Pre-Algebra - Addition and Subtraction

Simplify the expression.

Explanation

Re-write the expression to group like terms together.

Simplify.

What is $2x^{2}+3x^{2}$ simplified?

$5x^{2}$

$5x^{4}$

$6x^{2}$

$6x^{4}$

Explanation

To simplify a problem like the example above we must combine the like-termed variables.

Like terms are the terms that share the same variable(s) to the same power. In this example the like term is $x^{2}$ .

To combine like terms the variable $x^{2}$ stays the same and you add the numbers in front.

Perform the necessary addition, , to get $5x^{2}$ .

We have the simplified version of the equation, $5x^{2}$ .

$\frac{4}{5} + \frac{2}{3} = ?$

Write solution as an improper fraction.

$\frac{22}{15}$

$\frac{90}{15}$

$\frac{26}{15}$

$\frac{26}{5}$

Explanation

When adding or subtracting fractions, you must find the common denominator. This is best done by finding the least common multiple of the denominators, in this case 5 and 3. What is the lowest number that is divisible by both 5 and 3? Often, the easiest solution is to multiply the denominators together. This works most often with single digit numbers. Anything larger and you will have to find the least common multiple another way.

The LCM of 5 and 3 is 15 (5 x 3). Now you know that both fractions must have 15 on the bottom. Now, to convert 4/5 to ?/15, you must recognize how many times 5 goes into 15 (3), and multiply the numerator by that number. Therefore:

$\frac{4}{5}\times \frac{3}{3}=\frac{12}{15}$

Do the same with the other side.

$\frac{2}{3}\times \frac{5}{5}=\frac{10}{15}$

Now that the denominators match, all that's left is to add the numerators together.

$\frac{10}{15}+\frac{12}{15}=\frac{22}{15}$

This solution is already an improper fraction (the numerator is larger than the denominator), therefore you may leave the fraction as is.

Explanation

When a plus and minus sign meet, the sign becomes negative. When adding two negative numbers, we treat as an addition problem and add a minus sign in the end. Answer is .