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Chapter 13Fractions

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Chapter 13Fractions

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Lesson 13-1 Parts of a Whole

Lesson 13-2 Parts of a Set

Lesson 13-3 Problem-Solving Strategy: Draw a Picture

Lesson 13-4 Equivalent Fractions

Lesson 13-5 Simplest Form

Lesson 13-6 Problem-Solving Investigation: Choose a Strategy

Lesson 13-7 Compare and Order Fractions

Lesson 13-8 Add and Subtract Like Fractions

Lesson 13-9 Mixed Numbers

1313Fractions



Five-Minute Check (over Chapter 12)

Main Idea and Vocabulary

California Standards

Example 1: Write and Read Fractions


Example 3: Draw a Fraction Model

13-113-1 Parts of a Whole



• I will identify, write, and read fractions for parts of a whole.

• fraction

• numerator

• denominator



Standard 4NS1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalence of fractions.



Standard 4NS1.7 Write the fraction represented by a drawing of parts of a figure; represent a given fraction by using drawings; and relate a fraction to a simple decimal on a number line.


Write blue pieces

What fraction of the circle is blue?


5total pieces in all 8

Read five eighths or five divided by eight

Answer: So, of the whole circle is blue.58



What fraction of the circle is red?

A. 12

B. 35

C. 38

D. 34


What fraction of the figure is shaded?


Write parts shaded 3total equal pieces in all 6

Read three sixths or three divided by six

Answer: So, of the whole figure is shaded.36



What fraction of the figure is shaded?

A. 16

B. 56

C. 78

D. 34



Gina is decorating a card for her mother’s birthday.

She decides to put glitter on of the card. Draw a

picture to show this fraction.

23

Divide a rectangle into 3 equal parts. Shade two parts to show two thirds.



After Melinda’s party, she had of a pie left. Draw

a picture to show this fraction.

16

D.

A. B.

C.


Five-Minute Check (over Lesson 13-1)

Main Idea




Example 3: Fraction as a Quotient

13-213-2 Parts of a Set



• I will identify, read, write, and model fractions for parts of a set.


What fraction of the bicycles are red?


Write red bicycles 3total cars 5

Read three fifths or three divided by five

Answer: So, of the bicycles are red.35

numeratordenominator



What fraction of the triangles are orange?

A. 37

B. 27

C. 47

D. 35



What fraction of the helmets are not black?

Write helmets not black 5total helmets 7

Read five sevenths or five divided by seven

Answer: So, of the helmets are not black.57

numeratordenominator



What fraction of the circles are not blue?

A. 57

B. 35

C. 25

D. 12


Rafiq pops two bags of popcorn. If he shares the popcorn equally with six friends, what part of the bags of popcorn does each person receive?


Two bags are divided among 7 people.

Answer: So, each person receives 2 divided by 7 or

of the popcorn.

27



Rob and four friends shared 3 sticks of celery. What part of the celery did each person receive?

A. 25

B. 23

C. 34

D. 35



Main Idea


Example 1: Problem-Solving Strategy

13-313-3 Problem-Solving Strategy: Draw a Picture



• I will solve problems by drawing a picture.



Standard 4MR2.3 Use a variety of methods, such as words, numbers, symbols, charts, graphs, tables, diagrams, and models, to explain mathematical reasoning.


Brandi and her mom are at a pet store. The pet store has 15 reptiles. One third of the reptiles are turtles. Two are snakes, and the rest are lizards. How many of each reptile are there?



Understand

What facts do you know?

• There are 15 reptiles at the store.

• One third are turtles.

• Two are snakes.

• The rest are lizards.



Understand

What do you need to find?

• Find the number of each reptile.



Plan

Draw a picture to solve the problem.



Solve


• Draw 15 circles to show

the 15 reptiles. Since the

fraction is used, place

the circles in 3 equal

groups.

13


Solve


• To show the turtles, shade

of the circles. That is,

one of the three equal

groups. So, there are 5

turtles. There are 2

snakes, so shade 2 circles

to show the snakes.

13


Solve

Answer: So, there are 5 turtles, 2 snakes, and 8 lizards at the pet store.


• There are 8 circles not shaded. This is the number of lizards.


Check

Look back at the problem.

5 turtles + 2 snakes + 8 lizards = 15 reptiles

The pet store has 15 reptiles. So, the answer is correct.






