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Comparing Quantities

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Comparing Quantities

Study Guide

Key Definition

Comparing quantities involves converting different types of numbers (fractions, decimals, percentages) into the same form for easier comparison.

Important Notes

Remember to convert all quantities to the same form before comparison.
You can convert percentages to decimals by dividing by 100.
Convert fractions to decimals by dividing numerator by denominator.

Mathematical Notation

$\frac{a}{b}$ represents a fraction, where a is the numerator and b is the denominator.

$x.y$ represents a decimal.

$a \%$ represents a percentage.

Remember to use proper notation when solving problems.

Why It Works

By converting quantities to the same form, we can easily compare them using standard comparison operators (<, >, =).

Remember

Always simplify fractions and use the same number of decimal places (without changing the value), or compare the exact decimals when comparing.

Quick Reference

Fraction to Decimal:$\frac{a}{b} = a \div b$

Percent to Decimal:$a \% = a \div 100$

Understanding Comparing Quantities

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

We can compare quantities by converting them into the same form, such as all fractions, all decimals, or all percentages.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Which is greater, $\frac{1}{4}$ or 0.3?

Real-World Problem

Question Exercise

Intermediate

Homework Scenario

Jordan finished $\frac{3}{8}$ of his homework problems. Kate is done with 40% of her homework problems. Who has done more problems?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Fill in the blank with <, >, or =. 0.4 _ 45%

Challenge Quiz

Single Choice Quiz

Advanced

Which is greater, $\frac{5}{7}$ or 0.6?

Recap

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Review key concepts and takeaways