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# Operations with Fractions

Blaise Pascal
The French mathematician had been involved in imaginative and subtle work in geometry and other branches of mathematics. In 1645, Pascal invented the first calculating machine and sold it. His work in hydrostatics led to the invention of the

by

Tweet## Victoria Meeker

on 24 January 2013#### Transcript of Operations with Fractions

BY: Holly, Vanessa and Victoria 3.1 Using Models to multiply Fractions and Whole Numbers Blaise teaches you how! Hi, my name is Blaise Pascal. I invented one of the first mechanical calculators: the pascaline. 1. Write a multiplication statement for each set of fraction circles. Then find each product. 3.2 using models to multiply fractions 1. 3.3 Multiplying fractions 3.4 Multiplying mixed numbers 1. Write each mixed number as an improper fraction. 1623 Born in Clermont on June 19

1631 Moved to Paris

1636 Proved the 32-nd proposition of Euclid

1641 Designed a calculating machine the Pascaline to be completed in 1653

1650 Pascal suddenly abandoned his favorite pursuits to study religion

1653 Returned from his religious studies to administer his father's estate

1662 died at Paris on August 19 = A) B) = 2. Multiply.

A) 3x B) 12x A) B) 12x7

1 9 Vanessa went to Galaxy Land at West Edmonton Mall. She took $28 with her. She spend 4/7of her money on the rides. How much money did Vanessa spend on rides? 3. Find each product. A) 3x5 4 8 B) 4x9

2 5 2. A) Shade the rectangle to find each product. 1x3 2 4 B) 2x1 5 2 A) B) = 3/8 =2/10 =1/5 3. Noah used 5/8 of the money he had saved to buy a DVD player and 4 DVDS. The cost of the DVD player was 2/5 of the amount he spent. What fraction of his savings did Noah spend on the DVD player. 5 2 8 5 x = 5 2 8 5 x = 4 = 4x1 1 2 2

1 = = 5x1 1 4 = 1 5x 4x 1 2 5 4 3x 4 5 4 5 = 3x4 1 5 = 12 5 12x 7 9 = 7 9 84 9 = = 16 1 She spent $16 = 15 32 = 36 10 Find the common factors of each pair of numbers. A) 14,21 B)10,15 C)6,9 A) 7 B) 5 C) 3 2. 3x2 5 x 7 Shade the rectangles to find the product. 9 1 3 = 2 2 5 = 18 5 = = 1. = = 6

35 3. The sum of two fractions is 7/12. The product of the same two fractions is 1/12. What are the two fractions? 1 1

4 3 x = 1

12 1

4 1

3 + = 7

12 12 3 + 4 = 7 28 x 4 = 28 1 4 7 x 1 4 2 8 A) 2 3/10 B)4 1/8 C)3 5/9 A)23/10 B)33/8 C)23/9 2. Use estimation. Which number is each product closer to? A)2 1/8 x 3 3/4 CLOSEST TO: 6 or 8

