Fraction Operations Part 1 Slide 3 / 115 Slide 4 /...

$Page 1: Fraction Operations Part 1 Slide 3 / 115 Slide 4 / 115content.njctl.org/courses/math/5th-grade-math/fraction-operations... · Slide 1 / 115 Slide 2 / 115 5th Grade Fraction Operations$
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5th Grade

Fraction Operations Part 1

2015-10-08

www.njctl.org

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· Adding Fractions with Unlike Denominators· Subtracting Fractions with Unlike Denominators

· Adding Mixed Numbers with Unlike Denominators

· Subtracting Mixed Numbers with Unlike Denominators

Table of Contents

· Finding Common Denominators· Comparing Fractional Numbers

· Fractions as a form of division

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Return toTable of Contents

Fractions as a form ofdivision

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Fractions as a form ofdivision[This object is a pull tab]

Teac

her N

otes

For this activity, each student will need 7 index cards, card stock, or square or rectangular scrap paper and a pair of scissors to cut.

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Imagine you have 2 sandwiches. Use your two pieces of paper to represent the sandwiches. Share the sandwiches equally between 2 people.

How many sandwiches did each person get?

Write a division sentence to show represent this.

Derived from( (

http://www.njctl.org

http://www.njctl.org

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http://www.engageny.org/sites/default/files/resource/attachments/math-g5-m2-full-module.pdf





Imagine you have 2 sandwiches. Use your two pieces of paper to represent the sandwiches. Share the sandwiches equally between 2 people.



Derived from( (

[This object is a pull tab]

Ans

wer

Each person will get 1 sandwich.

2 2 = 1

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Fractions can be used to show the division operation.

2 2 = 1 can also be written as

2= 1

The fraction bar is a division bar.click

2

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Now imagine that there is only 1 sandwich. Use your paper and the scissors to show how you would share the sandwich equally between 2 people.


Write a division sentence to show represent this.click

Derived from( (


Now imagine that there is only 1 sandwich. Use your paper and the scissors to show how you would share the sandwich equally between 2 people.



Derived from( (

[This object is a pull tab]A

nsw

er

Each person will get 1 half of a sandwich.

1 2 = 1/2

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Now imagine that there is 1 sandwich and 3 people. Use your paper and the scissors to show how you would share the sandwich equally between 3 people.



Person 1 Person 3Person 2

Derived from( (


Now imagine that there is 1 sandwich and 3 people. Use your paper and the scissors to show how you would share the sandwich equally between 3 people.



Person 1 Person 3Person 2

Derived from( (


Ans

wer

Each person will get 1 third of a sandwich.

1 3 = 1/3





















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Now lets take 3 sandwiches and share them equally with 2 people. Turn and talk about how you can share these sandwiches. Use your paper and the scissors to show how you would share them.



Person 1 Person 2

click

Derived from( (


Now lets take 3 sandwiches and share them equally with 2 people. Turn and talk about how you can share these sandwiches. Use your paper and the scissors to show how you would share them.



Person 1 Person 2

click

Derived from( (


Ans

wer

Each person can get one whole sandwich, and half of the third sandwich.

Each person will get 1 and a half sandwiches.

3 2 = 1 1/2

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Imagine you have 2 different sandwiches. There are 5 people sharing them, and each person wants a taste of each sandwich. Use your two pieces of paper to represent the sandwiches. Share the sandwiches equally between 5 people.



To give everyone part of each sandwich, each sandwich must be divided into fifths. Each

person can have 1/5 of each sandwich. 1/5+1/5=2/5

click

Derived from( (


Imagine you have 2 different sandwiches. There are 5 people sharing them, and each person wants a taste of each sandwich. Use your two pieces of paper to represent the sandwiches. Share the sandwiches equally between 5 people.



To give everyone part of each sandwich, each sandwich must be divided into fifths. Each

person can have 1/5 of each sandwich. 1/5+1/5=2/5

click

Derived from( (


Ans

wer

Each person will get two-fifths of a sandwich.

2 5 = 2/5

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1 Which picture shows the division?

A

B

C

Derived from( (


1 Which picture shows the division?

A

B

C

Derived from( (


Ans

wer

A





























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2 Which pictures show the division?

