# How do you simplify 4\frac { 3} { 16} + 1\frac { 1} { 10} ?

Oct 23, 2016

$4 \frac{3}{16} + 1 \frac{1}{10} = 5 \frac{23}{80}$

#### Explanation:

NOTE: A raised dot ($\cdot$) indicates multiplication and is preferred to the elementary $\times$ because when handwriting one's work, the $\times$ and an $x$ too often look the same.

When adding mixed numbers, you must first change the fractional parts so that they have the same denominator. The Least Common Denominator of two (or more) fractions is equal to the Least Common Multiple of their denominators. Consider the prime factorization of each denominator.

$16 = 2 \cdot 2 \cdot 2 \cdot 2 = {2}^{4}$
$10 = 2 \cdot 5$

The Least Common Multiple of $16$ and $10$ will be the product of ${2}^{4} \cdot 5$, which is $80$. So, the Least Common Denominator of the two mixed numbers is $80$. Now, you need to change the two fractional parts of the mixed numbers.

$\frac{3}{16} = \frac{15}{80}$

$\frac{1}{10} = \frac{8}{80}$

Now the two mixed numbers can be added.

$4 \frac{3}{16} + 1 \frac{1}{10}$

$4 \frac{15}{80} + 1 \frac{8}{80}$

$5 \frac{23}{80}$