B)3 5/9 x 1 5/6 CLOSEST TO: 6 or 8

C)7 3/8x 2 4/5 CLOSEST TO:21 or 24 ANSWERS: A)2 1/8 is closest to 2, and 3 3/4 is closest to 4, so 2 x 4 = 8. The answer is 8. B) 3 5/9is closest to 4, and 1 5/6 is closest to 2, so 4 x 2 = 8, The answer is 8. C)7 3/8 is closest to 7, and 2 4/5 is closest to 3, so 7 x 3 = 21, The answer is 21. 3. Students baked cookies for a charity bake sale. Shannon baked 2 1/2 dozen cookies. Jack baked 2 1/6 times as many cookies as Shannon. Holly and Philip together baked 5 1/3 times the number of cookies Shannon baked. Calculate how many dozen Holly and Philip baked together. 2 1/2 x 5 1/3 = 2 x 5 16 3 40 3 = = 13 1/3 3.5 Dividing Whole Numbers and Fractions 1. Find each quotient. a) 5 / 2 3 b) 4 / 3 4 Answers: a) 5 1 X 3 2 R = 15/2 or 7 1/2 b) 4 1 X 4 3 = 16/3 or 5 1/2 2. Use fraction circles to find 6 3. Copy these boxes: . . a) write the digits 2, 4, and 6 in the boxes to find as many division expressions as possible. Answers: 2 / 4 6 1. = 3 2. 2 / 6 4 =1 1/3 3. 4 / 2 6 = 12 4. 4 / 6 2 =1 1 3 5. 6 / 2 4 = 12 6. 6 / 4 2 = 3 ANSWER: ANSWERS: ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: ANSWERS: 4 / 5 ANSWER: 3.6 Dividing Fractions 1. Write the reciprocal of each fraction. a) 5/9 b) 3/7 c) 7/8 d) 14/15 ANSWERS: a) 9/5 b) 7/3 c) 8/7 d) 15/14 2. Use multiplication to find each quotient. 7 2 / 4 3 / ANSWERS: 7 2 3 4 x = 21 8 = 2 5 8 a) a) b) b) 8 5 3 4 8 5 r x 4 3 r = 32 15 = 2 2 15 3. Use a number line to illustrate the quotient. 3 5 1 4 / 3 5 = 12 20 1 4 5 20 = 12 20 / 5 20 one 5/20 one 5/20 2/5 of 5/20 ANSWER: 2 2 5 3.7 Dividing Mixed Numbers 1. Divide. Estimate to check the quotient is reasonable. 1 7 8 / 1 1 4 ANSWER: 1 7/8 = 15/8 1 1/4 = 5/4 15 5 / 8 4 15 8 x 4 5 r 3/2 or 1 1/2 = 2. Brittany has a summer job in a bakery. One day she used 3 3/4 cups of chocolate chips to make muffins. A dozen muffins require 3/4 cup of chocolate chips. How many dozen muffins did Brittany make that day? 3 3 4 ANSWER: / 3 4 3 3 4 = 15 4 15 4 / 3 4 15 / 3 = 15 3 = 5 3. Write each mixed number as a improper fraction. a) 4 3 8 b) 1 7 10 c) 5 2 5 d) 6 1 6 ANSWERS: a) 35/8 b)17/10 c) 27/5 d) 37/6 3.8 Solving Problems with fractions. 1. Cassie worked on her math project for 3/4 h on Tuesday and 5/6 h on Wednesday. How long did Cassie work on her math project altogether. ANSWER: 3 4 + 5 6 = 9 12 + 10 12 = 1 7 12 2. Nick volunteered at a gift-wrapping booth for a local charity. He volunteered for 2 3/4 h and wrapped 11 gift boxes. His friend Chad volunteered 1 1/3 times as long. a) how long did Nick spend wrapping each gift box?

b) how many hours did Chad volunteer. ANSWER: a) 2 3 4 / 11 = 11 4 / 11 11 4 x 1 11 r = 1 4 b) 2 3 4 x 1 1 3 = 11 4 4 3 x = 3 11 = 3 2 3 3. Jacob mixed 2/3 of one can of yellow paint and 1/4 of one can of white paint to paint a wall in his bedroom. How much paint did he have all together. 2 3 + 1 4 = ------- 12 11 8 + 3= 3.9 Order of operations with fractions 1. Which operation do you do first? a) 1/3 x (7/8-3/4) b) (5/3 +7/12) x 4/9 You do the brackets in both equations first. ANSWER: 2. Evaluate: 5 16 - 3 8 x 2 3 ANSWER: 3 8 x 2 3 5 16 - 1 4 = 5 16 - 4 16 = 1 16 3. Evaluate: 1 8 x 3 4 x 7 5 7 10 Answer: = = 2 1. 2. 1 8 X 3 4 = 3/32 3. 3 32 X 2 1 = 3/16 3.1 Using Models to Multiply Fractions and Whole Numbers We know that repeated addition can be written as multiplication. So we can use a number line to divide whole and mixed numbers. As well as making fraction strips or circles. Mr. Pascal will be teaching you how in the next few slides. 3.2 Using Models to Multiply Fractions 3.2 is basically the same thing as 3.1. Keep trying i know you'll get it. This stuff is easy! 3.3 Multiplying Fractions Just follow along with me and I know it will come! Save any questions you have for the end for for now just have fun and do some MATH! 3.4 Multiplying Mixed Numbers What is the difference between a proper and improper fraction you ask? Well in an improper fraction the numerator is greater than the denominator. And vs versa for a proper fraction. 3.5 Dividing Whole Numbers and Fractions When you first studied division. you learned two ways: sharing and grouping. For example 20/5 can be thought of as, Sharing 20 items equally amoung 5 sets

Or grouping 20 items into sets of 5 To help you with this section recall that multiplication and division are inverse operations. 3.6 Dividing Fractions You have used grouping to divide a whole number by a fraction.

You have used sharing to divide a fraction by a whole number.