A

B

C

D

E

Derived from( (


2 Which pictures show the division?

A

B

C

D

E

Derived from( (


Ans

wer

A,B,C

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3 What division expression does the picture represent? Write your answer as a fraction.

Derived from( (


3 What division expression does the picture represent? Write your answer as a fraction.

Derived from( (


Ans

wer

6/4

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4 Carla was drawing a picture to show how 2 children can equally share 3 cookies. She then wrote an equation, and expressed her answer as a fraction.

Is her work correct?

If not, explain on your paper how to correct her answer.

Yes No

3 2 = 1 and 1 half = 1 1/2

Derived from( (


4 Carla was drawing a picture to show how 2 children can equally share 3 cookies. She then wrote an equation, and expressed her answer as a fraction.



Yes No

3 2 = 1 and 1 half = 1 1/2

Derived from( (


Ans

wer Yes































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5 Hillary was solving the same problem, but she did it differently.



Yes No

3 2 = six thirds = 6/3 = 2

Derived from( (


5 Hillary was solving the same problem, but she did it differently.



Yes No

3 2 = six thirds = 6/3 = 2

Derived from( (


Her drawing and her division expression is correct, but she divided 3 cookies in half and so she had 6 halves, not thirds.

Each child would get 3 halves which equals 1 and 1/2.

three halves = 1 1/2

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This fraction line represents division.

It can be read as:

27 over 527 out of 527 divided by 5

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FindingCommon

Denominators

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How many halves make a whole circle?

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How many fourths make half of this circle?

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How many sixths make 1/3 of this circle?

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How many eighths can fit in 1/4 of this circle?

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How many different combinations can you make to fill the circle?Keep track of what pieces you use. (You may need to rotate your pieces.)

1/8

1/4

1/21/3

1/61/7

1/5

Slide 30 / 115Fix the Sticks

You can use the set of Skip Counting Sticks to find common denominators for two fractions with unlike denominators. If you don't have a set of sticks, you can create them by listing the multiples of the denominator.

For the fractions and , line up the sticks this way for the denominator of each fraction:

Find the smallest number in the "denominator" sticks that is common in both fractions.

It's 12. The least common denominator of and is 12.

3 4

4 8 12 16 20 24 28 32 36

6 1218 24 30 36 42 48 54

...

...

1 6

3 4 1 6

3 4

1 6

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A quick way to find LCDs...

List multiples of the larger denominator, and stop when you find a common multiple for the smaller denominator.

Ex: and

Multiples of 5: 5, 10, 15

Ex: and

Multiples of 9: 9, 18, 27, 36

2 5

1 3

3 4

2 9

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11 Find the LCD of this pair of fractions.

2 4

1 6

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3 5

5 6

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2 9

1 3

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3 4

3 7

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5 6

3 8

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Comparing Fractional Numbers

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Comparing Fractional Numbers

Common DenominatorsWhen you have two fractions with common denominators, all you have to do is compare the numerators.

Unlike DenominatorsTo compare fractions with unlike denominators, you have to rewrite both fractions with a common denominator. Then, compare the numerators.

> 8 9

7 9

2 3 7 10

2 3

2030

=

7 10

2130

=< 2

3 7 10

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Compare the fractions

1. 4 2 7 5

4 7

2035

=

2 5

1435

=

4 2 7 5

>

2. 11 1317 17

11 1317 17

<

3. 4 3 5 4

4 5

1620

=

3 4

1520

=

4 3 5 4

>

click

click

click

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16 True or false?

4 7

2 3

>

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17 True or false?

5 6

5 8

>

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18 Compare the two fractions.

A >

8 11

3 4

B <

C =

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A >

3 12

1 4

B <

C =

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A >

4 9

5 8

B <

C =

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21 Ali has completed of his essay, and

Veronica has completed of her essay.

A Ali has completed more (>) than Veronica.

B Ali has completed less (<) than Veronica.

CAli and Veronica have completed the same amount (=).

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22 Sasha has eaten of her lunch, and

Cloe has eaten of her lunch.

A Sahsa has eaten more (>) than Cloe.

B Sasha has eaten less (<) than Cloe.

CSasha and Cloe have eaten the same amount (=).

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23 Liam knows of this weeks vocabulary

words, and Joshua knows of the words.

A Liam knows more (>) words than Joshua.

B Liam knows less (<) words than Joshua.

