Questions 0 + - = 9 8 7 1 2 3 4 5 6 c Introducing ALbert Einstein Chapter 3.1Using models to multiply fractions and whole numbers Repeating Multiplication Multiplying fractions Using model to multiply Fractions 4 x 5

6 Move 3 of a spot 4 times Chapter 3 Mind Map 1 1 1

+ +

5 5 5 = 3 5 It could also be 3 x 1

5 3 x 1

5 The answer is 3

5 The first number is how many models you draw

The second fraction is how many you draw Multiplication fraction You can multiply the fraction Start with the numerators 4x 5 = 20 The denominator 20

6 Put the fraction in a mixed fraction 3 2

6 Which can also be 3 1

3 The answer 3 1

3 Using number lines to multiply fractions 4 x 3

10 0 1 2 3 4 1 2 3 4 5 6 7 8 9

10 10 10 10 10 10 10 10 10 1 2 3 4 5 6 7 8 9

10 10 10 10 10 10 10 10 10 1 2 3 4 5 6 7 8 9

10 10 10 10 10 10 10 10 10 1 2 3 4 5 6 7 8 9

10 10 10 10 10 10 10 10 10 10 The answer is 12 this is in a improper fraction in a mixed number it is 1 1 10 5 1. It takes two- thirds h to pick all the apples on one tree at spring water farms. There are 24 trees. How long will it take to pick all the apples?

2. Sarah went to the West Edmonton Mall. She took $28 with her. She spent four- seventh of her money on the rides. How much money did Sarah spend on rides?

3. Laura takes three- fourth h to fill one shelf at the supermarket.

Henri can fill the shelves in two- thirds Laura's time.

There are 15 shelves. Laura and Henri work together

How long will it take to fill the shelves? Answers 1. 24 x 2 = 16

3 It will take 16 hours to pick the apples 2. 4 x 28 = 16

7 Sarah spent 16 dollars on rides at West Edmonton Mall 3. 4 1

2 It will take Laura and Henry 4 and a half hours Off To 3.2- Using models to multiply fractions Chapter 3.2 Using models to multiply Fractions 1. Einstein used five-eighth of the money he had saved to buy a DVD player and 4 dvds.The cost of the DVD player was two-fifth of the amount he spent. What fraction of his savings did Barry spend on the DVD

2.One-eighth of the seats in the movie theater were empty.

Two -seventh of the seats that were full were filled with teenagers. What fraction of the theater was filled with teenagers

3. Why is five- eighth of three-twelfths equal to three- eighth of

five -twelfth? Answers Questions Laura cut two- thirds of the grass on a lawn When multiplying fraction a quick strategy is to reduce. Using Pattern Blocks to Multiply Fractions Sarah cut one- half of the remaining grass what fraction of the lawn did Akiva cut Solution ..... The orange hexagon represent the lawn.

6 green triangles also represent the lawn.

4 green triangles represent the grass cut by Laura

2 green triangles represent the remaining grass.

Sarah cut one -half of the remaining grass.

One-half of the remaining grass is 1 green triangle.

One green triangle represents 1 -sixth 1 x 1 = 1

2 3 6 Multiplying Fractions 3 x 8

4 9 Does 3 go into 9 3 x 1

3x 3

cross out the 3

3 because a 1 and the 9 becomes a 3 Does 4 go into 8 4 x 1

4 x 2

cross out the fours

the four becomes a 1 and the 8 becomes a two 1 x 2

1 3 = 2

3 1. 1

4 Einstein spent one-fourth of his money on DVD's 2. 2 x 7 1

7 8 4 = 3. 5 x 3 = 5

8 12 32 3 x 5 = 5

8 12 32 See you In the clouds

Sneak Peek 3.3 Multiplying Fractions Chapter 3.3 Multiplying Fractions 3.4 Multiplying Mixed numbers 4 x 1

5 3 Questions 1. four -seventh of the grade 8 students voted to have spirit day. Three- fifth of those students wanted spirit day to be on the first day of classes. What fraction of the grade 8 students wanted Spirit Day to be on the first day of classes.

