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Solving One-Step Linear Equations with Mixed Numbers

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Solving One-Step Linear Equations with Mixed Numbers

Study Guide

Key Definition

A mixed number is a number expressed as the sum of a whole number and a fraction, such as $3 \frac{1}{4}$. It is often converted to an improper fraction like $\frac{13}{4}$ for easier calculations.

Important Notes

Convert mixed numbers to improper fractions for calculations.
Use inverse operations to solve equations.
Always simplify fractions where possible.
Mixed numbers provide a better sense of size.
Balance equations by performing the same operation on both sides.

Mathematical Notation

$\frac{a}{b}$ represents division of a by b

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

Converting mixed numbers to improper fractions simplifies calculations, allowing the use of inverse operations to solve equations efficiently.

Remember

Always convert mixed numbers to improper fractions for calculations, and use inverse operations to isolate the variable.

Quick Reference

Inverse Operations:$+$ becomes $-$, $-$ becomes $+$, $\times$ becomes $\div$, $\div$ becomes $\times$

Understanding Solving One-Step Linear Equations with Mixed Numbers

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Video explanation of this concept

Beginner

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Beginner Explanation

To solve simple one-step equations involving mixed numbers (addition or subtraction), first convert any mixed number into an improper fraction. For example, to solve 2\tfrac{1}{3} + x = 3, convert 2\tfrac{1}{3} to 7/3, then subtract 7/3 from both sides: x = 3 - 7/3 = 9/3 - 7/3 = 2/3. Always simplify your answer.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Solve $\frac{2}{3} + x = 1 \frac{1}{3}$

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

You have $1 \frac{1}{2}$ hours to finish homework. You spend $\frac{3}{4}$ hour on math. How much time is left?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Solve the equation $\frac{5}{4} + x = 2$.

Challenge Quiz

Single Choice Quiz

Advanced

What is $x$ if $2 \frac{2}{3} \times x = 4$?

Recap

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Review key concepts and takeaways