Algebraic Concepts

ISEE Lower Level Quantitative Reasoning · Learn by Concept

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ISEE Lower Level Quantitative Reasoning › Algebraic Concepts

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1

What is the value of in the equation below?

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CORRECT

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Explanation

To solve, you will need to divide both sides of the equation by 5.

The 5 cancels on the left side.

Divide to simplify.

2

If and , what is ?

CORRECT

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Explanation

Sometimes we use letters instead of numbers if we don't know what number ought to go in a certain place. Saying "" means that something plus eight equals fifteen, but we aren't yet certain what that "something" is. When we can, we solve the puzzle of what number that letter could be replaced with.

. , so must be replaced by .

. , so must be replaced by also.

We're looking for . To find this, we replace the letters with the numbers we found. and both equal , so .

, so . The correct answer is .

3

The toy panda weighs pounds less than the toy truck. The toy truck weighs pounds. Select the number sentence that gives the weight of the toy panda.

CORRECT

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Explanation

We are told that the toy panda weighs pounds less than the toy truck, which means we are going to subtract.

We are given that the toy truck weighs pounds, so we subtract from since the panda weighs pounds less than the toy truck.

is the correct number sentence.

4

If and , what is ?

CORRECT

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Explanation

Sometimes we use letters instead of numbers if we don't know what number ought to go in a certain place. Saying "" means that something plus eight equals fifteen, but we aren't yet certain what that "something" is. When we can, we solve the puzzle of what number that letter could be replaced with.

. , so must be replaced by .

. , so must be replaced by also.

We're looking for . To find this, we replace the letters with the numbers we found. and both equal , so .

, so . The correct answer is .

5

What is the value of in the equation below?

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CORRECT

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Explanation

To solve, you will need to divide both sides of the equation by 5.

The 5 cancels on the left side.

Divide to simplify.

6

If , which of the following number sentences are true?

CORRECT

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Explanation

Replace the variable with . Then solve using order of operation (PEMDAS).

7

If , which of the following number sentences are true?

CORRECT

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Explanation

Replace the variable with . Then solve using order of operation (PEMDAS).

8

Five more than a number is equal to of twenty-five . What is the number?

CORRECT

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Explanation

From the question, we know that plus a number equals of . In order to find out what of is, multiply by .

, or .

The number we are looking for needs to be five less than , or .

You can also solve this algebraically by setting up this equation and solving:

Subtract from both sides of the equation.

9

What is the value of given the expressions below?

CORRECT

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Explanation

In order to solve for the value of , the value of c and d must be solved for first.

Here, 1 must be added to each side of the equation.

Thus, is equal to .

10

Solve for n.

CORRECT

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Explanation

To solve this equation multiply both sides by