Albert Einstein Mr. Einstein teaches how to multiply fractions with models. Math Unit 3 Project

By: Spencer and Cole 8-2 3.1 Albert Einstein developed the practice of imaging

physical event and he developed expressing those ideas using calculus. He discovered the wonders of light, gravity, time, and the universe using his new discovered mathematical terms. Using Models to multiply fractions Whole Numbers Albert wants to multiply 4 x 3

5 Think of it as 4x3= 3+3+3+3

5 5 5 5 5 Now put all of the fifths together. Which will make 2 2/5. So 4 x 3/5= 2 2/5. Question 1 What would the multiplication

statement be for the fraction

circles and what is the product? Answer 1 There are 4 circles so 4 is multiplicand. In each circle 1\2 is filled so 1\2 is multiplier. 4 x 1\2 multiplicand multiplier When you add all your halves together they equal 2. + + + = 4 x 1\2 =2 Question 2 Find the product for the equation. Use fraction circles to help you. 2 x 3/4 Answer 2 Question 3 Multiply 7 x 3/4. Sketch a rectangle to help you. Answer 3 Sketch the base with 7 units the height with 1 and divide the height into fourths. The area of the shaded rectangle is base x height= 7 x 3/4. The area of each small rectangle is 1 x 1/4. So the shaded rectangle is 21 x 1/4 = 21/4. then 7 x 3/4 = 21/4 3.2 Using Models to

Multiply Fractions In Albert's class 3/4 of the grade 10 class tried out for basketball. 6/8 of the students made it. What fraction of students made the team. 3/4 of the team tried out. 6/8 made the team 12/ 24 are both colored. That can be reduced to 1/2. Half of the class made the team. Question 1 One day Albert went out to the supermarket to buy himself some apples, but when he got there he noticed that 1/4 were green, 2/8 were yellow and the rest were red. How many apples were red? Answer 1 1/4 were green 2/8 were yellow Question 2 Find each product using models. 3/4 x 2/6 3/5 x 7/8 1/4 x 2/3 Answer 2 Part 1 3/4 x 2/6 Answer 2 Part 2 1/4 x 2/3 Answer 2 Part 3 3/5 7/8 x Question 3 One eighth of Albert's classroom was not full. 2/7 of the people in the class had grey shirts. What is the fraction of the people without grey shirts? Answer 3 2/7 7/8 x 1/4 of the people were wearing grey shirts. 3.3 Multiplying Fractions 3.3 Multiplying Fractions In Albert Einsteins class students had trouble with multiplying fractions so this is what Einstein taught them to help them out. Example: 3/4 x 2/3 4 x 3= 12 So make the

model out of 12

squares Make sure that it is 4 horizontally and 3 vertically Now take the 3 from the 3/4 and put it on vertically on the diagram by putting it on the first vertical line. Than putting the 2 from 2/3 and put it on the first two squares of the horizontal line. Now since you cover two of the first horizontal line make sure you cover another squares in the second vertical line. Now that you are done you will have your answer. 6/12 is your

finale answer. 6/12 can

also be

known as

1/2! Question 1 One evening Albert went to go make a math book Albert only finished a couple pages, he had time to color 4/5 of the pages and he still has 2/3 of the book left to do. How many pages are colored in total? Answer 1 4/5 x 2/3 5 x 3= 15 4 vertically x 2 7/12 of the pages are colored. Question 2 Multiply! 2/4 x 5/7! Answer 2 2/4 x 5/7 4 x 7= 28 2 vertical x 5 10/28 Question 3 Albert took of his savings to a book store to shop, he spent 4/5 of 3/4 on math books. How much money did Albert have left? Math Answer 3 4/5 x 3/4 5 x 4= 20 4 vertically x 3 Albert had

12/20 dollars

left. 3.4 Multiplying Mixed Numbers 3.4 Multiplying Mixed Numbers 2 1/2 x 1 1/3

Write each mixed number as an improper fraction.

2 1/2= 2 + 1/2= 4/2 +1/2= 5/2

1 1/3= 1 + 1/3= 3/3 + 1/3= 4/3

5x4

------

2x3 = 20/6

20/6 / 2 = 10/3

10/3 = 3 1/3 2 1/2 1 1/3 2 x 1= 2 2 x 1/3= 2/3 1/3 x 1/2= 1/6 1/6 1/2 x 1= 1/2 1/2 Add all answers up with a common denominator.