2.Find each square root 5 2/5 x 2 3/6 5 3/6 we can use a chart to model the equation... Common Denominators What is the common denominator between 5 and 3? The common denominator is 15 4 x 3 5 x 1

5 x 3 5 x 3 Rewrite the Problem 12 x 5

15 15 3.5 dividing Whole numbers and fractions Next Section 3.4 1 a.) 4

9 b.) 16

25 3. The product of two- fractions is two thirds. One fraction is three- fifth. What is the other fraction? Chapter 3.4 Multiplying Mixed Fractions Answers 4 x 3 = 12

7 5 35 1. a.) 2. a.) 2 b.) 4

3 5 3. 10

9 Using Number Lines to divide whole numbers and fractions = 60

225 This fraction can be reduced 12

45 Using F.O.I.L to multiply mixed fractions Foil stands for First- Outer-Inner- Last 2 1

3 x 3 1

2 The first number is 2 and 3... 2 x 3 = 6 The inner number is one third and 3

3 x one third equals 1 The outer number is 2 and one half

one-half x 2 =1 The last number is one third and one half. One half x one third = one sixth Add all the numbers up... 6 + 1+ 1 +1

6 The answer is 8 one sixth Using Improper fractions to multiply mixed numbers 2 1 x 3 1

3 2 Change the mixed numbers into improper fractions 2 x 3 = 6 + 1 = 7 over 3 3 x 2 = 6+ 1 = 7 over 2 7 x 7

3 2 Solve 7 x 7 = 49

3x 2 = 6 49 divided by 6 = 8 the answer is 8 1

3 Questions 1.A restaurant in Edmonton , lists the prices on its menu in fractions of a dollar. Three friends have lunch at the restaurant. Each of 3 friends orders a veggie mushroom cheddar burger for 11 three quarters, with a glass of water

a.) what was the total bill before taxes?

b.) what was the total bill before taxes in dollars and cents?

2.During the school year, the swim team practise's 2 three quarters h per week. During the summer, the weekly practice time is increased to 2 one third times the school-year practice time. How many hours per week does the team practice during the summer? Answers 1.a.) 35 1 b.) $32. 25

4 2.) 6 5 or 6 hours and 25 minutes

12 To find out how many 1 are in 8 we can use a number line 2 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 count the jumps There are 16 half's in 8 We can also use a pizza diagram to model division 3 2 4 First draw 3 circles and then divide them into quarters. After that you count groups of 2 fourths 1 1 2 2 3 3 4 4 5 5 6 6 So, three divided by two-fourths equals 6 Use fraction circles to find... 5 3 8 Solution 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 3.6 Dividing Fractions 6 6 7 7 7 8 9 9 9 10 10 10 11 11 11 12 12 12 13 13 13 1 2 3 4 5 3.7 Dividing Mixed Numbers 6 8 9 7 10 11 12 13 14 16 15 Obstacle 1 Obstacle 2 Obstacle 3 Goal Start Use BEDMAS Congratulations you finished the nine sections with Albert Einstein

The treasure that you won is the nine sections that you learnt 3.9 Order or Operations with Fractions Brackets

Exponents

Division

Multiplication

Addition

Subtraction Remember from Left to Right Questions 1.a) 3.8 Solving Promblems with Fractions With Albert Einstein Laura, Sarah and Einstein evaluated this expression:

4 x ( 3 - 1) + 13 x 1

4 2 6 2

Laura's answer was five one- thirds, Sarah's answer was two one- twelfth and Joe's answer was four five- sixth

a.) who had the correct answer? Sarah's answer was correct 2. 14 / 14 x 5 + 11

15 3 8 4 answer Examples When solving problems it is important to understand what concept you are supposed to do.

Some key words is total suggests addition

less than suggests subtraction

times suggests multiplication

shared suggests dividing

When solving a problem the operation must make sense in the context of the problem Examples 1. Albert mixed two thirds one can of yellow paint and one forth of one can of white paint to paint a wall in his bedroom. How much paint did he have altogether. The key words are altogether wich suggests addition 2 + 1=

3 4 Put it in a common denominator which is 12 8 + 3= 11

12 12 12 Questions #1 Questions # 2 Questions # 3 Answers Sarah has a collection of 72 music CDs. One-sixth of the CDs are dance Music. one- fourth are hip hop, and three -eighth are country. The rest of the CDs are rock music. What fraction of her CDs are rock music? The Einsteins went on a driving vacation. They decided to travel one-third of the distance on the first day. Owing to bad weather, they had to stop for the night having gone only one-quarter of the distance the one-third point. What fraction of the total distance did they travel the first day? Laura used two five-sixth loaves of bread to make sandwiches for lunch. She made equal numbers of four different types of sandwiches. What fraction of a loaf of bread did Laura use for each type of sandwich? .1. Subtraction 5

