5 Minute Check Complete in your notebook. 9 3 1. 10 + 5 2. 4 + 5 2 1 9 3 1. 10 + 5 3 1 2. 4 + 5 2 1 3. 7 3 - 37 7 5 4. 9 8 - 2 6

5 Minute Check Complete in your notebook. 9 3 1. 10 + 5

5 Minute Check Complete in your notebook. 9 3 9 6 15 1 1. 10 + 5 = 10 + 10 = 10 = 1 2

5 Minute Check Complete in your notebook. 3 1 2. 4 + 5

5 Minute Check Complete in your notebook. 2. 4 + 5 = 20 + 20 = 20 3 1 15 4 19 2. 4 + 5 = 20 + 20 = 20

5 Minute Check Complete in your notebook. 2 1 3. 7 3 - 37

5 Minute Check Complete in your notebook. 3. 7 3 - 37 = 3 - 7 2 1 23 22 3. 7 3 - 37 = 3 - 7 7 x 23 22 x 3 7 x 3 - 7 x 3 161 66 95 11 21 - 21 = 21 = 4 21

5 Minute Check Complete in your notebook. 7 5 4. 9 8 - 2 6

5 Minute Check Complete in your notebook. 4. 9 8 - 2 6 = 8 - 6 7 5 79 17 4. 9 8 - 2 6 = 8 - 6 3 x 79 17 x 4 3 x 8 - 6 x 4 237 68 169 1 24 - 24 = 24 = 724

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Lesson 6.4.2 Multiply Fractions and Whole Numbers Thursday, Oct 2 Lesson 6.4.2 Multiply Fractions and Whole Numbers

Multiply Fractions and Whole Numbers Lesson 6.4.1 is estimation and will be incorporated into 6.4.2, 6.4.3 and 6.4.4.

Multiply Fractions and Whole Numbers Objective: To understand how to estimate and multiply fractions and whole numbers.

Multiply Fractions and Whole Numbers To multiply fractions, multiply the numerators and multiply the denominators, then simplify if needed. Example x = 3 2 6 3 4 x 5 = 20 = 10 x =

Multiply Fractions and Whole Numbers To multiply fractions, multiply the numerators and multiply the denominators, then simplify if needed. Example x = 3 2 6 3 4 x 5 = 20 = 10 x =

Multiply Fractions and Whole Numbers To multiply a fraction and whole number, convert the whole number to a fraction, then multiply as normal. What is14 as a fraction?

Multiply Fractions and Whole Numbers To multiply a fraction and whole number, convert the whole number to a fraction, then multiply as normal. Example 14 14 = 1

Multiply Fractions and Whole Numbers To multiply a fraction and whole number, convert the whole number to a fraction, then multiply as before. Example 1 5 x 14 x = 1 14 14 4 5 x 1 = 5 = 25

Multiply Fractions and Whole Numbers 1 5 x 14 When estimating the product of a fraction and whole number, make a multiples list for the smaller of either the whole number or the denominator.

Multiply Fractions and Whole Numbers 1 5 x 14 When estimating the product of a fraction and whole number, make a multiples list for the smaller of either the whole number or the denominator. 5: 5, 10, 15, 20…..

Multiply Fractions and Whole Numbers 1 5 x 14 Use a comparable number for the larger number that is in the multiples list. 5: 5, 10, 15, 20…..

Multiply Fractions and Whole Numbers 1 5 x 14 Use a comparable number for the larger number that is in the multiples list. 5: 5, 10, 15, 20…..

Multiply Fractions and Whole Numbers 1 5 x 14 Use a comparable number for the larger number that is in the multiples list. 5: 5, 10, 15, 20….. 5 x 15

Multiply Fractions and Whole Numbers 1 5 x 14 Use a comparable number for the larger number that is in the multiples list. 5: 5, 10, 15, 20….. 1 15 5 x 15 = 5 = 3

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 2 x 5 = Estimate? Which number is smaller, 2 or 5?

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 2 x 5 = Which number is smaller, 2 or 5? 2

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 2 x 5 = What is a comparable number for 5 that is in the multiples list of 2? 2: 2, 4, 6, 8,…..

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 2 x 5 = What is a comparable number for 5 that is in the multiples list of 2? 2: 2, 4, 6, 8,…..

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 2 x 5 = What is a comparable number for 5 that is in the multiples list of 2? 2: 2, 4, 6, 8,….. 2 4 2 x 4 = 4 =1

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 2 x 5 = Actual Product?

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 2 x 5 = Actual Product? 2 2 4 1 x 5 = 5 Is this a reasonable answer?

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 2 x 5 = Actual Product? 2 2 4 1 x 5 = 5 4 Is this a reasonable answer? 5 ≈1

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 4 2 x 5 = 5 A model can be used to represent this equation. Remember, 2 2 2 2 x 5 is the same as 5 + 5

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 4 2 x 5 = 5 A model can be used to represent this equation. + =

Multiply Fractions and Whole Numbers When multiplying a fraction by a whole number, the order of the factors does not change the product. This is true for any numbers and is an example of the Commutative Property. Example 2 2 2 x 5 = 5 x 2

Multiply Fractions and Whole Numbers 2 2 x 5 Is the same as 5 x 2 Which is asking What is 5 of 2?

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 6 x 3 = Estimate?

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 6 x 3 = Estimate? Since 3 and 6 are in the same multiples list the estimate and actual product will be the same. Actual Product?

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 6 x 3 = Actual Product? 6 2 12 1 x 3 = 3 = 4

Multiply Fractions and Whole Numbers Estimate and Multiply. 3 4 x 5 Do this on your own.

