of any given year, Earth completes approximately of its orbit around the Sun,while Venus completesapproximately its orbit.

15

13

The illustration shows what the positions of the planets would be on March 14 if they started at the same place on January 1 and their orbits were circular. To find out how much more of its orbit Venus completes than Earth, you need to subtract fractions.


Add. Write the answer in simplest form.

Additional Example 1A: Adding or Subtracting Fractions with Like Denominators

58

+ 18

58

+ 18

= 5 + 18

Add the numerators and keepthe denominator.

= 68

= 34 Simplify.


Subtract. Write the answer in simplest form.

Additional Example 1B: Adding or Subtracting Fractions with Like Denominators

911

– 411

911

–4

11= 9 – 4

11Subtract the numerators andkeep the denominator.

The answer is in the simplestform.

= 5 11



Check It Out: Example 1A

56

+ 16

56

+ 16

= 5 + 16

Add the numerators and keepthe denominator.

= 66

= 1 Simplify.



Check It Out: Example 1B

710

– 410

710

–4

10= 7 – 4

10Subtract the numerators andkeep the denominator.

The answer is in the simplestform.

= 3 10


To add or subtract fractions with different denominators, you must rewrite the fractions with a common denominator.

The LCM of two denominators is the lowest common denominator (LCD) of the fractions.

Helpful Hint

Two Ways to Find a Common Denominator

• Find the LCM (least common multiple)

of the denominators.• Multiply the denominators.



Additional Example 2A: Adding and Subtracting Fractions with Unlike Denominators

56

+ 78

56

+78

= 5 · 46 · 4

+ 7 · 38 · 3

The LCM of the denominator is 24.

= 2024

+ 2124

Write equivalent fractions. Add

= 4124

= 1 1724

is a reasonable answer.1 1724

Estimate 1 + 1 = 2



Additional Example 2B: Adding and Subtracting Fractions with Unlike Denominators

23

– 34

23

– 34

= 2 · 43 · 4

– 3 · 34 · 3 Multiply the denominators.

Write equivalent fractions. Subtract.

= 812

– 912

= – 112

is a reasonable answer.- 112

Estimate 1 – 1 = 0



– 27

+ 13

Multiply the denominators.

Write equivalent fractions. Add=

27

+13

=– 2 · 37 · 3

+ 1 · 73 · 7

–

Additional Example 2C: Adding and Subtracting Fractions with Unlike Denominators

= +– 721

621

121

is a reasonable answer. 121

Estimate - + = 012

12



Check It Out: Example 2A

25

+ 56

25

+56

= 2 · 65 · 6

+ 5 · 56 · 5


= 1230

+ 2530

Write equivalent fractions. Divide.

= 3730

=1 730

is a reasonable answer.1 730

Estimate 1/2 + 1 = 2



Check It Out: Example 2B

25

– 12

25

– 12

= 2 · 25 · 2

– 1 · 52 · 5 Multiply the denominators.

Write equivalent fractions. Subtract.

= 410

– 510

= 110

–

is a reasonable answer.- 110Estimate – = 01

212



– 35

+ 12


Write equivalent fractions. Add

=

35

+12

=– 3 · 25 · 2

+ 1 · 52 · 5

–

Check It Out: Example 2C

= +– 510

610

110

–

Is a reasonable answer.- 110

Estimate - + = 012

12


Additional Example 3: Astronomy Application

1 · 62 · 6

– 1 · 112 · 1

The LCM of the denominators is 12.

Write equivalent fractionsusing the common denominator.

Subtract.

12

– = 112

= 612

– 112

= 512

In one Earth year, Jupiter completes about of its orbit around the Sun, while Mars completes about of its orbit. How much more of its orbit does Mars complete than Jupiter?

12

112

Mars completes more of its orbit than Jupiter does. 512


Check It Out: Example 3

1 · 62 · 6

– 5 · 112 · 1

The LCM of the denominators is 12.

Write equivalent fractionsusing the common denominator.

Subtract.

12

– = 512

= 612

– 512

= 112

It takes Michelle hour to drive to work. It

takes Luke hour to drive to work. How much

longer does it take Luke to drive to work?

12

512

It takes Luke hour longer to drive to work.112


Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems


Lesson QuizAdd or subtract. Write each answer in simplest form.

112

13

2. 38

+ 58

1. 57

– 37

3. 4.12

– 14

5. You need a nail to go through a -inch door

and extend an extra inch. How long should the nail be?

114

778

1

in.118

27

+512

1112


1. Add. Write your answer in simplest form.

+

A. 0 C.

B. D. 1


1 2

1 9

4 9

5 9


2. Subtract. Write your answer in simplest form.

–

A. C.

B. or 1 D. 1


4 11

14 11

3 11

4 11

3 11

9 11

5 11


3. Add. Write your answer in simplest form.

+

A. C.

B. D. or 1


4 11

3 11

17

2424

17

3 8

1 3

7 17


4. Subtract. Write your answer in simplest form.

–

A. C.

B. D. or 4


4 7

6 7

13

6060

13

5 12

1 5

8 13


5. You need pounds of fruits to make a

pudding. Sam has pounds of fruits. How

much more does he need to make the pudding?

A. lb C. lb

B. lb D. lb


17

2419 24

17

3619

36

8 9

5 12

Date post:	17-Jan-2016
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3-5 Adding and Subtracting Fractions Warm Up Warm Up Lesson Presentation Lesson Presentation Problem...

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