# Question bf8be

Oct 5, 2017

$\frac{37}{24}$

#### Explanation:

In order to do this problem, you must first find the LCD (LCD is the least common denominator), which is $24$ in this case. It's $24$ because the smallest number that $8$ and $3$ both have in common is $24$.

Firstly, multiply $\frac{2}{3}$ (top and bottom) by $8$ in order to get $\frac{16}{24}$. Then you multiply $\frac{7}{8}$ (top and bottom) by $3$ to get $\frac{21}{24}$ and add

$\frac{16}{24} + \frac{21}{34}$

Your answer should be $\frac{37}{24}$

Oct 5, 2017

$\frac{37}{24} \mathmr{and} 1 \frac{13}{24}$

#### Explanation:

First, you need a common denominator; in this case, you can just multiply the denominators together:

$3 \times 8 = 24$

In other cases, you would need to find the least common multiple between two the denominators.

Now, you just need to add two fractions with that new common denominator we just found. Keep in mind, you can't just do

$\frac{2}{24} + \frac{7}{24}$

because that would change the VALUE of the two fractions (e.g. $\frac{2}{24}$ is smaller than $\frac{2}{3}$). So to make $\frac{2}{3}$ with a denominator of $24$ (but with the same VALUE), you have to multiply the numerator and denominator by $8$, which will give you $\frac{16}{24}$.

For the second fraction, you would multiply the numerator and denominator by $3$ to get $\frac{21}{24}$.

So we now have

$\frac{16}{24} + \frac{21}{24}$

You can safely add the two fractions because they have a common denominator, resulting in the final answer of $\frac{37}{24}$.

This is an improper fraction (e.g. the numerator is higher than the denominator). You can divide numerator and denominator to get a proper fraction, which in this case will be $1 \frac{13}{24}$.

Oct 5, 2017

It is very deliberate that I give a lot of detail. As you become more practiced you will be able to skip a lot of steps. You will learn the shortcuts and do a lot of it in your head.

#### Explanation:

A fraction's structure is such that you have:

$\left(\text{count")/("size indicator of what you are counting")->("numerator")/("denominator}\right)$

$\textcolor{b r o w n}{\text{You can ONLY DIRECTLY add or subtract counts if the size indicators are the same.}}$

color(green)([color(white)("d")2/3color(red)(xx1)color(white)("d")]+[color(white)("d")7/8color(red)(xx1)color(white)("d")]

color(green)([color(white)("d")2/3color(red)(xx8/8)color(white)("d")]+[color(white)("d")7/8color(red)(xx3/3)color(white)("d")]#

$\textcolor{w h i t e}{\text{ddddddd}} \frac{16}{24} + \frac{21}{24}$

$\textcolor{w h i t e}{\text{ddddddd}} \frac{16 + 21}{24}$

$\textcolor{w h i t e}{\text{ddddddddd}} \frac{37}{24}$

37 is a prime number so as a fraction it can not be simplified any further. However, you may write this as 1 and something

$\frac{37}{24} = \frac{24 + 13}{24}$

$\textcolor{w h i t e}{\text{ddd}} = \frac{24}{24} + \frac{13}{24}$

$\textcolor{w h i t e}{\text{ddd}} = 1 + \frac{13}{24}$

$\textcolor{w h i t e}{\text{ddd}} = 1 \frac{13}{24}$