Example 1: Find Equivalent Fractions

13-413-4 Equivalent Fractions



• I will find equivalent fractions.

• equivalent fractions



To find equivalent fractions, you can use multiplication or division.

Find three fractions that are equivalent to . 46



One Way: Multiply

Multiply the numerator and the denominator by the same number.

4 2×6 2

8=12

4 3×6 3

=18

12



Another Way: Divide

Divide the numerator and the denominator by the same number.

4 2÷6 2

2=3

Answer: So, , , or could be used to

represent .

812

23

1218

46



Find two fractions that are equivalent to .36

D. ,46

57

C. ,12

612

B. , 12

812

A. ,46

812





Key Concept: Simplest Form

Example 1: Write a Fraction in Simplest Form

Example 2: Real-World Example

13-513-5 Simplest Form



• I will write a fraction in simplest form.

• simplest form


Step 1 Find the common factors.


Write in simplest form.2024

Factors of 20: 1, 2, 4, 5, 10, 20

Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24

Common factors: 1, 2, and 4


Step 2 Divide by the greatest common factor, 4.


÷2024

44 =

56

Answer: So, in simplest form is .2024

56

The numbers 5 and 6 have no common factor other than 1.



Write in simplest form.2535

A. 56

B. 57

C. 45

D. 15


Stanley and his family spent 15 hours on a train ride to visit his grandparents. Write what part of one day he spent on the train as a fraction in simplest form.

Step 1 First, write a fraction.


15 hours spent on train24 total hours in a day


Step 2 Divide by common factors.


÷1524

33 =

58

A common factor of 15 and 24 is 3.

The only common factor of 5 and 8 is 1.

Answer: So, simplifies to . Stanley and his

family spent of a day on the train.

1524

58

58



Dion spent 3 hours of his day playing basketball. Write what part of one day he spent playing basketball as a fraction in simplest form.

A. 28

day

B. 58 day

C. 18

day

D. 324

day



Main Idea


Example 1: Problem-Solving Investigation

13-613-6 Problem-Solving Investigation: Choose a Strategy



• I will choose the best strategy to solve a problem.



Standard 4MR2.2 Apply strategies and results from simpler problems to more complex problems.



ANICA: My class visited the zoo. I learned that one sixth of the animals at the zoo are reptiles. There are 420 animals at the zoo. How many animals are reptiles?

YOUR MISSION: Find how many animals are reptiles.



Understand

What facts do you know?

• There are 420 animals at the zoo.

• One sixth of the animals are reptiles.

What do you need to find?

• Find how many animals are reptiles.



Plan

Solve a simpler problem. First, find one sixth of a smaller number. Then, multiply to find one sixth of 420.



Solve

Find one sixth of 42.


Draw 42 circles in 6 equal rows. Circle one of the six equal groups.


Solve

So, one sixth of 42 equals 7. Now multiply.


THINK What number can you multiply 42 by to equal 420? Then multiply 7 by the same number.

42× 10420

7× 10

70

Answer: So, 70 of the animals at the zoo are reptiles.


Check


Since 70 × 6 = 420, then 70 is one sixth of 420. The answer is correct.



Main Idea


Example 1: Compare Fractions

Example 2: Compare Fractions

Example 3: Order Fractions

13-713-7 Compare and Order Fractions



• I will compare and order simple fractions.



Standard 4NS1.9 Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.


Use the data table shown. Which insect is longer, a mosquito or a whirligig beetle?


You can use models to compare

and . First, you want the

denominators to be the same.

So, find an equivalent fraction

for that will give it a

denominator of 2.

14

14

38



×14

22

28

=

mosquito28

whirligig beetle

38

Answer: The model shows that < . So,

the whirligig beetle is longer.

28

38



Which measurement is longer, in. or in.?26

23

A. 26

B. 23


Use the data table shown. Which insect is longer, a field cricket or a lightning bug?




You need to compare

and .58

12

12

× 44

48

=

Answer: So, the field cricket is longer than the lightning bug.



Which is the shorter length, or ?12

13

A. 12

B. 13



Order , , from least to greatest.12

56

13



13

< 12

< 56

One Way: Number Lines

Use a number line.



Another Way: Equivalent Fractions

12

× 33

,36

= 13

× 22

= 26

Find equivalent fractions with the same denominator.



Another Way: Equivalent Fractions

Compare the numerators. Order from least to greatest.

