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ISEE Middle Level Math : Algebraic Concepts

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

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All ISEE Middle Level Math Resources

6 Diagnostic Tests 303 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #265 : How To Find The Solution To An Equation

What is the value of the expression $7-4+(5-3)^{2{}}-25\div5$ ?

Possible Answers:

Correct answer:

Explanation:

Below are the steps for solving the expression:

$7-4+(5-3)^{2{}}-25\div5$

First, parentheses are solved for.

$7-4+(2)^{2{}}-25\div5$

Next, we take the square of 2, and can also solve for 25 divided by 5.

7-4+4-5

The -4 and +4 cancel each other out, leaving

7-5

This reduces to 2, the correct answer.

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Example Question #2 : How To Solve One Step Equations

Alegra is taking a cooking class with friends. It is 40 dollars for every two people who participate because people are supposed to work in pairs. But if someone does not have a partner, that person can still participate but must pay $30 for him or herself. Alegra's four best friends participate in the class with her, and they divide the cost evenly. What is the total cost per person?

Possible Answers:

22 dollars

30 dollars

60 dollars

20 dollars

Correct answer:

22 dollars

Explanation:

Since Alegra is taking the class with 4 friends, that means there are a total of 5 people. This means that there are 2 pairs of friends, and one alone friend.

Below are the prices that will be charged based on this make up:

2 pairs of people at 40 dollars per pair = 80 dollars

1 solo person at 30 dollars per person = 30 dollars

80 dollars plus 30 dollars is 110 dollars, the grand total.

When 110 dollars is divided by 5, the answer is 22. Therefore, 22 dollars is the correct answer.

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Example Question #266 : How To Find The Solution To An Equation

Solve for .

$\frac{3x}{7}=\frac{4}{3}$

Possible Answers:

$\frac{27}{9}$

$\frac{3}{7}$

$\frac{9}{28}$

$\frac{28}{9}$

Correct answer:

$\frac{28}{9}$

Explanation:

$\frac{3x}{7}=\frac{4}{3}$

To solve, we will need to isolate . Begin by cross-multiplying:

$3x\times3=4\times7$

9x=28

Divide both sides by 9.

$x=\frac{28}{9}$

The fraction cannot be reduced, making it our final answer.

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Example Question #2 : How To Solve Two Step Equations

On average, 1 in 50 apples that grow in an orchard will not be harvested. Of those, half will rot on the ground. If 500 apples are growing in an orchard, how many will rot on the ground?

Possible Answers:

Correct answer:

Explanation:

If there are 500 apples and 1 in 50 will remain unharvested, then we can find the number of unharvested apples by multiplying.

$500\times \frac{1}{50}=10$

10 apples will remain unharvested. Of those, half will rot on the ground. Multiply to find how many apples rot on the ground.

$10\times\frac{1}{2}=5$

5 apples will rot on the ground.

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Example Question #267 : How To Find The Solution To An Equation

Solve for :

$3x=4(2+4^{2})-5$

Possible Answers:

$\frac{67}{3}$

None of these

$\frac{22}{3}$

Correct answer:

$\frac{67}{3}$

Explanation:

Start by evaluating the right side of the equation using order of operations.

$3x=4(2+4^{2})-5$

3x=4(2+16)-5

3x=4(18)-5

3x=72-5

3x=67

Divdie both side by 3 to solve for the variable.

$x=\frac{67}{3}$

The fraction acnnot be simplified.

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Example Question #457 : Algebra

Solve:

$6^{3}*2=$

Possible Answers:

432

423

324

234

Correct answer:

432

Explanation:

First perform the cubing:

$6^{3}=216$

Then multiply:

216*2=432

Answer: 432

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Example Question #461 : Algebra

Solve:

$7^{2}*19=$

Possible Answers:

931

391

139

Correct answer:

931

Explanation:

First complete the squaring:

$7^{2}=49$

Then multiply:

49*19=931

Answer: 931

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Example Question #462 : Algebra

Solve:

$2^{4}*20=$

Possible Answers:

320

323

110

230

Correct answer:

320

Explanation:

First look at any numbers that have exponents:

$2^{4}=16$

Then multiply:

16*20=320

Answer: 320

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Example Question #463 : Algebra

Solve:

$3^{3}*30=$

Possible Answers:

990

800

810

900

Correct answer:

810

Explanation:

First do the cubing:

$3^{3}=27$

Then multiply:

27*30=810

Answer: 810

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Example Question #464 : Algebra

$9^{2}*12=$

Possible Answers:

980

972

978

910

Correct answer:

972

Explanation:

First perform the squaring:

$9^{2}=81$

Then multiply:

81*12=972

Answer: 972

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All ISEE Middle Level Math Resources

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ISEE Middle Level Math : Algebraic Concepts

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

All ISEE Middle Level Math Resources

Example Questions

Example Question #265 : How To Find The Solution To An Equation

Example Question #2 : How To Solve One Step Equations

Example Question #266 : How To Find The Solution To An Equation

Example Question #2 : How To Solve Two Step Equations

Example Question #267 : How To Find The Solution To An Equation

Example Question #457 : Algebra

Example Question #461 : Algebra

Example Question #462 : Algebra

Example Question #463 : Algebra

Example Question #464 : Algebra

All ISEE Middle Level Math Resources

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