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Multiplying and Dividing with Decimals

Master multiplying and dividing with decimals with interactive lessons and practice problems! Designed for students like you!

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Multiplying and Dividing with Decimals

Study Guide

Key Definition

When multiplying decimals, ignore (do not align) the decimal points, multiply the numbers as whole numbers, then count the total decimal places in the factors to place the decimal point in the product. When dividing, move the decimal point in the divisor until it becomes a whole number, and move the decimal in the dividend the same number of places; then divide.

Important Notes

For addition and subtraction, align decimal points. For multiplication, treat the factors as whole numbers and place the decimal in the product based on total decimal places.
$0.25 \times 0.5 = 0.125$
Convert the divisor to a whole number when dividing decimals (shift the decimal point in both numbers equally).
Practice helps reinforce correct decimal placement.
Use estimation to check whether your answer is reasonable.

Mathematical Notation

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems.

Why It Works

Multiplying and dividing decimals uses the same numerical operations as with whole numbers. The only extra step is tracking how far the decimal point must move so that place value is preserved in the result.

Remember

Always count the decimal places in each factor (for multiplication) or shift the decimal equally in both numbers (for division) before determining the final answer.

Quick Reference

Multiplying Decimals:$0.25 \times 0.5 = 0.125$

Understanding Multiplying and Dividing with Decimals

Choose your learning level

Watch & Learn

Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

Example (Multiplication – Beginner): To find $0.25 \times 0.5$, first ignore the decimals and multiply $25 \times 5 = 125$. There are three decimal places altogether (two in 0.25 and one in 0.5), so count three places from the right: $0.125$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $0.3 \times 0.4$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

If a bottle of water costs $1.75$ dollars and you want to buy $3.5$ bottles, how much will it cost?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

You are making half of a recipe. One full recipe needs $0.25$ cups of sugar. How much sugar do you need for half a recipe?

Challenge Quiz

Single Choice Quiz

Advanced

What is $0.125 \div 0.05$?

Recap

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Review key concepts and takeaways