Lesson 1: Fraction Basics Reviewed

Learning Target #1 – I can model with diagrams and use appropriate math language to demonstrate my understanding of fractions.

A fraction is simply two whole numbers, or one whole number divided by another whole number.

The top number is called the_________________ and the bottom number is called the _____________

Types of Fractions

_________________ - The denominator is greater than the numerator such as____________

Model:

__________________- The numerator is greater than the denominator such as_____________

Model:

__________________- A whole number and a proper fraction such as_________________

Model:

Reducing Fractions to Simplest Terms- ie. Create an equivalent fraction in lowest terms.

3681

16 1824

1352

Compare the following Fractions! Write > o < or = between each pair of fractions

3102790 58

712 3 916 3

35

Create Equivalent Fractions to determine the larger fraction. Circle the larger fraction.

¿¿=1320

∨ 710

=¿¿

22

Write a >, <, or = in each . Create equivalent fractions to compare!

18524 37

34

351525

Converting between Improper and Mixed Fractions

Learning Targets #2 – I can reduce fractions to lowest terms and convert between improper and mixed fractions.Mixed Fraction Steps to change Improper Fraction

2 34 improper fraction

mixed fraction175

Convert the following to a mixed number or an improper fraction in lowest terms

Try these: a) 9070 b) 9828 c) 4 57 d) 3 13

Write a mixed number or proper fraction in lowest terms at each lettered point.

Put the following fractions on the number line below: 2 35 ,155, 185

23

Practice: Pattern Blocks and Fractions

24

25

26

Lesson 2: Multiplication of Fractions

Learning Target #3 – I can multiply fractions.

Learning Target #5 – I can solve problems using the correct fraction operation(s), showing all steps and answering in a sentence with correct units.

Understanding Multiplication with Pattern Blocks

The word “of ” or “as many as” means multiplication. For Example, 14of 12means¿

Mathematically we show the following work:

Multiplying a Fraction and a whole number

Question Addition Multiplication Lowest Terms3× 23

27

Multiplying Proper Fractions

Rules:

Use the above rules to do the following!

a) 12×35

d) 56×45

b) 23×12 e)34 ×

815

c)35×29 f) 310×

59

****Another Method of Multiplying Proper Fractions is crossing out common Factors

a) 12×35 d) 56×

45

b) 23×12 e)34 ×

815

c)35×29 f) 310×

59

28

Step 1- Multiply the top of the fractions (numerators)Step 2- Multiply the bottom of the fractions (denominators)Step 3- Reduce the fraction if possible to lowest terms

g) 185 ×209 h) 45 ×

23× 916

Word Problems:

1. A limousine that seats 10 people is two-fifths full. How many people are seated in the limousine?

2. In a grade 8 class, 35 of the students walk to school. Of these students,

12 get rides when it

rains. What fraction of this class gets rides when it rains? If the class has 30 students, how many students will get a ride when it rains?

29

Lesson 3: Multiplying Improper Fractions and Mixed Numbers

Warm-up

Express each mixed number as an improper fraction

a) 434 b)2

78 c) 6

13 d) 3

47

Express each improper fraction as a mixed number in lowest terms

a) 136 b)

272 c)

6015 d)

904

To find the product of mixed numbers:

a) 212×1 34 b) 4

12×2 13

c) 4×112×2 12 d) 2

34×1 13×3 12

Word Problems Continued

30

Change all mixed numbers or whole numbers to improper fractions Then cross out common factors Multiply and reduce

Example 1: Jan is making a recipe that calls for six scoops of flour. She wants to make only 23 of the

recipe. How many scoops of flour will she need to use?

Example 2: Sam bought 34 of a kilogram of cottage cheese. He ate

38 of it for lunch. What fraction of

the cottage cheese was left for lunch the next day? ________kg

Example 3: Angie paid 35of the regular price to purchase a Lulu Lemon jacket. The regular price was

$85. How much did she pay for the jacket?

