How to divide variables - ISEE Middle Level Math

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

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.

To simplify, we want to get the same base in both the numerator and the denominator. This will allow us to easily manipulate the exponents.

We can write:

and

Replace the fraction with these values and simplify.

To simplify, we want to get the same base in both the numerator and the denominator. This will allow us to easily manipulate the exponents.

Replace the denominator with this value and simplify.

A trick to find multiples of 9 is that when the sum of the digits in a number is divisible by 9, then the full number is also divisible by 9.

When the digits of 963 are added together, the sum is 18.

18 is divisible by 9, and so the number 963 must also be divisible by 9.

Check your work:

If Jack and Jenny paint the vases together, they will paint 5 vases per hour since Jack's rate of painting is 3 vases per hour, while Jenny's rate is 2 vases per hour.

If there are 30 vases to paint, and they paint 5 vases per hour, it will take 6 hours to paint all the vases because 30 divided by 5 is 6.

Factors are multiplied together to reach a specific target number. When you divide a target number by one of its factors, the result is always a whole number.

In this case, we can evaluate the numbers that can be multiplied to get 56.

12 is not a factor of 56. When you divide 56 by 12, the answer is not a whole number.

The number 756 can be segmented into 700 and 56. Given that 700 is divisble by 7 (700 divided by 7 is 100) and that 56 is divisible by 7 (56 divided by 7 is 8), 756, as the aggregate of 700 and 56, is also divisble by 7.

The mathematical translation of the square root of 64 divided by the square of 2 is:

A quick trick to remember is that a number is divisible by 3 when the digits of that number add up to a sum that is also divisible by 3.

For example, we know that the number 85,962 must be divisible by 3 because:

30 is divisible by 3; therefore, 85,962 must also be divisible by 3.

In contrast, adding the digits of the other answer choices will give numbers that are not divisible by 3, indicating that the other answer choices are also not divisible by 3.

When 130 is divided by 13, the result is the whole number, 10.

130 is the only answer option that results in a whole number when divided by 13, making it the correct answer.

Given that Jeff has 2 bags, each containing 24 chips, he has a total of 48 chips because 2 times 24 is equal to 48.

There are four total people sharing the chips (Jeff + three friends). We divide the total number of chips by 4 to get our answer.

Given that 36 is divisible by 6, it follows that 360 would be divisble by 60 (as both numbers are multiplied by 10). A multiple of 360, such as 3,600 would also be divisible by 60.

Given that none of the other answer choices listed are divisble by 60, the correct answer is 3,600.

Given that Gina can chop 2 carrots in a minute, and that Bob can chop 3 carrots in a minute, they will be able to chop 5 carrots in a minute if they work together.

If there are 60 carrots, it will take 12 minutes for them to chop up all the carrots, because 60 divided by 5 is 12.

Therefore, 12 is the correct answer.

When dividing by variables you must deal with the like variables first.

Since there are variables on the numerator and denominator, you would divide them together.

The constants will divide regularly and the variables will cancel out

.

The other variables are left alone so the final answer will just be

.

For this division problem, you must deal with the like terms.

You will divide the constants and then divide the variables.

and then

because when dividing exponents with common bases, you just subtract the exponents.

The variable remains unchanged and your answer is,

.

Simplify the following expression:

When we are dividing variables, we can simpligy by subtracting the exponent of the variable on bottom from the variable on the top.

So because t has an exponent of 4 on top and 2 on the bottom, the new exponent will be:

Do the same for our other two exponents (x and p) to get the following

Making our answer: