How to simplify expressions - HSPT Math

"The product of nine and a number" is . "Twice the number" is , and "The sum of six and twice the number" is .

"The product...added to the sum..." is ; simplify to get

First find the exponent value:

Then find the value of

Finally, solve the entire expression with the known values:

The answer is 36.

First convert each mixed number into and improper fraction

Then convert the operation to multiplication and flip the second fraction

Reduce where possible and multiply to solve:

The answer is

Use the distributive property:

When solving this problem we need to remember our order of operations, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable to a number, so we move to the next step.

Multiplication: We can distribute (or multiply) the .

Addition/Subtraction: Remember, we can't add a variable to a number, so the is left alone.

In order to add variables the terms must be like. In order for terms to be like, the variables must be exactly alike also being raised to the same power by the exponent.

In this case the like terms are and . Just because there is a 1 in the exponent for the first term doesnt mean it is different from the second term. With exponents if a variable does not show an exponent, that means it is still to the first power.

We add the coefficients of the like terms. The coefficient is the number in front of the first variable, in this case it is 1 for both terms because of the identity property of multiplication stating any variable, term, or number multiplied by 1 is itself.

Our last term is not like because the variable is raised to a different power than the other two. In this case we do not combine it to the like terms, we just add it to the end of the term.

When solving this problem we need to remember our order of operations, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable to a number, so we move to the next step.

Multiplication: We can distribute (or multiply) the .

Addition/Subtraction: Remember, we can't add a variable to a number, so the is left alone.

Now we have

This problem looks strange since it mostly contains variables, in particular unknown variables. Still remember the order of operations: parentheses, exponents, multiplication, division, addition, and subtraction. We still use those operations in this case. All we must do is move the variables around to solve for .

In this case we can subtract (additive inverse) to the other side first.

Rewrite our problem.

Stop for a moment and look at the progress. Go back to the original question, solve for . Our problem shows about to be multiplied to , but we do not necessarily have to multiply because we can divide by to both sides of the equation, which would save us a step as well as have B by itself.

Multiply the numbers and multiply the variables:

Answer:

Add the numbers and keep the variable:

Answer:

Multiply the numbers and multiply the variables:

Answer:

Subtract the numbers and keep the variable:

Answer:

Add the numbers and keep the variable:

Answer: