Multiplying Decimals and Whole Numbers 6.1.3.1 Multiply and divide decimals and fractions, using efficient and generalizing procedures, including standard algorithms. 6.2.2.1 Apply the associative, commutative, and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers

I can… Self Assessment Multiply decimals and whole numbers Use the associative and associative properties of multiplication Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

Using Base Ten Blocks to Multiply Decimals     Flat = one (1) Stick = one tenth (0.1) cube = one hundredth (0.01)

Multiplying Decimals by Whole Numbers Tenths

Multiply 5 x 0.3 Shade in 0.3 five times using a different color each time. 5 x 0.3 = 1.5

4 x 0.6 4 x 0.6 = 2.4

3 x 0.7 Shade in 0.7 three times using a different color each time. 3 x 0.7 = 2.1

Multiplying Decimals by Whole Numbers Using Models Hundredths

Multiply 4 x 0.19 Shade 0.19 four times .             4 x 0.19 = 0.76

Multiply 5 x 0.25 Shade 0.25 five times .               5 x 0.25 = 1.25

Multiply 3 x 0.35             3 x .35 = 1.05

Standard Algorithm When multiplying a decimal by a whole number, multiply as normal Then count the number of decimal places and hop to the left Add zeros if needed!!!!!

Remember…. When decimal is out of sight, it is always to the right! Standard Algorithm Remember…. When decimal is out of sight, it is always to the right! Example: Find 14.2 x 6 14.2 x 6 85 2 There is one place to the right of the decimal point. . . Count the same number of places from right to left.

Remember…. When decimal is out of sight, it is always to the right! Your turn…. Remember…. When decimal is out of sight, it is always to the right! Example: Find 11.4 x 8 11.4 x 8 91 2 There is one place to the right of the decimal point. . . Count the same number of places from right to left.

Try Again… If there are not enough decimal places in the product, you need to add zero to the left. Find: 2 x 0.018 0.018 x 2 0 036 There are three digits behind the decimal. . .

Properties of Multiplication Commutative Associative

Here are two families of commuters. Commuter B Commuter A Commuter A & Commuter B changed lanes. Remember… commute means to change. Commuter A Commuter B

The Commutative Property A x B = B x A

Properties of Multiplication Commutative Associative

Here are three associates. B B calls A first He calls C last A C If he called C first, then called A, would it have made a difference? NO!

The Associative Property The parentheses identify which two associates talked first. (A x B) x C = A x (B x C) B B A C THEN A THEN C

I can… Self Assessment Multiply decimals and whole numbers Use the associative and associative properties of multiplication Self Assessment 5- I can do it without help & teach others. 4- I can do this with no help, but I don’t know if I can explain it. 3- I can do this with a little help. 2- I can do this with a lot of help! 1- I don’t have a clue.

Daily Check 4.1 in your math notebook Evaluate: 0.057 x 7 A car averaged 52.755 miles per hour for 4 hours. How far did the car travel? A student calculated that 39.75 x 41 = 1629.75. Is that answer reasonable? (HINT: try estimating) Tell whether the associative or commutative property of multiplication lets you rewrite each problem 2.5 x 17 x 4 = 17 x 2.5 x 4 1.25 x (4 x 7.8) = (1.25 x 4) x 7.8