Question

How do you add `2 3/4 + 1 4/5`?

Answer 1

All you do is multiply the number outside the fraction by the denominator (the bottom number of the fraction), and add the product to the numerator (the top of the fraction), leaving the denominator as it was.

So, first we multiply 2 by 4, which is 8, and then add that to the numerator, 3. We leave the denominator as 4 however. Then, we multiply 1 by 5, which is 5, and then add that to the numerator, 4, leaving the denominator as 5.

This leaves us with

`11/4 + 9/5`

Now we need to get a common denominator. The LCM (Lowest common multiple) of 4 and 5, the denominators, is 20. To get to 20 from 4, we multiply by 5. to get to 20 from 5, we multiply by 4. So...

`(11/4) * 5+ (9/5) * 4`

`(55/20) + (36/20)`

=`91/20`

Answer 2

`4 11/20` which is the value same as `91/20`

Explanation:

Adding the whole number part `color(blue)(2+1=3)`

Dealing with the fractions.

A fractions structure is such that we have:

`("numerator")/("denominator") ->("count")/("size indicator of what you are counting")`

You CAN NOT DIRECTLY add or subtract the counts (numerators) unless the size indicators (denominators) are the same.

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

`color(green)( [3/4color(red)(xx1)]+[4/5color(red)(xx1)] color(white)("dddd")=color(white)("dddd")[3/4color(red)(xx5/5)]+[4/5color(red)(xx4/4)] )`

`color(green)(color(white)("dddddddddddddddddddd")=color(white)("d")color(white)("dddddd")15/20color(white)("dd")+color(white)("ddd")16/20)`

`color(green)(=31/20 = 1 11/20)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Putting it all back together

`color(blue)(3)color(green)(+1 11/20) =4 11/20`

Note that `4 11/20` is the same as `91/20`

Unless instructed otherwise it is good practise to write the solution in the same format as the question.