ISEE Middle Level Math : Algebraic Concepts

Study concepts, example questions & explanations for ISEE Middle Level Math

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Example Questions

Example Question #475 : Algebra

 

Possible Answers:

Correct answer:

Explanation:

When 10 has an exponent, simply add the appropriate number of zeroes:

Then multiply:

Answer: 

 

Example Question #286 : How To Find The Solution To An Equation

What is the value of y in the equation

 

 ?

Possible Answers:

Correct answer:

Explanation:

The first step in solving this problem is to add together the numbers in parentheses:

Next, add 40 to both sides of the equation. 

Finally, subtract y from each side to get the answer. 

Example Question #286 : How To Find The Solution To An Equation

What is the value of  in the equation below?

Possible Answers:

Correct answer:

Explanation:

The first step is to combine the numbers in the equation that can be added together.

Next subtract  from each side to isolate the

Now divide each side by 3

Example Question #476 : Algebra

Solve:

Possible Answers:

Correct answer:

Explanation:

To solve, divide each side by 11:

Answer: 

Example Question #491 : Algebraic Concepts

Which of the following phrases can be written as the algebraic expression  ?

Possible Answers:

The correct answer is not given among the other responses

Three times the difference of fifty and a number

Three times a number subtracted from fifty

The cube of the difference of fifty and a number

The cube of a number subtracted from fifty

Correct answer:

The cube of a number subtracted from fifty

Explanation:

 is  subtracted from fifty;  is the cube of a number. Therefore,  is "the cube of a number subtracted from fifty."

Example Question #121 : Hspt Mathematics

Billy is at the store purchasing flowers for his mother, his grandmother, and his friend. He finds roses on sale by the half dozen (6), tulips selling by the dozen (12), and daisies selling groups of 18. 

Billy wants to have the same number of flowers in each bouquet, so that he is able to give everyone the same number of each flower. How many bundles of roses, tulips, and daisies will he have to buy so he has the same amount of each? (Please answer by roses, tulips, then daisies.)

Possible Answers:

Correct answer:

Explanation:

This is a least common multiple problem because we want to have the same number of each flower; meaning if I have 10 roses in each bouquet I should have 10 tulips and 10 daisies as well. In order to solve this problem we should break down the story problem. Let's look at the numbers we are having to work with: 6, 12, 18. 

To do least common multiple we must look at the prime factors of each number and we can list them out. A factor is simply a number multiplied by a number to give us a product. A prime number is a number that contains only two factors, one of them being 1 and the other its own number.

So lets list the prime factors of 6, 12, and 18

 (2 and 3 are both prime numbers, and factors of 6)

 (2 x 2 = 4. 4x3=12 We have to say 2 x 2 because 4 is not a prime number). 

Now we have the prime factors listed out for each of our numbers. Next is a fun trick. We must choose which number contains the most of each prime factor. In this case which number contains the most 2's? (12; because 12 has two 2 prime factors). Which number contains the most 3's? (18; because 18 has two 3 prime factors). 

Our next step is to multiply the most of our prime factors so in this case:

36 is our least common multiple. So now what do you think we can do with this number? Well the 36 means that is the lowest number of flowers we need of each type in order to have an equal amount of each for the boquets. 

Knowing this, if we need 36 roses, and we are able to buy 6 roses per bundle. We need 6 bundles of roses, because 36 divided by 6 is 6. If we get 12 tulips by the bundle, we take 36 divided by 12 to give us 3 bundles of tulips needed. Lastly we can buy 18 daisies per bundle, 36 divided by 18 gives us 2 bundles needed giving us our answers 6, 3, 2 (bundles of roses, tulips, and daisies). 

Example Question #492 : Algebraic Concepts

Which of the following statements demonstrates the commutative property of multiplication?

Possible Answers:

None of the examples in the other responses demonstrates the commutative property of multiplication.

Correct answer:

Explanation:

The commutative property of multiplication states that two numbers can be multiplied in either order to obtain the same product. Of the given responses, only

demonstrates this property, so it is the correct choice.

Example Question #292 : Equations

Which of the following statements demonstrates the associative property of multiplication?

Possible Answers:

None of the examples in the other responses demonstrates the associative property of multiplication.

Correct answer:

Explanation:

The associative property of multiplication states that to multiply three numbers, any two can be multiplied first, followed by multiplying the product by the third. Of the statements given, only 

demonstrates this property, so it is the correct choice.

Example Question #293 : Equations

Which of the following statements demonstrates the inverse property of addition? 

Possible Answers:

None of the examples in the other responses demonstrates the inverse property of addition.

Correct answer:

Explanation:

The inverse property of addition states that for every real number, a number exists, called the additive inverse, such that the number and its inverse have sum 0. Of the statements given, only 

demonstrates this property, so it is the correct choice.

Example Question #495 : Algebraic Concepts

Which of the following statements demonstrates the associative property of addition?

Possible Answers:

None of the examples in the other responses demonstrates the associative property of addition.

Correct answer:

Explanation:

The associative property of addition states that to add three numbers, any two can be added first, followed by adding the sum to the third. Of the statements given, only 

demonstrates this property, so it is the correct choice.

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