• Understand different types of fractions

Converting Mixed Numbers and Improper Fractions

Convert an Improper Fraction to a Mixed Number

Switching between mixed numbers and improper fractions is a handy skill in math, especially when it comes to adding or subtracting fractions. A mixed number combines a whole number with a fraction, while an improper fraction has a numerator larger than its denominator. Here’s a quick guide on how to transform an improper fraction into a mixed number, breaking it down into simpler, more understandable parts.

How To: Convert an Improper Fraction to a Mixed Number

1. Divide the denominator into the numerator.
2. Identify the quotient, remainder, and divisor.
3. Write the mixed number as [latex]\text{quotient} {\Large\frac{\text{remainder}}{\text{divisor}}}[/latex] .

Convert the improper fraction [latex]{\Large\frac{33}{8}}[/latex] to a mixed number.

Show Solution

[latex]{\Large\frac{33}{8}}[/latex]
Divide the denominator into the numerator.	Remember, [latex]{\Large\frac{33}{8}}[/latex] means [latex]8\overline{)33}[/latex] .
Identify the quotient, remainder, and divisor.
Write the mixed number as [latex]\text{quotient} {\Large\frac{\text{remainder}}{\text{divisor}}}[/latex] .	[latex]4{\Large\frac{1}{8}}[/latex]
So, [latex]{\Large\frac{33}{8}}=4{\Large\frac{1}{8}}[/latex]

Convert a Mixed Number to an Improper Fraction

Converting a mixed number to an improper fraction is just as straightforward as the reverse process we’ve covered. It’s about combining the whole number and the fraction part into one fraction. This conversion is crucial for performing various arithmetic operations with mixed numbers. Let’s go through the simple steps to make this transformation.

How To: Convert a Mixed Number to an Improper Fraction

1. Multiply the whole number by the denominator.
2. Add the numerator to the product found in Step [latex]1[/latex].
3. Write the final sum over the original denominator.

Convert the mixed number [latex]10{\Large\frac{2}{7}}[/latex] to an improper fraction.

Show Solution

[latex]10{\Large\frac{2}{7}}[/latex]
Multiply the whole number by the denominator.
The whole number is [latex]10[/latex] and the denominator is [latex]7[/latex].
Simplify.
Add the numerator to the product.
The numerator of the mixed number is [latex]2[/latex].
Simplify.
Write the final sum over the original denominator.
The denominator is [latex]7[/latex].	[latex]{\Large\frac{72}{7}}[/latex]