# Please solve  15 1/2 + 16 1/4 - 12 5/8 - 14 1/6 ?

$4 \frac{23}{24}$

#### Explanation:

There are a couple of ways to approach this - we can convert the mixed numbers to improper fractions (which will result in big numerators when we get a common denominator) or we can rewrite the expression this way:

$15 + \frac{1}{2} + 16 + \frac{1}{4} - \left(12 + \frac{5}{8}\right) - \left(14 + \frac{1}{6}\right)$

Let's distribute the negative signs:

$15 + \frac{1}{2} + 16 + \frac{1}{4} - 12 - \frac{5}{8} - 14 - \frac{1}{6}$

and now regroup the expression with whole numbers grouped together and fractions grouped together:

$\left(15 + 16 - 12 - 14\right) + \left(\frac{1}{2} + \frac{1}{4} - \frac{5}{8} - \frac{1}{6}\right)$

We can simplify the whole number part of the expression:

$5 + \left(\frac{1}{2} + \frac{1}{4} - \frac{5}{8} - \frac{1}{6}\right)$

And now let's focus on the fractions. We need the Lowest Common Denominator, which is 24 and can be found by using prime factorizations:

$2 = 2$
$4 = 2 \times 2$
$8 = 2 \times 2 \times 2$
$6 = 2 \times 3$

And now we grab the largest grouping of each prime. There are three 2s (in the 8) and a single 3 (in the 6), so we have:

$L C D = 2 \times 2 \times 2 \times 3 = 24$

$5 + \left(\frac{1}{2} \left(1\right) + \frac{1}{4} \left(1\right) - \frac{5}{8} \left(1\right) - \frac{1}{6} \left(1\right)\right)$

$5 + \left(\frac{1}{2} \left(\frac{12}{12}\right) + \frac{1}{4} \left(\frac{6}{6}\right) - \frac{5}{8} \left(\frac{3}{3}\right) - \frac{1}{6} \left(\frac{4}{4}\right)\right)$

$5 + \left(\frac{12}{24} + \frac{6}{24} - \frac{15}{24} - \frac{4}{24}\right)$

$5 + \left(- \frac{1}{24}\right)$

Let's now see that we can express the number 5 as $4 + 1$:

$4 + 1 - \frac{1}{24}$

and we can express 1 as $\frac{24}{24}$:

$4 + \frac{24}{24} - \frac{1}{24}$

$4 + \frac{23}{24} \implies 4 \frac{23}{24}$

Jun 26, 2018

Deal with the whole numbers first

$15 - 14 = 1$
$16 - 12 = 4$
$4 + 1 = 5$

Then the fractions

$\frac{1}{2} + \frac{1}{4} = \frac{2}{4} + \frac{1}{4} = \frac{3}{4}$

$\frac{3}{4} - \frac{5}{8} = \frac{6}{8} - \frac{5}{8} = \frac{1}{8}$

$\frac{1}{8} - \frac{1}{6} = \frac{3}{24} - \frac{4}{24} = - \frac{1}{24}$

Putting these together

$5 + - \frac{1}{24}$

$4 \frac{24}{24} - \frac{1}{24} = 4 \frac{23}{24}$

Jul 20, 2018

$= 4 \frac{23}{24}$

#### Explanation:

$\textcolor{b l u e}{15} \frac{1}{2} + \textcolor{b l u e}{16} \frac{1}{4} - \textcolor{red}{12} \frac{5}{8} - \textcolor{red}{14} \frac{1}{6}$

$= \textcolor{b l u e}{31} \frac{1}{2} + \frac{1}{4} - \textcolor{red}{26} \frac{5}{8} - \frac{1}{6}$

$= 5 \frac{12 + 6 - 15 - 4}{24} \text{ } \leftarrow$ find the common denominator

$= 5 \frac{18 - 19}{24} = 4 + \textcolor{m a \ge n t a}{1} \frac{18 - 19}{24} \text{ }$ (convert $\textcolor{m a \ge n t a}{1 = \frac{24}{24}}$)

$= 4 \frac{\textcolor{m a \ge n t a}{24} + 18 - 19}{24}$

$= 4 \frac{23}{24}$

Aug 10, 2018

$4 \frac{23}{24}$

#### Explanation:

$15 \frac{1}{2} + 16 \frac{1}{4} - 12 \frac{5}{8} - 14 \frac{1}{6}$

$\therefore = \frac{31}{2} + \frac{65}{4} - \frac{101}{8} - \frac{85}{6}$

$\therefore = \frac{372 + 390 + 303 - 340}{24}$

$\therefore = \frac{119}{24}$

$\therefore = 4 \frac{23}{24}$