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Dividing Decimals

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Dividing Decimals

Study Guide

Key Definition

In dividing decimals, the $dividend$ is divided by the $divisor$ to obtain the $quotient$.

Important Notes

Always estimate your answer by rounding to check if the result is reasonable.
Shift the decimal place in both the divisor and dividend to simplify division.
If necessary, multiply both dividend and divisor by the same power of 10 to eliminate decimals.
Place the decimal in the quotient directly above its position in the dividend.
Cross-check your solution with the estimated answer.

Mathematical Notation

$\div$ represents division

$\frac{a}{b}$ is a fraction representing division

$\times$ represents multiplication

Remember to use proper notation when solving problems

Why It Works

Multiplying both the dividend and divisor by the same power of 10 is equivalent to multiplying the entire division expression by 1, which does not change its value. Shifting the decimal points in this way converts decimals into whole numbers, making long division straightforward while keeping the quotient unchanged.

Remember

Keep the relationship between the dividend and divisor consistent when moving decimal places.

Quick Reference

Division:$\frac{dividend}{divisor} = quotient$

Understanding Dividing Decimals

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

When dividing a decimal by a whole number, divide as usual ignoring the decimal point, then place the decimal in the quotient above its position in the dividend. Example: 2.4 ÷ 3 → divide 24 ÷ 3 = 8, so 2.4 ÷ 3 = 0.8.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is $\frac{0.56}{0.7}$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $7.2$ meters of ribbon to divide evenly across $0.8$ meter pieces. How many pieces can you make?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Find the quotient of $\frac{0.2}{0.3}$.

Challenge Quiz

Single Choice Quiz

Advanced

Calculate $\frac{1.3}{0.4}$

Recap

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Review key concepts and takeaways