2 + 3/6 + 4/6 + 1/6

2 + 8/6 8/6= 1 2/6 = 1 1/3

2 + 1 1/3= 3 1/3

3 1/3 Question 1 Write the mixed number and improper fraction represented by each picture. Answer 1 = = = 3 1/2 7/2 2 1/5 11/15 1 6/7 13/14 Question 2 Multiply using area models. 3 2/3 X 2 1/5 Answer 2 3 2/3x2 1/5= (3x2)+(2/3x2)+(3x1/5)+(2/3x1/5) = 6+4/3+3/5+1/2 = 6+40/30+18/30+15/30 = 6+73/30 = 6+30/30+30/30+3/30 = 6+2+1/10 = 8 1/10 2x3=6 3 2 1/5 2/3 1/5x3=3/5 2/3x1/5=2/10 2x2/3=4/3 Question 3 Multiply using area models. 4 3/8 x 1 1/4 Answer 3 4 3/8x1 1/4= (4x1)+(4x1/4)+(1x3/8)+(3/8x1/4) = 5+4/4+3/8+1/8 = 5+8/8+3/8+1/8 = 5+12/8 =5+8/8+4/8 = 5+1+4/8 =6 4/8 4x1=5 4 3/8 1 1/4 4x1/4=4/4 1x3/8 3/8x1/4=4/32 3.5 Dividing Whole Numbers

and fractions 3.5 Use a model to divide. 5 3/5 Think, how many 3/5 are in 5 holes. Use fraction circles in fifths to model 5. 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 6 6 6 7 7 7 8 8 8 Count the groups of 3/5

There are 8 groups of 3/5

and there is 1/5 left over.

The diagram shows that

1/5 is 1/3 of 3/5

So 5 3/5= 8 1/3. Question 1 Find the answer! 4 3/4 Answer 1 1 1 1 2 2 2 3 3 3 4 4 4 5 5 5 4 3/4= 5 1/4 Question 2 3 4/6 Answer 2 1 1 1 1 2 2 2 2 3 3 3 3 4 4 4 4 3 4/6= 4 2/4 Question 3 3 5/8 Answer 3 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4 4 4 3 5/8= 4 4/5 3.6 Dividing Fractions 3.6 Dividing Fractions There are two ways to divide fractions,

common denominator and a number line. Common Denominator 4/5 1/10 A common denominator for this

problem would be 10. 4/5=8/10 So, 4/5 1/10= 8/10 1/10 Number Line This means that how man 1/10

are in 8/10. 0 1 1/10 2/10 3/10 4/10 5/10 6/10 7/10 8/10 9/10 1/10 x 8 This is the same as 8 1= 8

So, 4/5 1/10=8 Question 1 3/4 4/8 Answer 1 Common Denominator 3/4 and 4/8 would have a common denominator of 8. So it takes 2 4's to get 8.

You would also have to

times the 3 by 2. So that would be

6/8 4/8=1.5 3/4 4/8=1.5 Question 2 1/2 1/8 Answer 2 1 0 1/8 2/8 3/8 4/8 1/2 5/8 6/8 7/8 8/8 1/8 1/8 1/8 1/8 1/2 1/8= 4 Question 3 7/12 1/4 Answer 3 Number Line Common Denominator 7/12 and 1/4 would have a common denominator of 12 It takes 3 4's to get 12.

and you would also

have to times the 1 by

3. So that would be

7/12 1/4= 2 1/3 7/12 1/4= 2 1/3 3.7 Dividing Mixed Numbers 3.7 Divide 1 7/8 ÷ 1 1/4 Change the mixed numbers to improper fractions 1 7/8=15/8 and 1 1/4=5/4 So, 1 7/8 ÷ 1 1/4 = 15/8÷5/4 = 15/8x4/5 =3/2x1/1 3x1 = 2x1 =3/2, or 1 1/2 Estimate to check. 1 7/8 is close to 2. 1 1/4 is close to 1. Since 1 7/8 is less than 2 and 1 1/4 is greater than 1,

