Adding, Subtracting, and Multiplying Decimals

Lesson 1 of 2

In this lesson:

• Add and subtract decimals by aligning place values
• Multiply decimals using area models and partial products
• Use estimation to check every answer

Learning Objectives for This Lesson

1. Add and subtract decimals by aligning place values and regrouping
2. Multiply decimals using area models or place value reasoning
3. Use estimation to judge reasonableness before and after calculating
4. Represent operations with models and connect to written methods
5. Explain each step using place value language

What Do You Already Know About Decimals?

You already read, write, and compare decimals:

• Each place is 10 times the place to its right
• 0.5 = 5 tenths; 0.25 = 25 hundredths
• Whole-number addition uses place value alignment — so do decimals

Today: How do we compute with decimals using the same reasoning?

Aligning Place Values for Addition

Adding decimals works like adding whole numbers — align digits by place value.

• Tenths line up with tenths
• Hundredths line up with hundredths
• The decimal points line up automatically

Adding Decimals Column by Column

Maya ran 3.72 km Monday, 1.5 km Tuesday.

Estimate: 4 + 2 = about 6

• Hundredths: 2 + 0 = 2
• Tenths: 7 + 5 = 12 → regroup
• Ones: 3 + 1 + 1 = 5

Answer: 5.22 km — reasonable

Subtracting Decimals by Regrouping Across Places

Goal: 5.00 km. Ran 3.72 km. Remaining?

Estimate: 5 − 4 = about 1

• Hundredths: 0 − 2 → regroup → 10 − 2 = 8
• Tenths: 9 − 7 = 2
• Ones: 4 − 3 = 1

Answer: 1.28 km — reasonable

Check-In: Add Decimals with Regrouping

Solve this problem:

• First, estimate the answer
• Then add by place value, regrouping as needed

Pause and try before the next slide.

Answer: Regrouping in Two Place Values

Estimate: 0.6 + 0.8 = about 1.4

• Hundredths: 4 + 8 = 12 → regroup
• Tenths: 6 + 7 + 1 = 14 → regroup
• Ones: 0 + 0 + 1 = 1

1.42 is close to 1.4 — correct

Practice: Add and Subtract with Decimals

Solve each problem. Estimate first, then compute.

1. 12.3 − 8.57 = ?
2. 6.4 + 2.85 = ?

Write your estimates and then your exact answers. Advance for solutions.

Answers: Decimal Addition and Subtraction Practice

Problem 1: 12.3 − 8.57

• Estimate: 12 − 9 = about 3
• Exact: 12.30 − 8.57 = 3.73 — reasonable

Problem 2: 6.4 + 2.85

• Estimate: 6 + 3 = about 9
• Exact: 6.40 + 2.85 = 9.25 — reasonable

Connecting Addition Skills to Multiplication

Addition and subtraction use place value alignment and regrouping.

Multiplication builds on the same skills with a new question:

• What kind of unit does the product have?
• Tenths × tenths = hundredths

Tenths Times Tenths Equals Hundredths

What is 0.3 × 0.7?

Think: 3 tenths × 7 tenths = 21 hundredths = 0.21

Worked Example: Whole Number Times Decimal

A ribbon costs $0.35 per foot. You need 4 feet. Total cost?

Estimate: 4 × $0.40 = about $1.60

Answer: $1.40 — close to our estimate of $1.60

Partial Products for Multi-Digit Decimals

Solve 2.4 × 1.3. Estimate: 2.5 × 1 = 2.5

• 2 × 1 = 2
• 2 × 0.3 = 0.6
• 0.4 × 1 = 0.4
• 0.4 × 0.3 = 0.12

3.12 — close to estimate of 2.5

Check-In: Both Factors Less Than One

What is 0.6 × 0.5?

Before you compute, think:

• Both factors are less than 1
• The product must be less than both factors
• If your answer exceeds 0.5, something is wrong

Solve it and check your reasoning.

Answer: Why the Product Is Less Than Both

Estimate: about 0.5 × 0.5 = 0.25

• 0.30 is less than both 0.6 and 0.5 — correct
• Close to estimate of 0.25

Common error: Getting 3.0 — estimation catches it instantly

Practice: Multiply Whole and Decimal Numbers

Solve each problem. Estimate first.

1. 3 × 0.25 = ?
2. 0.4 × 0.8 = ?

Write your estimates, compute, and compare. Advance for solutions.

Answers: Checking Multiplication with Estimation

Problem 1: 3 × 0.25

• Estimate: 3 × = 0.75
• Exact: 75 hundredths = 0.75

Problem 2: 0.4 × 0.8

• Estimate: about 0.5 × 1 = 0.5
• Exact: 32 hundredths = 0.32 (less than both factors)

Key Takeaways from Lesson One

• Add/subtract: Align place values — tenths with tenths, hundredths with hundredths
• Multiply: Tenths × tenths = hundredths; use the area model
• Estimate first: Always estimate, then compute, then compare

Watch out: Aligning digits from the right instead of by decimal point

Coming Up in Lesson 2

Dividing Decimals and Mixed Operations

• Divide decimals using the equivalent-whole-number strategy
• Understand why dividing by less than 1 gives a larger quotient
• Combine all four operations in real-world problems
• Explain your reasoning using place value language