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Mixed Number

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Mixed Number

Study Guide

Key Definition

A mixed number is expressed as the sum of a whole number and a fraction, such as $3\frac{1}{4}$.

Important Notes

Mixed numbers give a good idea of the size of a number.
Improper fractions are often easier for calculations.
To convert a mixed number to an improper fraction: multiply the whole number by the denominator, add the numerator, and place this result over the original denominator.
Example: $3\frac{1}{4} = \frac{13}{4}$
Converting back involves dividing the numerator by the denominator.

Mathematical Notation

$\frac{a}{b}$ represents a fraction with a numerator $a$ and a denominator $b$

$+$ represents addition

$-$ represents subtraction

$\times$ represents multiplication

$\div$ represents division

Remember to use proper notation when solving problems

Why It Works

Mixed numbers are useful for estimating and understanding the magnitude of numbers, while improper fractions are efficient for calculations like multiplication and division.

Remember

To convert a mixed number to an improper fraction, use the formula: $whole \times denominator + numerator$

Quick Reference

Conversion:$\text{mixed number }=\frac{(\text{whole}\times\text{denominator}+\text{numerator})}{\text{denominator}}$

Understanding Mixed Number

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

A mixed number combines a whole number with a fraction, like $2\frac{1}{2}$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

Convert $2\frac{3}{4}$ to an improper fraction.

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Sarah baked $3\frac{1}{2}$ pies for a party. How many halves of a pie does she have?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If you have $5\frac{3}{4}$ gallons of paint, how many $\frac{3}{4}$ gallon containers can you fill?

Challenge Quiz

Single Choice Quiz

Advanced

Convert $7\frac{5}{6}$ to an improper fraction.

Recap

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Review key concepts and takeaways