Example 4: Jeff is putting in new carpet in his family room. The room measures

10 12ft. by 8 34ft. How much area (l ×w ¿ will the carpet cover (round area to 2 decimal places)? If the

carpet costs $3.50/ft2, how much will Jeff spend on new carpet?

Example 5: Avi usually runs 12 km per day. For a race he must run 2 ¼ times the distance he runs every day. What is the distance of the race.

31

Assignment: Fraction word problems and “Did you hear about…”

Practice: Multiplication Word Problems

1. Shriya worked 4 days at the Gap for 3 ½ h each day. She was paid $12/h?a) How many hours did Kristi work that week? Show your thinking.

b) How much did Shriya earn that week?

2. Jupiter completes about 225 rotations every 24 hours (one Earth day). How many rotations

does Jupiter complete in one Earth year (365 days)? Show your thinking.

3. A sailboat is sailing at 412km/h. If the weather conditions and the current do not change, how

far will the sailboat travel in 213 h? Show your thinking.

4. The distance to Grandma’s house is 45 of the distance to Aunty Harveer’s house. If Aunty

Harveer’s house is 312 hours away, how long will it take to get to Grandma’s house if you

travel at the same speed?

32

5. If takes 25 of a tank of gas to get to school and back each day. How much gas is used over 10

school days? Show your thinking.

6. Nick is 214 times as old as Brianne. When Brianne celebrates her 14th birthday, how old will

Nick be?

33

34

Lesson 4: Dividing Fractions! Using the Inverting Method!

Learning Target #4 – I can divide fractions.Refer to Learning Target #5

Dividing Whole Numbers

How do we write whole numbers as a fraction?

12 = 5 = 400 =

What is the reciprocal of the above numbers? _________ _________ _________

For now, think of the reciprocal as ____________________ , this means the “reciprocal” of 12 is

“reciprocal” of 5 is

“reciprocal” of 400 is and so on

A shortcut method to dividing fractions by a whole number is multiplying the fraction by the reciprocal of the whole number. See the following example:

Model of Situation

a) 14÷3

b) 25 ÷2

Dividing Fractions and Mixed Numbers

Use the diagrams to determine how many 12s there are in 3.

There are ____ halves in three.

Division statement:

35

How many 14 s are in 2.

There are ____ quarters in two.

Division statement:

How many 14 s are there in

34 ? Division statement:

How many 16s are there in

23? Division statement:

Now we will do the division of fractions using the rules rather than diagrams.

a) 3÷ 12 b) 2÷ 14

c) 34÷ 14 d) 23 ÷

16

RULE:

PRACTICE:

36

i.23÷ 14 ii.

78÷ 14 iii. 2 1

2÷3 34 iv. 3 1

6÷1 23

Division Word Problems

Example 1: Four students equally shared 12 of a cake. What fraction of the cake did each student eat?

Example 2: Tim uses 16 of a tank of gasoline in a five-day work week driving to work. On average,

what fraction of a tank he uses for each round trip?

Example 3: It takes 212 scoops of flour to make one cake. How many cakes do 15 scoops of flour

make?

Example 4: Janelle feeds her cat 45 of a tin of cat food each day. Janelle has 12 tins of cat food. How

many days’ supply of cat food does Janelle have?

Assignment: Dividing Fractions; Division Word Problems and Models

37

38

Practice: Fraction Division Word Problems and Models:

1. Use a rectangle model to show the quotient of 23÷3.

2. Use a rectangle model to show the quotient of 2÷ 15.

3. A board that is 35 of a metre long is cut in half. What fraction of a metre is each piece. Write a division

statement and solve the problem.

4. Teressa finds 912 of a chocolate bar to share with herself and 3 friends. What fraction of a chocolate

bar does each person get? Write a division statement and solve the problem.

5. Alisha needed 34 L of gasoline to mow the lawn. There was 3 34 L of gasoline in the container. How

many times can she mow the lawn before refilling the container? Show all calculations.

