Question

How do you add `3\frac { 7} { 10} + 4\frac { 1} { 15} + 2\frac { 2} { 13}`?

Answer 1

`9\frac { 359} { 390}`

Explanation:

Okay, so first you put all the fractions into a Common Denominator what this means is that all the bottom numbers have to be equal.

So let's add the first two numbers first

`3\frac { 7} { 10} + 4\frac { 1} { 15}`

What is a common denominator for `15` and `10`: the answer is `30`.

A brief overview of a common denominator: to find the common denominator list the multiples of `15` and `10`. For 15 it would be:

`15 (15 * 1 = 15)`

`30 (15 * 2 = 30)`

Therefore, we could conclude that since the multiples of `10` are pretty simple.

`10 * 1 = 10`

`10 * 2 = 20`

`10 * 3= 30`

We found a common denominator: `30`!

So next we multiply each number the top and the bottom the same so if we multiple `10` by `3` to equal `30`; we do the same for the top number so

`7 * 3 =21`

Same goes for the other number we multiplied `15` by `2` to find `30` and we do the same for the top

`1 * 2 = 2`

But we don't do anything to the whole number because it's not a part of the fraction! Therefore the numbers are going to look like

`3\frac { 21} { 30} + 4\frac { 2} { 30}`

Which equals this is all just addition which I shouldn't be explaining

`7\frac { 23} { 30`

Now we do the next part

`7\frac { 23} { 30} + 2\frac { 2} { 13}`

A common multiple of `13` and `30` would be `390`.

Which sounds like a lot but is just a multiple of `9` for `13` and a multiple of `13` for `30`.

So we do the same thing we did above.

`9\frac { 359} { 390}`

Which cannot be simplified!

Remember always simplify during tests or quizzes if you don't you will definite loose points; which is a frugal way to lose points after all that hard work.

Answer 2

`9color(white)(.) 359/390`

Explanation:

Split the numbers so that we have:
`(3+4+2)+(7/10+1/15+2/13)`

The brackets are only there to highlight the grouping of numbers.

This gives: `9+(7/10+1/15+2/13)`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Dealing with the fractional group of numbers")`

A fractions structure is: `("count")/("size indicator")->("numerator")/("denominator")`

You can not directly add the 'counts' (numerators) unless the
'size indicators' (denominators) are all the same.

`color(brown)("A sort of cheat method for a common denominator")`

`color(white)(3)15`
`ul(color(white)(3)13) larr" Multiply"`
`150`
`ul(color(white)(1)45)larr" Add"`
`195 larr" both 15 and 13 are factors of this number"`

The last digit of 195 is 5 so 195 can not have 10 as a whole number factor. So lets try changing the 5 into 0

`195`
`ul(color(white)(19)2) larr" multiply"`
`390 larr" all of 10, 15 and 13 will divide into this number"`
.........................................................................................

`390-:10=39`
`390-:15=26`
`390-:13=30`

`color(green)([7/10color(red)(xx1)]color(white)(..)+color(white)(..)[1/15color(red)(xx1)]color(white)(..)+color(white)(..)[2/13color(red)(xx1)]`

`color(green)([7/10color(red)(xx39/39)]+color(white)(.)[1/15color(red)(xx26/26)]color(white)(.)+color(white)(.)[2/13color(red)(xx30/30)]`

`color(green)(" "[273/390]" "+" "[26/390]" "+" "[60/390] )`

`color(white)(.)`

`color(green)(" "359/390)`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Putting it all together")`

`" "color(blue)(9 359/390)`