You will now investigate dividing a fraction by a fraction. Stay strong were almost done! 3.8 Solving Problems with Fractions When solving word problems, it is important to identify the operation or operations needed to solve the problem. This is what Mr. Pascal has told us so it must help a lot. Keep that in mind throughout the section. 3.9 Order of Operations With Fractions Every fraction can be written as a decimal. So, we use the same order of operations for fractions as for whole numbers and decimals. After this your done! So push through and have fun! Thanks for watching! Have a fantastic day! / / 7 5 7 10 7 5 x 10 7

Full transcript1631 Moved to Paris

1636 Proved the 32-nd proposition of Euclid

1641 Designed a calculating machine the Pascaline to be completed in 1653

1650 Pascal suddenly abandoned his favorite pursuits to study religion

1653 Returned from his religious studies to administer his father's estate

1662 died at Paris on August 19 = A) B) = 2. Multiply.

A) 3x B) 12x A) B) 12x7

1 9 Vanessa went to Galaxy Land at West Edmonton Mall. She took $28 with her. She spend 4/7of her money on the rides. How much money did Vanessa spend on rides? 3. Find each product. A) 3x5 4 8 B) 4x9

2 5 2. A) Shade the rectangle to find each product. 1x3 2 4 B) 2x1 5 2 A) B) = 3/8 =2/10 =1/5 3. Noah used 5/8 of the money he had saved to buy a DVD player and 4 DVDS. The cost of the DVD player was 2/5 of the amount he spent. What fraction of his savings did Noah spend on the DVD player. 5 2 8 5 x = 5 2 8 5 x = 4 = 4x1 1 2 2

1 = = 5x1 1 4 = 1 5x 4x 1 2 5 4 3x 4 5 4 5 = 3x4 1 5 = 12 5 12x 7 9 = 7 9 84 9 = = 16 1 She spent $16 = 15 32 = 36 10 Find the common factors of each pair of numbers. A) 14,21 B)10,15 C)6,9 A) 7 B) 5 C) 3 2. 3x2 5 x 7 Shade the rectangles to find the product. 9 1 3 = 2 2 5 = 18 5 = = 1. = = 6

35 3. The sum of two fractions is 7/12. The product of the same two fractions is 1/12. What are the two fractions? 1 1

4 3 x = 1

12 1

4 1

3 + = 7

12 12 3 + 4 = 7 28 x 4 = 28 1 4 7 x 1 4 2 8 A) 2 3/10 B)4 1/8 C)3 5/9 A)23/10 B)33/8 C)23/9 2. Use estimation. Which number is each product closer to? A)2 1/8 x 3 3/4 CLOSEST TO: 6 or 8

B)3 5/9 x 1 5/6 CLOSEST TO: 6 or 8

C)7 3/8x 2 4/5 CLOSEST TO:21 or 24 ANSWERS: A)2 1/8 is closest to 2, and 3 3/4 is closest to 4, so 2 x 4 = 8. The answer is 8. B) 3 5/9is closest to 4, and 1 5/6 is closest to 2, so 4 x 2 = 8, The answer is 8. C)7 3/8 is closest to 7, and 2 4/5 is closest to 3, so 7 x 3 = 21, The answer is 21. 3. Students baked cookies for a charity bake sale. Shannon baked 2 1/2 dozen cookies. Jack baked 2 1/6 times as many cookies as Shannon. Holly and Philip together baked 5 1/3 times the number of cookies Shannon baked. Calculate how many dozen Holly and Philip baked together. 2 1/2 x 5 1/3 = 2 x 5 16 3 40 3 = = 13 1/3 3.5 Dividing Whole Numbers and Fractions 1. Find each quotient. a) 5 / 2 3 b) 4 / 3 4 Answers: a) 5 1 X 3 2 R = 15/2 or 7 1/2 b) 4 1 X 4 3 = 16/3 or 5 1/2 2. Use fraction circles to find 6 3. Copy these boxes: . . a) write the digits 2, 4, and 6 in the boxes to find as many division expressions as possible. Answers: 2 / 4 6 1. = 3 2. 2 / 6 4 =1 1/3 3. 4 / 2 6 = 12 4. 4 / 6 2 =1 1 3 5. 6 / 2 4 = 12 6. 6 / 4 2 = 3 ANSWER: ANSWERS: ANSWER: ANSWER: ANSWER: ANSWER: ANSWER: ANSWERS: 4 / 5 ANSWER: 3.6 Dividing Fractions 1. Write the reciprocal of each fraction. a) 5/9 b) 3/7 c) 7/8 d) 14/15 ANSWERS: a) 9/5 b) 7/3 c) 8/7 d) 15/14 2. Use multiplication to find each quotient. 7 2 / 4 3 / ANSWERS: 7 2 3 4 x = 21 8 = 2 5 8 a) a) b) b) 8 5 3 4 8 5 r x 4 3 r = 32 15 = 2 2 15 3. Use a number line to illustrate the quotient. 3 5 1 4 / 3 5 = 12 20 1 4 5 20 = 12 20 / 5 20 one 5/20 one 5/20 2/5 of 5/20 ANSWER: 2 2 5 3.7 Dividing Mixed Numbers 1. Divide. Estimate to check the quotient is reasonable. 1 7 8 / 1 1 4 ANSWER: 1 7/8 = 15/8 1 1/4 = 5/4 15 5 / 8 4 15 8 x 4 5 r 3/2 or 1 1/2 = 2. Brittany has a summer job in a bakery. One day she used 3 3/4 cups of chocolate chips to make muffins. A dozen muffins require 3/4 cup of chocolate chips. How many dozen muffins did Brittany make that day? 3 3 4 ANSWER: / 3 4 3 3 4 = 15 4 15 4 / 3 4 15 / 3 = 15 3 = 5 3. Write each mixed number as a improper fraction. a) 4 3 8 b) 1 7 10 c) 5 2 5 d) 6 1 6 ANSWERS: a) 35/8 b)17/10 c) 27/5 d) 37/6 3.8 Solving Problems with fractions. 1. Cassie worked on her math project for 3/4 h on Tuesday and 5/6 h on Wednesday. How long did Cassie work on her math project altogether. ANSWER: 3 4 + 5 6 = 9 12 + 10 12 = 1 7 12 2. Nick volunteered at a gift-wrapping booth for a local charity. He volunteered for 2 3/4 h and wrapped 11 gift boxes. His friend Chad volunteered 1 1/3 times as long. a) how long did Nick spend wrapping each gift box?

