Adding mixed fractions

Addition Of Mixed Fractions

Concept

A mixed number is one that combines an integer and a fraction. They can be expressed initially as improper fractions and then broken down into their mixed number form.

Rules

The steps for adding mixed numbers:
1. Add the fractions. If the results are an improper fraction, rename as a mixed number
2. Add the whole numbers.
3. Write your answer in lowest terms.

Example

Add.
$\fn_phv 5\frac{2}{5}+3\frac{4}{5}$

Solution

1. Add the fractions. If the results are an improper fraction, rename as a mixed number
$\fn_phv \frac{2}{5}+\frac{4}{5}=\frac{6}{5}=1\frac{1}{5}$
2. Add the whole numbers, including the renamed improper fraction.
$\fn_phv 5+3+1=9$
3. Write your answer in the lowest terms.
$\fn_phv {\color{Red} 9\frac{1}{5}}$

Practice Adding Mixed Fractions

Practice Problem 1

Add.
$\fn_phv 3\frac{3}{7}+4\frac{1}{7}$
$Adding mixed fractions Practice Problem 1$

Numerator – the number above the line in a common fraction showing how many of the parts indicated by the denominator there are.

Denominator – the bottom number in a fraction that shows the number of equal parts an item is divided into. It is the divisor of a fraction.

Proper Fraction – a fraction that is less than one, with the numerator less than the denominator

Improper Fraction – a fraction that is greater than one, with the numerator bigger than the denominator

Like Fractions– fractions with denominators that are same.

Unlike Fractions– fractions with denominators that are different.

Mixed Number – a combination of a whole number and a fraction.

Pre-requisite Skills
Equivalent Fractions
Improper fractions to mixed numbers
Add Like Fractions
Subtract Like Fractions
Add and Subtract Like Fractions

Related Skills
Add and Subtract Fractions with Like Denominators
Add and Subtract Fractions with Unlike Denominators
Estimate Products of Fractions
Multiply Fractions
Multiply Mixed Numbers
Divide Fractions
Divide Mixed Numbers
Multiply Rational Numbers
Divide Rational Numbers