# What is 8 1/4 div 3?

Apr 18, 2018

$2 \frac{3}{4} \text{or } \frac{11}{4}$

#### Explanation:

So we start off with with this:

$\frac{8 \left(\frac{1}{4}\right)}{3}$

This means that we have 8 wholes and a fourth. To get this in fraction form:
1.Take the number in front of the fraction times the denominator

$8 \cdot 4 = 32$ quarters

2.Now plus the numerator to get the total number of quarters

$32 + 1 = 33$ quarters

So now we have: $\frac{\frac{33}{4}}{3}$

We can extend the 3 to $\frac{3}{1}$

It's the exactly the same thing just different numbers.

Now we have:

$\frac{\frac{33}{4}}{\frac{3}{1}}$

Now we divide them by flipping the bottom one and then multiplying so we get:

$\frac{33}{4} \times \frac{1}{3} = \frac{33}{12}$

Now we can simplify by dividing by three in the numerator and in the denominator so we get

$\frac{11}{4} = 2 \frac{3}{4}$

Hope this helps =).

Apr 18, 2018

$2 \frac{3}{4}$

A lot of detail given so you can see the way everything works. In reality you would use a lot less lines.

#### Explanation:

Consider the $\div 3$ this has the same outcome as $\times \frac{1}{3}$
So now we have:

$\textcolor{b l u e}{8 \frac{1}{4} \times \frac{1}{3}}$

Consider the $8 \frac{1}{4}$. Write as $8 + \frac{1}{4}$

Multiply by 1 and you do not change the value. However, 1 comes in many forms

color(green)( [8 color(red)(xx1)]+1/4 color(white)("dddd")-> color(white)("dddd")[8color(red)(xx4/4)]+1/4

color(green)(color(white)("ddddddddddddd")-> color(white)("ddd.dd")[32/4]color(white)("d")+1/4= 33/4

$\textcolor{g r e e n}{8 \frac{1}{4} = \frac{33}{4}}$

Putting it all back together we have:

$\textcolor{b l u e}{\frac{33}{4} \times \frac{1}{3}}$

color(green)((33xx1)/(4xx3)color(white)("dd") =color(white)("dd") (33xx1)/(3xx4)color(white)("dd") =color(white)("dd") cancel(33)^11/cancel(3)^1xx1/4color(white)("d")=color(white)("d")11/4

color(blue)(11/4color(white)("dd") ->color(white)("dd")2 3/4 larr" Same format as in the question")

Apr 19, 2018

$\frac{11}{4} = 2 \frac{3}{4}$

#### Explanation:

To divide with fractions:

• Make improper fractions.
• multiply by the reciprocal
• cancel where possible
• multiply straight across

$8 \frac{1}{4} \div 3$

$= \frac{33}{4} \times \frac{1}{3}$

$= {\cancel{33}}^{11} / 4 \times \frac{1}{\cancel{3}}$

$= \frac{11}{4}$

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

Answer in the same format as the question, so give the answer as a mixed number,