How do you evaluate 5/8+5/6?

Jul 10, 2016

By finding a common denominator or using a pretty cool trick. Answer is in the explanation.

Explanation:

The least common multiple between 6 and 8 is 24.

$8 \cdot 3$ is 24 so we must multiply its 5 by 3 which is 15 making the first fraction $\frac{15}{24}$.

$6 \cdot 4$ is 24 so we must multiply its 5 by 4 which is 20 making the second fraction $\frac{20}{24}$.

Now we can add 15 and 20 to get $\frac{35}{24}$ which is our final answer.

There's another method that I think is much easier and quicker however it may be a more difficult concept to grasp. I will illustrate it using variables.

If you're adding two fractions, $\frac{a}{b} + \frac{c}{d}$, the final fraction will be $\frac{a d + b c}{b d}$. If we apply this to the current problem we will get $\frac{5 \cdot 6 + 5 \cdot 8}{6 \cdot 8} = \frac{30 + 40}{48} = \frac{70}{48} = \frac{35}{24}$

Jul 12, 2016

$1 \textcolor{w h i t e}{.} \frac{11}{24}$

Explanation:

A fraction is split up into 2 parts

$\left(\text{Part 1")/("Part 2") -> ("count of how many you have")/("size indicator of what you are counting}\right)$

The size indicator is how many it take to make 1 of something.

$\left(\text{Part 1")/("Part 2") -> ("numerator")/("denominator}\right)$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{red}{\text{You can not directly add or subtract the counts unless}}$$\textcolor{red}{\text{they have the same size indictor (denominator).}}$

Both 8 and 6 will divide exactly into 24. So we will make both of the denominators 24.

$\textcolor{b l u e}{\text{Consider } \frac{5}{8}}$
Note that $3 \times 8 = 24$

Multiply by 1 but in the form of $1 = \frac{3}{3}$

$\textcolor{b l u e}{\frac{5}{8} \times 1 \text{ "=" " 5/8xx3/3 " "=" } \frac{15}{24}}$

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
$\textcolor{b l u e}{\text{Consider } \frac{5}{6}}$
Note that $4 \times 6 = 24$

Multiply by 1 but in the form of $1 = \frac{4}{4}$

$\textcolor{b l u e}{\frac{5}{6} \times 1 \text{ "=" "5/6xx4/4" "=" } \frac{20}{24}}$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$\textcolor{g r e e n}{\text{Putting it all together in detail}}$

$\textcolor{g r e e n}{\text{With practice you will be able to do a lot of this in your head and}}$$\textcolor{g r e e n}{\text{jump steps.}}$

$\frac{5}{8} + \frac{5}{6} \text{ " =" "color(blue)(15/24+20/24)" "=" } \frac{15 + 20}{24}$

$\textcolor{w h i t e}{. .}$

But $15 + 20 = 35 = 24 + 11$

$\textcolor{w h i t e}{. .}$

$= \frac{24 + 11}{24}$

$= \frac{24}{24} + \frac{11}{24}$

$1 + \frac{11}{24}$

$= 1 \frac{11}{24}$