# Decimals – Multiplying and Dividing

## 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.