Reteaching. Properties of Operations

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1 - Properties of Operations The commutative properties state that changing the order of addends or factors in a multiplication or addition expression does not change the sum or the product. Examples: The associative properties state that changing the grouping of addends or factors in a multiplication or addition expression does not change the sum or the product. Example: (9 3) 7 9 (3 7) 2 (5 7) (2 5) 7 The identity properties state that adding 0 to a number or multiplying a number by will not change that number. Example: You can use these properties to simplify mathematical phrases. Example: 20 (3 5) 20 (5 3) Commutative Property of Multiplication (20 5) 3 Associative Property of Multiplication 00 3 Simplify Identity Property of Multiplication 900 Simplify. Name the property being used (3 2) 5 3 (2 5) Solve using mental math (0 3) Course Lesson -

2 -2 Order of Operations To find the value of an expression follow the order of operations. First, do all operations inside parentheses. Next, multiply and divide from left to right. Then, add and subtract from left to right. Example Find the value of 6 (3 4) Work inside parentheses. (3 4) Multiply next Then, add Example 2 Compare 0 (6 2) and (0 6) 2. First, find the value of each expression. Then, use, =, or to compare. 0 (6 2) (0 6) So, (6 2) (0 6) Find the value of each expression.. 3 (4 ) (5 3) 2 a. 4 a. 5 3 b. 2 b. 24 c. 3 c (6 2) 3 4 Use R,, or S to complete each statement (3 4) 6. (2 4) 3 2 (4 3) (6 3) (2 5) (5 2) 9. 5 (2 3) (5 2) (9 7) 8 (2 9) 7 Course Lesson -2

3 -3 Understanding Decimals Ones 2 Tenths Hundredths Thousandths and 369 thousandths Standard form: To find the value of a digit, multiply the digit by its place value. 9 stands for or Expanded form: To round to the nearest tenth, look at the value to the right (hundredths) because 6 5, round up. 2.4 Write each decimal in words Write each decimal in standard form. 7. seven tenths 8. one tenth 9. four hundredths 0. seven hundredths. twenty-two hundredths 2. forty-six hundredths Write each decimal in expanded form Round each decimal to the underlined place Find the value of the digit 6 in each number Course Lesson -3

4 -4 Adding and Subtracting Decimals Add First estimate Then follow these steps. Line up the decimal points. 2 Add as you would add 3 Place the decimal point. Write in any needed zeros. whole numbers. Regroup when needed To subtract decimals, follow similar steps. Work from right to left and regroup when needed. Place the decimal point to complete the subtraction. First estimate and then find each sum Estimate Estimate Estimate Sum Sum Sum Use mental math to find each sum First estimate and then find each difference Estimate Estimate Estimate Difference Difference Difference Compare to your estimate. Estimate Estimate Estimate Difference Difference Difference Course Lesson -4

5 -5 Multiplying Decimals Multiply This drawing can help you find Each small square is hundredth or 0.0. Each column or row is 0 hundredths or tenth or 0.. Compare the result from the model to the result of multiplying the factors. 0.3 decimal place.4 + decimal place decimal places Write a multiplication statement to describe each model.. 2. For each product, place the decimal point in the correct place Find each product Shade 3 rows across to represent 0.3. Shade 4 columns down to represent.4. The area where the shading overlaps is 42 hundredths or When multiplying decimals, first multiply the factors as though they are whole numbers. Then add the number of decimal places in each factor to find the number of decimal places in the product Course Lesson -5

6 -6 Dividing Decimals Find the quotient You can use a model to estimate the quotient. Draw a model for.52. Since each square is 0.0, 40 squares represent 0.4. Circle groups of 0.4. There are close to four groups of 0.4. The quotient is about 4. Multiply the dividend and 2 Divide as with whole 3 Place the decimal point in the divisor by 0 so that the numbers. quotient above its place in the divisor is a whole number. dividend. Insert zeros as placeholders if necessary q.52 4q5.2 4q5.2 n 2n 2n Use the model to find each quotient is close to Estimate, then find each quotient. 4. 3q q q q q.35 Course Lesson -6

2. Perform the division as if the numbers were whole numbers. You may need to add zeros to the back of the dividend to complete the division

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