,26

,36

56

,13

,12

56

Answer: So, the order from least to greatest is

, , . 13

12

56



Order , , from least to greatest.14

16

23

A. , ,14

16

23

B. , ,16

23

14

C. , ,23

14

16

D. , ,16

14

23





Key Concept: Add Fractions

Key Concept: Subtract Fractions

Example 1: Add Fractions

Example 2: Subtract Fractions

13-813-8 Add and Subtract Like Fractions



• I will add and subtract fractions.

• like denominators



Reinforcement of Standard 3NS3.2 Add

and subtract simple fractions (e.g., determine

the + is the same as ).18

38

12


Step 1 Add the numerators. Keep the same denominator.


Rex spent hour reading Saturday morning and

hour reading Saturday evening. How much time

did he spend reading in all?

14

24

14 +

24 =

2 + 14

=34


Step 2 Write in simplest form.


is in simplest form.34

Answer: So, Rex spent of an hour reading on

Saturday.

34


B. 25 day


Sherita spent of the day writing emails to her

friends in the morning and of the day writing

letters to more of her friends in the evening.

How much time did Sherita spend writing in all?

15

15

A. 15 day C.

35 day

D. 55 day



Levi ran of a mile before football practice and

of a mile after football practice. How much

farther did he run before practice?

23

13

You need to subtract and .23

13



23 –

13 =

13

Subtract the numerators.

Keep the same denominator.

The answer is in simplest form, so you don’t need to reduce.

Answer: So, Levi ran of a mile more before practice.13



Janice ate of a bag of chips on Monday. On

Tuesday, she ate more of that bag of chips.

How much more did she eat on Monday than

Tuesday?

610

310

A. 3

10 bag

B. 4

10 bag

C. 5

10 bag

D. 9

10 bag





Example 1: Real-World Example

Example 2: Mixed Number to Improper Fraction

Example 3: Mixed Number to Improper Fraction

Example 4: Use a Number Line

13-913-9 Mixed Numbers



• I will write mixed numbers and improper fractions.

• mixed number

• improper fraction



Standard 4NS1.5 Explain different interpretations of fractions, for example, parts of a whole, parts of a set, and division of whole numbers by whole numbers; explain equivalents of fractions.



Standard 4NS1.9 Identify on a number line the relative position of positive fractions, positive mixed numbers, and positive decimals to two decimal places.


Each lasagna has 10 slices. There are 13 slices left.

What fraction of the lasagna is left?




One Way: Mixed Number

Count the wholes and the parts.

1010

310

+ = 1310

or 1 310



Another Way: Improper Fraction

Count the parts.

1310

Answer: So, or 1 of the lasagna is left.

1310

310



What fraction of the pizza is left?

A. 1 38

B. 38

C. 1 58

D. 1 12



Write 1 as an improper fraction.35

Write the mixed number as the sum of a whole and part.

135 = 1 + 3

5

Write the whole number as a fraction.

= 35

55 +

Add.= 5 + 35

= 85

Answer: 1 35

85=




A. 139

B. 9

15

C. 149

D. 159


Divide the numerator by the denominator.


Write as a mixed number.103

3 103

9 –1

R1

Answer: So, = 3 .13

103



Write as a mixed number.134

A. 4 13

B. 2 54

C. 3 41

D. 3 14



Identify point A on the number line. Write it as a mixed number and an improper fraction.

Each interval on the number line is one half.

So, point A is 1 . 12




112 = 1

222 +

= 2 + 12 = 3

2

Answer: So, the number on the number line is

1 or12

32.



Identify point A on the number line. Write it as an improper fraction.

A. 32

B. 52

C. 54

D. 23


1313Fractions

1313Fractions

Five-Minute Checks

Math Tool Chest

Image Bank

1313Fractions

To use the images that are on the following four slides in your own presentation:

1. Exit this presentation.

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3. Select an image, copy it, and paste it into your presentation.

1313Fractions

1313Fractions

1313Fractions

Lesson 13-1 (over Chapter 12)

Lesson 13-2 (over Lesson 13-1)








1313Fractions

(over Chapter 12)

Haddie spends $24 on 3 tickets to play miniature golf. At this rate, how much will 10 tickets cost?

A. $70

B. $90

C. $80

D. $72

1313Fractions

(over Lesson 13-1)

Write the fraction that names part of the whole.