24

2. Multiplication 1

12

3. Division 17

24 Solve! The answer is 2 7

8 Solve 87 - (11 + 9) x 2

10 5 4 3 Answer 5 11

15 Using a number line to divide mixed numbers 15

10 15

10 14

10 0 1 2 3 4 5 44

10 Solve 4 2 / 1 1

5 2 Using Common Denominators to Divide Mixed Numbers Divide 4 2

5 1 1

2 The answer is 2 14

15 You can go into it twice with fourteen-fifeteenth left over First put it into a improper fraction 22

5 3

2 The common denominator is

10. Put the fraction under 10 22 x 2 = 44

5 x 2 = 10 3 x 5= 15

2 x 5=10 44 15 = 44 /15 is 2 14

1o 10 15 Using Multiplication to Divide mixed numbers 4 2

5 1 1

2 Change it into improper fraction 22 3

5 2 Use reciprocal Reciprocal is when you leave the first fraction alone, change division to mulitiplication and switch three- halves to two-thirds Whenever using reciprocal put a tiny r next to the number that changed 22 x 2 = 44

5 3 15 r Questions 1. Maxine took twelve and a half hours to build a model airplane. She worked for one and one-quarter h each evening. How many evenings did Maxine take to complete the model?

2. Glenn ran three and one-third laps in eleven andtwo-thirds min. Assume Glenn took the same amount of time to complete each lap. How lond did Glenn takte to run one lap?

3. Amelia has her own landscaping buissness. She ordered ten and five-eighth loads of topsoil to fill large concrete planters. Each planter holds one and a half loads of topsoil. Calculate the numbers of planters that amelia can fill Answers 1. 10

2. 3 1

2

3. 10 5 / 1 1 = 7 1

8 2 12 Albert Einstein Quotes # 1 Using common denominators to divide fractions Divide 4 1

5 10 Use a common denominator 8 1

10 10 This fraction means how many one tenths are in 8 tenths The answer is 8 8 8 Questions Answers Using Multiplication to divide fractions You can use reciprocal to dive fractions 3 1

5 4 The reciprocal rule is to leave the first number alone change division to multiplication and swith one-quarter to four-oneths 3 x 4= 12

5 1 5 change it to a mixed fraction the answer is 2 2

5 Questions

1. As a busboy in a resteraunt, Albert takes one-twelveth h to clear and reset a table. How many tables can Alberts clear in two thirds h? Question

2.To conduct a science experiment each pair of students require one-sixteenth cup of vinegar. The science teacher has three-fourth cup of vinegar. How many pairs of students can conduct the experiment? Question 3.Replace each box with a fraction to make each equation true. a.)2

3 8

9 = b.)1

4 = 9

20 Answers 1. 8

2.12

3. a.) 3 b.) 5

4 4 1. How many one-quarter size sheets can be cut from five sheets of paper?

2. How many two-thirds cup servings are in 6 cups of fruit?

3. Laura feeds her cat four-fifth of a tin of cat food each day. Laura has 12 cans of cat food. How many days' suppy of cat food does Laura need? 1. 20

2. 9

3.15 Done by Albert Einstein, Sarah and Laura When we multiply fractions we can use repeated addition, repeated addition can also be written as multipucation

eg. 3 x 2 can be written as 2 + 2 + 2 Fun facts about Albert Einstien Einstien was a child who was born with an abnormal big head and was unable to talk fluently until he was nine

Two of Einstein's least favorite things were haircuts and socks.

Two of Einstein's favorite things were the violin and sailing.

Einstein named his violin 'Lina'.

Einsien actually failed his 1st college entrance exam, and had to go to a secondary school in Switzerland. We can use modles to represent fractions, lets use counters to modle the eqation

4 x 6

6 10 first we want to modle a full set of tenths, now because there are six counters in 6/10, circle 6 counters 4 4 4

Hello my name is Albert Einstien. I was born

in 1921 on 14 March 1879 in

Ulm, Kingdom of Württemberg, German Empire. I am a theoretical physasist and I created the theory of relativity, and E=mc2. Today I am here to teach you about multiplying and dividing fractions. Fun Fact # 1 Albert Einstein failed his collage entrance exam and had to go to secondary school in switzer land Fun fact # 2 Albert Einstein divorced and married his first cousin! Fun fact # 3 Albert Einstein was born with a big head so doctors thought that he wasn't smart Also Einstein has a daughter Fun Fact # 4 and #5 Albert started talking when he was four but still he wasn't fluent until the age of nine At the age of five Einstein's father gave him a compass for his brother which started a revolution his brain. Albert failed every course except for math and science Put your hand on a hot stove for a minute and it seems like an hour. Sit with a pretty girl for an hour and it seems like a minute. That’s relativity. Fun fact # 6 Einstein hated haircuts and socks but he loved the violin and sailing

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# Chapter 3 Mind Map

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