the quotient will be less than 2. So, 1 7/8÷1 1/4 is about 2÷1=2 Since 1 1/2 is close to 2, the quotient is reasonable. 0 1 2 1 1/4 1 7/8 Question 1 Use a number line. To divide: 4 2/5÷1 1/2 Answer 1 4 2/5=22/5 and 1 1/2=3/2 Write each fraction with a common denominator. Since 2 and 5 have no common factors, a common denominator is 2x5=10. 22/5=44/10 and 3/2=15/10 So, 4 2/5÷1 1/2=44/10÷15/10 This means: How many tenths are in 44 tenths? one 15/10 one 15/10 14/10 leftover 44/10 or 4 2/5 5 4 3 2 1 0 From the number line , there are 2 groups of 15 tenths with remander of 14 tenths From the number line, 14 tenths is 14/15 of 15 tenths So, 4 2/5÷1 1/2=2 14/15 0 10/10 15/10 14/10 Question 2 Use multiplication. 3 2/3÷5 1/4 Answer 2 Put it into improper fractions, 3 2/3÷5 1/4=11/3÷21/4 Reciprocal 21/4 =4/21 So, 22/5÷21/4=22/5÷4/21 = 22x4 5x21 =88/105 Question 3 Use common denominators. Divide:4 2/5÷1 1/2 Question 3 4 2/5=22/5 and 1 1/2=3/2 22/5=44/10 and 3/2=15/10 So, 4 2/5÷1 1/2=44/10÷15/10 =44÷15 =44/15, or 2 14/15 3.8 Solving Problems with Fractions 3.8 When solving word problems it is important to identify the operation or operations needed to solve the problem. To identify the operation: -Think about the situation. -Make sense of the problem by explaining it in your own words, drawing a picture, or using a model. -Think about what is happening in the problem. Sometimes, key words can help you identify the operation. "total": adding, "less than": subtracting, "times": multiplying, "shared": dividing Question 1 Kassie worked on her science project for 3/4 h on Tuesday and 5/6 h on Wednesday. She spent Thursday finishing her math homework. a) How long did Kassie work on her science project altogether? b) How much longer did Kassie work on the project on Wednesday than Tuesday? c) Altogether, Kassie spent 2h on school work over three days. How long did she spend on her math homework? Answer 1 Part 1 a) Add: 3/4+5/6 =19/12 =12/12+7/12 =1 7/12 3/4+5/6=9/12+10/12 Kassie worked on her science project for 1 7/12 h. Answer 1 Part 2 b) The words "longer... than" suggest subtraction. To find how much Kassie worked on Wednesday and Tuesday, Subtract: 5/6 - 3/4 5/6 - 3/4=10/12 - 9/12 =1/12 Answer 1 Part 3 c) Kassie worked 1/12h on Wednesday than on Tuesday. The word "altogether" suggests subtraction. However, to find the time Kassie spent doing math homework, we subtract. From part a), we know Kassie spent 1 7/12 h on her science project.Altogether, Kassie spent 2h on school work over the 3 days. So, the time spent on her math homework is: 2 - 1 7/12= 1 12/12 - 1 7/12 = 5/12 Kassie spent 5/12h on her math homework. Question 2 Dakota volunteered at a gift-wrapping booth for a local charity. He volunteered for 2 3/4 h and wrapped 11 gift boxes. His friend Brittany volunteered 1 1/3 times as long. a) How long did Dakota spend wrapping each gift box? b) How many hours did Brittany volunteer? Answer 2 Part 1 a) We are given a time for many and we have ti find time for one; this suggests division. 2 3/4÷11 Write the mixed number as an improper Fraction. 2 3/4=11/4 So, 2 3/4÷11=11/4÷11/1 =11/4x1/11 = 11x1 4x11 =1/4 Dakota spent 1/4h wrapping each gift. Answer 2 Part 2 b) The words "times as long" suggests multiplication. So Brittany volunteered 1 1/3 of the 2 3/4 that Dakota volunteered. 2 3/4 x 1 1/3 Write the mixed numbers as improper fractions. 2 3/4=11/4 and 1 1/3=4/3 So, 2 3/4x1 1/3=11/4x4/3 11x4 = 4x3 =11/3 =3 2/3 Brittany volunteered for 3 2/3 h. Question 3 Chad mixed 2/3 of one can of yellow paint and 1/4 of can of white paint to paint a wall in his bedroom. How much paint did he have altogether? Answer 3 The word "altogether" suggests subtraction. You need to find a common denominator between the two then add them. 2/3=8/12 and 1/4=3/12 8+3=11 =11/12 3.9 Order of Operations with Fractions 3.9 Evaluate: 3/4-2/3÷4/5x(1/8+1/4) = 3/4-2/3÷4/5x3/8 =3/4-5/6x3/8 =3/4-5/16 =7/16 Question 1 Evaluate:1/2x3/5+1/4 Answer 1 =1/2x3/5+1/4 =2/5+1/4 =9/20 Question 2 Evaluate: 1/8x3/4x7/5÷7/10 Answer 2 =1/8x3/4x7/5÷7/10 =3/32x7/5÷7/10 =21/160÷7/10 =3/16 Question 3 Evaluate: 4/9x(2/3-1/6)-1/8x4/3 Answer 3 =4/9x(2/3-1/6)-1/8x4/3 =4/9x1/2-1/8x4/3 =2/9-1/8x4/3 =2/9-1/5 =1/45 The End. 1 1/2 A common denominator between

these fractions would be 8. So that would be another 2/8 with the 2/8.

so that would be 4/8 or 1/2. Since that is 1/2 already that means that 1/2 has to be red. 4/8 or 1/2 is red! Common denominator is 12 3/4 x 2/6= 12 9 x 4 = 36 12 / = 3 Common denominator is 12 1/4 x 2/3= 3 x 8/12= 24/12 =2 Common denominator is 40 3/5 x 7/8= 24 x 35/40 =840 2/7 x 7/8= 1/4

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