Question

Question #35ec3

Answer 1

`5 5/6`

Explanation:

I know this looks like a lot, but I promise it's not scary! It's very fast when you don't have to read the words in my instructions, I promise :)

The first step when you're working with fractions is to make them into improper fractions. We're going to do this with both of your fractions, so let's see it with the first fraction seen in the question: `3 1/2`

First, you want to multiply your whole number (in this case, 3) by your bottom number, or denominator (in this case, 2). Then, we add the answer to your top number, or numerator.

`3 * 2 = 6`
`1 + 6 = 7`

Since we got 7, the new fraction we have for this question is `7/2`.

Repeat the process for the second fraction. Note that it is negative, but we do not do anything special for that. Solve it as if it were positive, just don't forget to keep your negative sign once you find your answer! Watch:

`2 * 3 = 6`
`1 + 6 = 7`

This gives you `7/3`, but remember we started with a negative fraction, so you actually have `-7/3`!

Your question should now look like `7/2 - (-7/3)`.

Let's simplify it one more time before we get our hands dirty. Since two negatives make a positive, you can instead write:

`7/2 + 7/3`

Now, when you are adding or subtracting a fraction, you have to have the same number. The quickest way to do this is multiplying the first fraction by the second fraction's denominator (remember this means the bottom number), and then the second fraction by the first fraction's denominator. This goes as follows for the first fraction:

`7 * 3 = 21`
`2 * 3 = 6`
New fraction is `21/6`

Repeat for the second fraction.

`7 * 2 = 14`
`3 * 2 = 6`
New fraction is `14/6`

Your new problem should look like `21/6 + 14/6`. See how they have the same denominator? Now you just add the two numerators (remember, this means the top number) and keep your denominator the same!

`21 + 14 = 35`, so your fraction is `35/6`.

If your teacher wants this simplified, you can divide `35` by `6` and leave your remainder as the numerator, like this:

`35-:6 = "5, r 5"`

Finally, your answer is `5 5/6`.

Answer 2

See a solution process below:

Explanation:

First, because "minus a minus is a plus" we can rewrite this expression as:

`3 1/2 + 2 1/3`

Next, to add these two numbers, first convert them to improper fractions:

`3 1/2 = 3 + 1/2 = (2/2 xx 3) + 1/2 = 6/2 + 1/2 = (6 + 1)/2 = 7/2`

`2 1/3 = 2 + 1/3 = (3/3 xx 2) + 1/3 = 6/3 + 1/3 = (6 + 1)/3 = 7/3`

Then, we need to put each fraction over a common denominator:

`7/2 xx 3/3 = 21/6`

`7/3 xx 2/2 = 14/6`

We can next add the numerators from the two fractions over the common denominator:

`21/6 + 14/6 = (21 + 14)/6 = 35/6`

Now, we can convert the improper fraction into a mixed number, if necessary:

`35/6 = (30 + 5)/6 = 30/6 + 5/6 = 5 + 5/6 = 5 5/6`

Answer 3

`35/6 = 5 5/6`

Explanation:

Let's first get rid of mixed numbers and have improper fractions instead

`3 1/2 = 7/2`

`2 1/3 = 7/3`

Now the problem looks like this:

`7/2 - (-7/3)`

We know that two minuses make a plus so:

`7/2 +7/3`

We have to find a common denominator otherwise we won't be able to add the fractions. To find a common denominator, multiply the denominators together to find one.

`2*3 = 6`

This means that `7/2` is multiplied by 3 and `7/3` by 2. Make sure to multiply both the numerator and the denominator by the given number. Then add them.

`7/2 *3/3 + 7/3*2/2 = 21/6 + 14/6 = 35/6`

You can leave it as an improper fraction or as mixed number.

`35/6 = 5 5/6`