CLiam and Joshua knowthe same amount (=) of words.

Slide 49 / 115Internet links for more practice

Finding fractions on a number line link

Comparing Fractions Model

http://visualfractions.com/GrampStrict/findgrampystrict.html

http://visualfractions.com/FindGrampstrict.html

http://nlvm.usu.edu/en/nav/frames_asid_159_g_2_t_1.html?from=topic_t_1.html

http://nlvm.usu.edu/en/nav/frames_asid_159_g_2_t_1.html?from=topic_t_1.html

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Adding Fractions with Unlike

Denominators

Return to Table of Contents

Slide 51 / 115

Adding Fractions with Unlike Denominators

To add fractions with unlike denominators, rewrite the fractions as equivalent fractions with a common denominator. Then, add the fractions. (Using the LCD is often the fastest method, as it requires the least amount of simplification.)

Make sure your answer is in simplest form.

4 9 5 8

+

4 9

5 8

+ 32724572

+

7772

= 1 5 72

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+ +

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Try these!Click the boxes to see work and answers.Be sure to simplify all answers.

2 5 1 4

+

8 20 5 20

+

1320

3 7 2 8

+

24561456

+

3856

= 1928

= 1 2740

4 5 7 8

+

32403540

+

6740

Slide 54 / 115

Adding Fractions with Unlike Denominators link

Internet Link for Practice

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24 2 5 1 3

+

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http://nlvm.usu.edu/en/nav/frames_asid_106_g_2_t_1.html?from=grade_g_2.html

http://nlvm.usu.edu/en/nav/frames_asid_106_g_2_t_1.html?from=grade_g_2.html

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25 3 10 2 5

+

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26 5 8 3 5

+

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27

3 4

7 9

+

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28 5 7

1 3

+

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29 Two friends get their hair cut. Natasha

gets of a foot cut off, and Briar gets

of a foot cut off. What is the total length

of hair the two friends get cut off?

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30 On Monday Bobby completes of his

science project. On Thursday he

completes of the project. What fraction

of the project is completed after these

two days of work?

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31 Yolanda used of her new beads to

make a necklace. She then used of the

beads to make a bracelet. What fraction

of her beads has she used so far?

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Subtracting Fractions

with Unlike Denominators


Slide 64 / 115

Subtracting Fractions withUnlike Denominators

To subtract fractions with unlike denominators, rewrite the fractions as equivalent fractions with a common denominator. Then, subtract the fractions. (Using the LCD is often the fastest method, as it requires the least amount of simplification.)

Make sure your answer is in simplest form.

4 9

3 8

4 9 3 8

32722772 5 72

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2 5 1 4

8 20 5 20

3 20

Try these!Click the boxes to see work and answers.Be sure to simplify all answers.

3 7 2 8

24561456

1056

= 5 28

4 5 3 8

32401540

1740

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32 4 5 1 7

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33 2 3 1 6

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34 6 7 3 5

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35 3 4

5 9

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36

3 5

1 6

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37 It is of a mile to Alyssa's best

friend's house. So far she has walked

of a mile to her friend's house. How

much farther does she have to walk?

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38 A recipe for pancakes calls for of a cup of

milk. Deven only has of a cup of milk. How

much more milk does Deven need?

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39 Use the chart to solve the problem. How much less rain fell on Wednesday than on Thursday?

Rainfall in inches

Wednesday

Thursday

Friday

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AMAZING FRACTIONS Quick Review

Slide 75 / 115

A few reminders...

1. If the problem is written in a horizontal format, rewrite the fractions in a vertical format.

2. Check for a common denominator. Rewrite with a common denominator if necessary.

3. Double check the sign to see if you are doing addition or subtraction.

4. Make sure you write your answer in simplest form.

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40 4 5

3 5

+

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41 4 9

2 9

+

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42 6 8

4 8

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43 6 7

4 5

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44 2 3

1 5

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45 3 4

2 3

+

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46 Rebecca painted of a mural. Justina

painted of it. How much of the mural

did the girls paint?

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47 Mr. Phillips class completed of their

project for the science program on

Monday. On Tuesday, they completed

another of it. How much more did they

complete on Tuesday than on Monday?

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48 On Saturday of the plants in Ms.

Drake's flower bed had flowers on them.

On Sunday another of them had

flowers on them. What fraction of her

plants have flowers on them now?