Multiply Fractions and Whole Numbers Estimate and Multiply. 3 4 x 5 ≈ 3 4 3 12 2 1 x 5 = 5 =25 Work done in my head: 4:4, 8, 12……. 4 3 12 1 X 4 = 4 = 3

Multiply Fractions and Whole Numbers If the numerators and denominators have a common factor you can simplify before multiplying.

Multiply Fractions and Whole Numbers If the numerators and denominators have a common factor you can simplify before multiplying. To simplify before multiplying, convert all numbers to prime factors.

Multiply Fractions and Whole Numbers If the numerators and denominators have a common factor you can simplify before multiplying. Example 5 9 3 x 10 = Convert all numbers are prime factors (which means they have no factors other than one and itself).

Are there any factors that appear in the numerator and denominator? Multiply Fractions If the numerators and denominators have a common factor you can simplify before multiplying. Example 5 9 3 x 10 = 5 3x3 3 x 2x5 = Are there any factors that appear in the numerator and denominator?

Are there any factors that appear in the numerator and denominator? Multiply Fractions If the numerators and denominators have a common factor you can simplify before multiplying. Example 5 9 3 x 10 = 5 3x3 3 3 x 2x5 = 2 Are there any factors that appear in the numerator and denominator?

We can prove this by multiplying the original. Multiply Fractions If the numerators and denominators have a common factor you can simplify before multiplying. Example 5 9 3 x 10 = 5 3x3 3 1 3 x 2x5 = 2 =12 We can prove this by multiplying the original.

We can prove this by multiplying the original. Multiply Fractions If the numerators and denominators have a common factor you can simplify before multiplying. Example 5 9 45 3 1 3 x 10 = 30 = 2 =12 5 3x3 3 1 3 x 2x5 = 2 =12 We can prove this by multiplying the original.

Multiply Fractions and Whole Numbers Estimate and Multiply. 3 4 x 14 Do this on your own.

Multiply Fractions and Whole Numbers Estimate and Multiply. 3 4 x 14 ≈ 9 3 2x7 21 1 2x2 x 1 = 2 =10 2

Multiply Fractions and Whole Numbers Estimate and Multiply. 1 3 x 9 Do this on your own.

Multiply Fractions and Whole Numbers Estimate and Multiply. 1 3 x 9 ≈ 3 1 3 x 3 3 x 1 = 3

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 5 x 15 Do this on your own.

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 5 x 15 ≈ 6 2 3x5 6 5 x 1 = 1 = 6

Multiply Fractions and Whole Numbers Estimate and Multiply. 1 7 x 8 Do this on your own

Multiply Fractions and Whole Numbers Estimate and Multiply. 1 7 x 8 ≈ 1 1 8 8 1 7 x 1 = 7 = 17

Multiply Fractions and Whole Numbers Estimate and Multiply. 3 8 x 11 Do this on your own

Multiply Fractions and Whole Numbers Estimate and Multiply. 3 8 x 11 ≈ 3 3 11 33 1 8 x 1 = 8 = 48

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 3 x 10

Multiply Fractions and Whole Numbers Estimate and Multiply. 2 3 x 10 ≈ 6 2 10 20 2 3 x 1 = 3 = 63

Multiply Fractions and Whole Numbers 4 A sloth spends 5 of it’s life asleep. If a sloth lives to be 28 years old, how many years does it spend asleep? (Do this on your own)

Multiply Fractions and Whole Numbers 4 A sloth spends 5 of it’s life asleep. If a sloth lives to be 28 years old, how many years does it spend asleep? 5 x 28 ≈ 24 4 28 112 2 5 x 1 = 5 = 225

Multiply Fractions and Whole Numbers One evening, 2/3 of Mrs. Thorne’s students watched a reality TV show. Of Mrs. Lombardo’s students, 4/5 watched the same reality show. Which teacher had more students watch the show? (Do this on your own)

Multiply Fractions and Whole Numbers One evening, 2/3 of Mrs. Thorne’s students watched a reality TV show. Of Mrs. Lombardo’s students, 4/5 watched the same reality show. Which teacher had more students watch the show? Mrs. T 2 2x2x3x3 24 3 x 1 = 1 =24 Mrs. L 4 5x6 24 5 x 1 = 1 = 24

Multiply Fractions and Whole Numbers Natalie multiplied 2/3 by 123 and got 156. Is this a reasonable answer?

Multiply Fractions and Whole Numbers Natalie multiplied 2/3 by 123 and got 156. Is this a reasonable answer? No, because if you multiply a whole number by a fraction the answer will always be less than the whole number.

Multiply Fractions and Whole Numbers The male Cuban tree frog is about 2/5 the size of the female. The average size of the female is shown below. What is the size of the average male? Do this on your own.

Multiply Fractions and Whole Numbers The male Cuban tree frog is about 2/5 the size of the female. The average size of the female is shown below. What is the size of the average male? 2 12 2 6 x 5 = 5 =2 5

Multiply Fractions and Whole Numbers Write a problem involving the multiplication of a whole number and fraction with a product that is between 8 and 10. Do this on your own.

Multiply Fractions and Whole Numbers Write a problem involving the multiplication of a whole number and fraction with a product that is between 8 and 10. Sample: 3 36 12 x 4 = 4 =9

Multiply Fractions and Whole Numbers Find Noah’s mistake and correct it.

Multiply Fractions and Whole Numbers 3 24 4 x 8= 4 =6 Find Noah’s mistake and correct it. He multiplied both top and bottom by 8.

Multiply Fractions and Whole Numbers Agenda Notes Homework – Homework Practice 6.4.2 Show all work Due Friday, Oct 3 Mid-Chapter 6.4 Quiz Wednesday, Oct 8