A. 24

B. 34

C. 14

D. 4

1313Fractions

(over Lesson 13-1)

Write the fraction that names part of the whole.

A. 13

B. 1

D. 14

C. 23

1313Fractions

(over Lesson 13-1)

Which picture correctly shows ?25

A.

D.

B.

C.

1313Fractions

(over Lesson 13-1)

Which picture correctly shows ?56

A.

D.

C.

B.

1313Fractions

(over Lesson 13-2)

Find the fraction that represents red eggs.

A. 9

12

B. 123

C. 3

12

D. 129

1313Fractions

(over Lesson 13-2)

Find the fraction that represents yellow eggs.

A. 4

12

B. 8

12

C. 124

D. 3

12

1313Fractions

(over Lesson 13-2)

Find the fraction that represents blue eggs.

A. 7

12

B. 125

C. 4

12

D. 5

12

1313Fractions

(over Lesson 13-2)

Find the fraction that represents not blue eggs.

A. 1212

B. 7

12

C. 3

12

D. 4

12

1313Fractions

(over Lesson 13-2)

Find the fraction that represents blue and red eggs.

A. 4

12

B. 7

12

C. 8

12

D. 9

12

1313Fractions

(over Lesson 13-2)

Find the fraction that represents blue, red and yellow eggs.

A. 8

12

B. 1212

C. 5

12

D. 1112

1313Fractions

(over Lesson 13-3)

Solve. Use the draw a picture strategy. A pizza is cut into 12 equal slices. Half of the pizza has sausage and peppers on it, two slices have eggplant, and the rest of the pizza is plain cheese. What fraction of the pizza is plain?

A. or12

612

B. or23

812

C. or34

912

D. or13

412

1313Fractions

(over Lesson 13-4)

A. 47

D. 23

C. 48

B. 28

Which is an equivalent fraction for ?24

1313Fractions

(over Lesson 13-4)

A. 13

D. 14

C. 23

B. 34


15

1313Fractions

(over Lesson 13-4)

A. 48

C. 23

B. 9

12

D. 1215


10

1313Fractions

(over Lesson 13-4)

A. 43

D. 12

C. 34

B. 35


1313Fractions

(over Lesson 13-5)

Write in simplest form. If it is in simplest form,

write simplest form.

25

A. 15

D. simplest form

B. 12

C. 4

10

1313Fractions

(over Lesson 13-5)



28

A. 24

D. simplest form

B. 14

C. 12

1313Fractions

(over Lesson 13-5)



33

A. 13

D. simplest form

B. 16

C. 1

1313Fractions

(over Lesson 13-5)



35

A. 13

D. simplest form

B. 15

C. 25

1313Fractions

(over Lesson 13-5)



39

A. 13

D. simplest form

B. 19

C. 12

1313Fractions

(over Lesson 13-6)

Julio and Alvino are doing yard work to raise money

for a class field trip. Julio works 1 hours and

Alvino works 2 hours every day for a week. If they

each make $4 per hour, how much did they make

that week?

12

A. $84

B. $96

C. $98

D. $100

1313Fractions

(over Lesson 13-7)

A. <

B. >

C. =

25

13

Compare. Write <, >, or =.

1313Fractions

A. <

B. >

C. =

(over Lesson 13-7)


34

35

1313Fractions

A. <

B. >

C. =

(over Lesson 13-7)


46

23

1313Fractions

A. <

B. >

C. =

(over Lesson 13-7)


14

56

1313Fractions

A. <

B. >

C. =

(over Lesson 13-7)


57

58

1313Fractions

(over Lesson 13-8)

A. 69

D. 13

B. 23

C. 6

18

Find the sum. Write in simplest form.

+ = __39

39

1313Fractions

(over Lesson 13-8)

D. 57

B. 1

A. 5

14

C. 5

12


+ = __17

47

1313Fractions

(over Lesson 13-8)

A. 42

D. 28

C. 1

B. 48


+ = __24

24

1313Fractions

(over Lesson 13-8)

A. 13

D. 16

C. 39

B. 99

Find the difference. Write in simplest form.

– = __69

39

1313Fractions

(over Lesson 13-8)

D. 45

C. 25

B. 35

A. 4

10


– = __510

110

1313Fractions

(over Lesson 13-8)

A. 12

D. 25

B. 65

C. 2

10


– = __45

25

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