# Decimals - Multiplying and Dividing

## Learning Topics:

Estimate products, multiply decimals & whole numbers, multiply decimals, estimate quotients, divide decimals by whole numbers, round quotients, divide decimals, solve word problems.

## Learning Objectives for all Multiplying and Dividing Decimals lessons in Unit 13.

#### Estimating Decimal Products

The student will be able to:

• Define estimate, product, factors, estimation and compatible numbers.
• Examine several strategies for estimating decimal products.
• Examine examples using these strategies to estimate decimal products.
• Recognize that estimates will vary depending on the strategy being used.
• Determine if an estimated product is an overestimate or an underestimate.
• Determine if an answer is reasonable using estimation.
• Examine five interactive exercises with real-world problems involving decimals.
• Analyze each problem to identify the given information.
• Formulate a strategy for solving each problem.
• Apply estimation strategies to solve problems.

#### Multiplying Decimals and Whole Numbers

The student will be able to:

• Define powers, decimal digits and partial products.
• Examine how a decimal number changes when it is multiplied by powers of ten.
• Examine how a decimal number changes when it is divided by powers of ten.
• Recognize, each time we multiply by a power of ten, the decimal point is moved one place to the right.
• Recognize, each time we divide by a power of ten, the decimal point is moved one place to the left.
• Examine examples in which a decimal is multiplied by a whole number.
• Identify the number of decimal digits in a decimal.
• Recognize that placement of the decimal point is very important
• Examine detailed examples in which the product is estimated and computed.
• Compare the estimate with the product to verify the answer makes sense.
• Explain how (two) partial products are found.
• Examine examples in which three partial products are found.
• Describe the procedure for multiplying a decimal by a whole number.
• Examine patterns of numbers being multiplied, and list each product using mental arithmetic.
• Perform multiplication of a decimal and a whole number.
• Identify where to place the decimal point in the product.
• Apply multiplication procedures to complete five interactive exercises.

#### Multiplying Decimals

The student will be able to:

• Recognize, when multiplying two decimals that are each less than one, the product will be less than each of the factors.
• Examine detailed examples in which the product of two decimals is estimated and computed.
• Compare the estimate with the product to verify the answer makes sense.
• Connect decimal multiplication with place value.
• Recognize that the sum of the number of decimal digits in each factor will yield the number of decimal digits in their product.
• Describe the procedure for multiplying two decimals.
• Perform multiplication of two decimals.
• Evaluate a product by comparing it with an estimate.
• Identify where to place the decimal point in the product.
• Apply decimal multiplication procedure to complete five interactive exercises.

#### Estimating Decimal Quotients

The student will be able to:

• Define quotient
• Examine examples that use compatible numbers to estimate decimal quotients.
• Recognize why compatible numbers is a good strategy for estimating decimal quotients.
• Determine if an estimated quotient is an overestimate or an underestimate.
• Determine if an answer is reasonable using estimation.
• Connect overestimates and underestimates with the real world.
• Estimate decimal quotients.
• Apply estimation strategies to complete five interactive exercises.

#### Dividing Decimals by Whole Numbers

The student will be able to:

• Identify the divisor, the dividend and the quotient in examples presented.
• Examine detailed examples in which the quotient of a decimal by a whole number is estimated and computed.
• Compare the estimate with the quotient to verify that the answer makes sense.
• Describe the procedure for dividing a decimal by a whole number.
• Recognize that the divisor can be greater than the dividend in a division problem.
• Examine detailed examples in which the divisor is greater than the dividend.
• Describe the procedure for dividing a decimal by a whole number when the divisor is greater than the dividend.
• Examine patterns of numbers being divided, and list each quotient using mental arithmetic.
• Perform division of a decimal by a whole number.
• Identify where to place the decimal point in the quotient.
• Apply division procedures to complete five interactive exercises.

#### Rounding Decimal Quotients

The student will be able to:

• Examine detailed examples in which decimal is divided by a whole number.
• Recognize when to round a decimal quotient.
• Recognize, when rounding decimal quotients, we must divide to one more place than we are rounding to.
• Describe the procedure for dividing a decimal by a whole number and then rounding the quotient.
• Perform division of a decimal by a whole number and then rounding the quotient.
• Apply decimal division strategies to complete five interactive exercises.

#### Dividing Decimals By Decimals

The student will be able to:

• Recognize that multiplying both the divisor and dividend by the same power of ten maintains the equality of an expression.
• Examine detailed examples in which two decimals are divided to find the quotient.
• Examine detailed examples in which two decimals are divided, and the quotient is rounded.
• Examine division problems that involve currency.
• Describe the procedure for dividing two decimals.
• Apply decimal division procedures to complete five interactive exercises.

#### Solving More Decimal Word Problems

The student will be able to:

• Examine examples of real-world problems involving decimals.
• Examine the solution presented for each problem.
• Examine five interactive exercises with real-world problems involving decimals.
• Analyze each problem to identify the given information.
• Formulate a strategy for solving each problem.
• Apply decimal strategies to solve problems.

#### Practice Exercises

The student will be able to:

• Examine ten interactive exercises for all topics in this unit.
• Determine which strategies and procedures are needed to complete each practice exercise.
• Compute answers by applying appropriate strategies and procedures
• Self-assess knowledge and skills acquired from this unit.

#### Challenge Exercises

The student will be able to:

• Evaluate ten interactive exercises with word problems for all topics in this unit.
• Determine which strategies and procedures are needed to complete each exercise.
• Apply decimal strategies and procedures to solve routine and non-routine word problems.
• Synthesize all information presented in this unit.
• Connect decimals to the real world.
• Develop problem-solving skills.

#### Solutions

The student will be able to:

• Examine the solution for each exercise presented in this unit.
• Identify which solutions need to be reviewed.
• Compare solutions to completed exercises.
• Identify and evaluate incorrect answers.
• Amend and label original answers.
• Identify areas of strength and weakness.
• Decide which strategies and procedures need to be reviewed from this unit.