Question

What is `8 1/4 div 3`?

Answer 1

`2 3/4 "or " 11/4`

Explanation:

So we start off with with this:

`(8(1/4))/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*4=32` quarters

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

`32+1=33` quarters

So now we have: `(33/4)/3`

We can extend the 3 to `3/1`

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

Now we have:

`(33/4)/(3/1)`

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

`33/4xx1/3=33/12`

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

`11/4 = 2 3/4`

Hope this helps =).

Answer 2

`2 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 `-:3` this has the same outcome as `xx1/3`
So now we have:

`color(blue)(8 1/4xx1/3)`

Consider the `8 1/4`. Write as `8+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`

`color(green)(8 1/4 = 33/4)`

Putting it all back together we have:

`color(blue)(33/4xx1/3)`

`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")`

Answer 3

`11/4 =2 3/4`

Explanation:

To divide with fractions:

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

`8 1/4 div 3`

`= 33/4 xx1/3`

`= cancel33^11/4 xx1/cancel3`

`=11/4`

`= 2 3/4`

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