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AddingMixed Numbers



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Adding Mixed Numberswith Unlike Denominators

To add mixed numbers with unlike denominators, rewrite the fractions as equivalent fractions with a common denominator . Add the fractions. Then, add the whole numbers. Make sure your answer is in simplest form.

2 1 6

+ 1 2 5

2 5 30

+ 1 1230

3 1730

5 7 9

+ 2 2 3

5 7 9

+ 2 6 9

7 13 9

= 8 4 9

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1212

+ 1 12

= 1312

=x 49 1 3

8 3 4

+

x 4

x 3x 3

=

9 4 12

8 9 12

+

17 1312

= 18 1 12

1st-Find

Common Denominator(click here)

3rd-RenameFraction

(click here)

2nd-Add

Fractions(click here)

Steps to add and simplify.

Slide 88 / 115

10 1 5

Try this...

9 1 2

+ 7 10

click

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6 1 6

Try this...

3 5 12

+ 3 42

click

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49

A

5 3 4

+ 2 7 12

=

7 1612

B 8 4 12

C

7 5 8

D

8 1 3

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50

A

2 3 8

+ 5 5 12

=

7 1924

7 8 20

B

7 8 12

C

8 7 12

D

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51

5 2 10

5 5 12

A

3 1 4

+ 2 1 6

=

B

5 1 2

C

6 5 12

D

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52

14 3730

A

9 2 5

+ 5 5 6

=

B 14 7 11

14 3740

C

15 7 30

D

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531 2

3+ 2 1

2=

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54 Find the sum.

5 2 10

+ 7 4 10

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55 A recipe for sugar cookies needs

cups of flour. A recipe for oatmeal

cookies needs cups of flour. How

much flour altogether are needed to make

the two recipes?

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56 Jasmin made a necklace that is

inches long. Diandra made one that is

inches long. What is the total length of

the two necklaces?

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57 A recipe calls for cups of peanuts

and cups of walnuts. How many cups

of nuts in all are needed for the recipe?

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SubtractingMixed Numbers



Slide 100 / 115Subtracting Mixed Numbers


To subtract mixed numbers with unlike denominators, the fractions as equivalent fractions with a common denominator . Subtract the fractions. Then, subtract the whole numbers. Make sure your answer is in simplest form.

2 1 5

1 1 6

2 6 30

1 5 30

1 1 30

5 7 9

2 1 3

5 7 9

2 3 9

3 4 9

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In this problem, you can not subtract two thirds from one third, because the first numerator is smaller than the second. When this happens, you need to borrow from the whole number.

How many thirds are in 1 whole?

How many fifths are in 1 whole?

How many ninths are in 1 whole?

Pull

113 - 2

3

Slide 102 / 115

3

3 5

=

2 5 5

2 8 5

To borrow a whole number:

Take one from the whole number and write it as a fraction.

+

3 3 5

=

(Click the denominator)

Then, add the new mixed # and the fraction.

5 5

+2So, 3 3

5 = 2 8 5

Slide 103 / 115

5 1 4

3 7 12

5 3 12

3 7 12

4 1212

3 7 12

3 12

4 1512

3 7 12

1 8 12

1 2 3

Click

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Slide 104 / 115

9

4 5 8

8

4 5 8

8 8

4 3 8

Click

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58 Can this problem be solved without borrowing?

Yes or No

3 1 2

1 4

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59 Can this problem be solved without borrowing?

Yes or No

7 2 3

3 4

6

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60What does 17 become when borrowing? 3

10

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61What does 9 become when borrowing? 2

5

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62

2 1 12

A

1 2224

B

4 1 6

2 1 4

=

1 1112

C

1 1 12

D

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63

A

3 1321

B

6 2 7

3 2 3

=

3 8 21

2 2 3

C

2 1321

D

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64

A

6 1 6

B

15 8 1012

=

7 5 6

7 1 6

C

6 2 12

D

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65 Two items in a package have a combined

weight of pounds. If one item weighs

pounds, how much does the other

item weigh?

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66 My brother is years old. My sister is

years younger than my brother. How

old is my sister?

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67 Keith bought pounds of dried fruit.

He ate pounds of it. How much dried

fruit is left?

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68 A board is 8 feet long. If you cut off feet of it, how much is left?

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