Question

How do you solve `-5/13 + (-3 5/7)`?

Answer 1

See a solution process below:

Explanation:

First, rewrite the expression as:

`-5/13 - 3 5/7`

Next, convert the number on the right from a mixed number to an improper fraction:

`3 5/7 = 3 + 5/7 = (7/7 xx 3) + 5/7 = 21/7 + 5/7 = (21 + 5)/7 = 26/7`

Then, put each fraction over a common denominator:

`5/13 = 7/7 xx 5/13 = (7 xx 5)/(7 xx 13) = 35/91`

`26/7 = 13/13 xx 26/7 =(13 * 26)/(13 xx 7) = 338/21`

We can now rewrite the expression again and perform the subtraction:

-35/91 - 338/91 = (-35 - 338)/91 = -373/91#

If necessary, we can convert this number to a mixed number:

`373/91 = -(364 + 9)/91 = -(364/91 + 9/91) = -(4 + 9/91) = -4 9/91`

Answer 2

`-5/13+(-3 5/7)` simplifies to `-373/91` or `-4 9/91`.

Explanation:

This is an expression, not an equation, so it cannot be solved, but it can be simplified.

Given:

`-5/13+(-3 5/7)`

Simplify the parentheses.

`-5/13-3 5/7`

Convert `3 5/7` to an improper fraction by multiplying the denominator by the whole number and adding the numerator, placing the result over the denominator.

`3 5/7=(7xx3+5)/7=26/7`

Rewrite the expression.

`-5/13-26/7`

In order to add or subtract fractions, they must have the same denominator, called the least common denominator (LCD) or least common multiple (LCM).

Since `13` and `7` are prime numbers, the LCD is the product of `13` and `7`.

`13xx7=91`

In order to make the denominators the same, multiply each fraction by a fraction equal to `1` that will not change the value, but will make both denominators `91`. For example, `5/5=1`

`-5/13xxcolor(teal)(7/7)-26/7xxcolor(magenta)(13/13)`

Simplify.

`-35/91-338/91`

`(-35-338)/91`

`-373/91`

Convert `-373/91` to a mixed fraction. To do this, divide `-373` by `91`. Take the first whole number and make the remainder the numerator over `91`.

`"-373-:91` `=` `-4` `"R"` `9`

`-373/91=-4 9/91`