6. Jean-Pierre walked 4 12 km in 1 14 h. If he walked at a steady pace, how fast did he walk in kilometres

per hour? Shall all calculations.

39

7. A running track used in a competition is 25km in length. How many laps is a 1500 m race? There are 1000

m in 1 km. Show all steps and calculations.

Lesson 5: Adding and Subtracting Fractions

Refer to Learning Target #5Learning Target #6 – I can add and subtract fractions

Adding and Subtraction with Pattern Blocks

Try This: Pattern Blocks: 36+13

To add or subtract fractions:

1. ________________must be the same

40

2. You may have to create __________________fractions to create common ________________ before adding or subtracting

3. Only add or subtract the _______________ keep the _________________.4. Final answers must be in lowest terms

1. 312

+ 712

=2. 89−49=¿ 3. 14 + 2

3=¿

4. 35−12=¿ 5. 11

12−34= 6.1 2

5+3 45 =

7. 6 25+2310

=8.7 25−3 3

4+ 310

=¿

Adding and Subtraction Word Problems – Express final answer as a proper fraction or mixed number fraction.

1. Devin ate 625 chocolate bars from a box of 10 chocolate bars. How many chocolate bars were

left?

2. Addison came home from school feeling very hungry so she ate 13of a pound of cookies. She

was still hungry so she ate another 38 of a pound cookies. How many pounds of cookies did

Addison eat altogether?

41

3. Manraj put 134 teaspoons of salt into a bowl. Then he added 2

16 teaspoons of sugar. He then

mixed the sugar with the salt and removed 712 of a teaspoon of the salt/sugar mixture. How

much of the mixture remained in the bowl?

Assignment: Addition/Subtraction of Fractions worksheet; How’s Business?; FractionWord Problems; “Why did the Termite like expensive hotels?

42

43

44

45

46

47

Lesson 6: Applying Fractions Operations

Learning Target #7: I can do order of operations using BEDMAS to answer questions with mixed operations.

Warm –Up -Mixed Operations – Recall to add or subtract fractions a ___________________ denominator is required. This is not the case with multiplying or division!!!

310

+ 110

34−16

6 34+2 12

6 12×2 34

57÷5

Applying Order of Operations to Fractions

Recall BEDMAS: B E D or M A or S

a) 2÷ 14 +3× 12 b) 56−

13×2 c) 2 14 ÷ (1 34 +1 1

4 )

d) 7× 12−2÷35 e) 3

2÷(12+ 14 )÷ 34 f) 2 1

4−12×(34−1

8 )

48

Word Problems

Example 1: Bal earns $25/h as a machine operator in sawmill. For time worked above 40 hours in a week, he earns time-and-a-half. How much time does Bal earn for working 46 hours in a week?

Note: time-and-a-half means to paid for 112h for each hour of work done.

Example 2: A recipe for chocolate chip cookies requires 12 cup of brown sugar and

14 cup of granulated

sugar. This recipe makes 12 cookies. If this recipe is used to make five dozen cookies, What is the total amount of sugar required?

Practice Problems:

1. A pancake mix calls for 412 cups of flour and 2

14 cups of water to make 18 pancakes. How

many cups of each ingredient is needed to make only six pancakes.

2. Alexis earns $24/h as traffic controller. For time worked above 30 hours she will earn time and

a quarter (114). If she works a total of 36 hours, what is her total pay?

49

Assignment: Order of operations sheet next page!

Apply Order of Operations and Calculate!

1. 23+ 13× 12 2.

58−14× 34

3. 59÷ 23+ 34 4.

56÷ 14−2 16

5 ( 25+ 14 )× 23 6. ( 56−34 )÷ 18

7. 23÷ 13× 16+ 49 8. 1

910

−25× 14 ÷

13

9. 214−38÷ 516× 2532 10.

23÷ 821×(2 1220+1 35 )

11. ( 12−14 )÷ 316+4 12× 112 12. (8 13−2)÷ 23×(3+1 25 )

50

51