## Related calculator: Fractions Calculator

Adding mixed numbers is quite easy.

We know that mixed number consists of integer part and fractional part.

To add mixed numbers three steps are needed:

1. Convert each mixed number to improper fraction.
3. Convert improper fraction to mixed number if needed (and if possible).

Example 1. Find ${1}\frac{{3}}{{5}}+{2}\frac{{4}}{{9}}$.

Convert each mixed number into improper fraction: ${1}\frac{{3}}{{5}}=\frac{{8}}{{5}}$ and ${2}\frac{{4}}{{9}}=\frac{{22}}{{9}}$.

Now add fractions: $\frac{{8}}{{5}}+\frac{{22}}{{9}}=\frac{{{8}\cdot{9}}}{{{5}\cdot{9}}}+\frac{{{22}\cdot{5}}}{{{9}\cdot{5}}}=\frac{{72}}{{45}}+\frac{{110}}{{45}}=\frac{{182}}{{45}}$.

Convert fraction to mixed number: $\frac{{182}}{{45}}={4}\frac{{2}}{{45}}$.

Answer: ${4}\frac{{2}}{{45}}$.

Next example.

Example 2. Find $-{2}\frac{{1}}{{6}}+{3}\frac{{1}}{{2}}$.

Convert each mixed number into improper fraction: $-{2}\frac{{1}}{{6}}=-\frac{{13}}{{6}}$ and ${3}\frac{{1}}{{2}}=\frac{{7}}{{2}}$.

Now add fractions: $-\frac{{13}}{{6}}+\frac{{7}}{{2}}=-\frac{{13}}{{6}}+\frac{{{7}\cdot{3}}}{{{2}\cdot{3}}}=-\frac{{13}}{{6}}+\frac{{21}}{{6}}=\frac{{8}}{{6}}$.

Reduce fraction: $\frac{{8}}{{6}}=\frac{{4}}{{3}}$.

Convert fraction to mixed number: $\frac{{4}}{{3}}={1}\frac{{1}}{{3}}$.

Answer: $\frac{{4}}{{3}}={1}\frac{{1}}{{3}}$.

Next example.

Example 3. Find ${2}+{5}\frac{{8}}{{11}}$.

Since first number has no fractional part, we can easier add numbers.

Add integer parts: ${2}+{5}={7}$ and fractional part leave the same.

Warning. This works only when we add either both positive numbers or both negative numbers.

Answer: ${7}\frac{{8}}{{11}}=\frac{{85}}{{11}}$.

Now, take pen and paper and do following exercises.

Exercise 1. Find ${5}\frac{{1}}{{6}}+{3}\frac{{7}}{{8}}$.

Answer: $\frac{{217}}{{24}}={9}\frac{{1}}{{24}}$.

Next exercise.

Exercise 2. Find ${7}\frac{{4}}{{9}}+{\left(-{2}\frac{{5}}{{6}}\right)}$.

Answer: $\frac{{83}}{{18}}={4}\frac{{11}}{{18}}$.

Next exercise.

Exercise 3. Find $-{5}\frac{{1}}{{6}}+{\left(-{3}\frac{{7}}{{8}}\right)}$.

Answer: $-\frac{{217}}{{24}}=-{9}\frac{{1}}{{24}}$.

Next exercise.

Exercise 4. Find ${3}\frac{{5}}{{6}}+\frac{{5}}{{7}}$.

${3}\frac{{5}}{{6}}+\frac{{5}}{{7}}=\frac{{23}}{{6}}+\frac{{5}}{{7}}=\frac{{161}}{{42}}+\frac{{30}}{{42}}=\frac{{191}}{{42}}={4}\frac{{23}}{{42}}$.

Answer: $\frac{{191}}{{42}}={4}\frac{{23}}{{42}}$.

Next exercise.

Exercise 5. Find $-{5}\frac{{1}}{{6}}+{7}$.

Here we just can't add fractional parts to obtain ${2}\frac{{1}}{{6}}$. This is not correct, because one of the addends is negative and another is positive.

We do it as always.

$-{5}\frac{{1}}{{6}}+{7}=-\frac{{31}}{{6}}+\frac{{42}}{{6}}=\frac{{11}}{{6}}={1}\frac{{5}}{{6}}$.

Answer: $\frac{{11}}{{6}}={1}\frac{{5}}{{6}}$.

If you are not sure whether it is possible to add integer parts, use the three-step method. It guarantees correct answer.