b) how many hours did Chad volunteer. ANSWER: a) 2 3 4 / 11 = 11 4 / 11 11 4 x 1 11 r = 1 4 b) 2 3 4 x 1 1 3 = 11 4 4 3 x = 3 11 = 3 2 3 3. Jacob mixed 2/3 of one can of yellow paint and 1/4 of one can of white paint to paint a wall in his bedroom. How much paint did he have all together. 2 3 + 1 4 = ------- 12 11 8 + 3= 3.9 Order of operations with fractions 1. Which operation do you do first? a) 1/3 x (7/8-3/4) b) (5/3 +7/12) x 4/9 You do the brackets in both equations first. ANSWER: 2. Evaluate: 5 16 - 3 8 x 2 3 ANSWER: 3 8 x 2 3 5 16 - 1 4 = 5 16 - 4 16 = 1 16 3. Evaluate: 1 8 x 3 4 x 7 5 7 10 Answer: = = 2 1. 2. 1 8 X 3 4 = 3/32 3. 3 32 X 2 1 = 3/16 3.1 Using Models to Multiply Fractions and Whole Numbers We know that repeated addition can be written as multiplication. So we can use a number line to divide whole and mixed numbers. As well as making fraction strips or circles. Mr. Pascal will be teaching you how in the next few slides. 3.2 Using Models to Multiply Fractions 3.2 is basically the same thing as 3.1. Keep trying i know you'll get it. This stuff is easy! 3.3 Multiplying Fractions Just follow along with me and I know it will come! Save any questions you have for the end for for now just have fun and do some MATH! 3.4 Multiplying Mixed Numbers What is the difference between a proper and improper fraction you ask? Well in an improper fraction the numerator is greater than the denominator. And vs versa for a proper fraction. 3.5 Dividing Whole Numbers and Fractions When you first studied division. you learned two ways: sharing and grouping. For example 20/5 can be thought of as, Sharing 20 items equally amoung 5 sets

Or grouping 20 items into sets of 5 To help you with this section recall that multiplication and division are inverse operations. 3.6 Dividing Fractions You have used grouping to divide a whole number by a fraction.

You have used sharing to divide a fraction by a whole number.

You will now investigate dividing a fraction by a fraction. Stay strong were almost done! 3.8 Solving Problems with Fractions When solving word problems, it is important to identify the operation or operations needed to solve the problem. This is what Mr. Pascal has told us so it must help a lot. Keep that in mind throughout the section. 3.9 Order of Operations With Fractions Every fraction can be written as a decimal. So, we use the same order of operations for fractions as for whole numbers and decimals. After this your done! So push through and have fun! Thanks for watching! Have a fantastic day! / / 7 5 7 10 7 5 x 10 7