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ISEE Middle Level Math : Algebraic Concepts

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Example Questions

Example Question #91 : Algebraic Concepts

Gina can chop 2 carrots in a minute. Bob can chop 3 carrots in a minute. How long (in minutes) will it take them to chop 60 carrots, if they work together?

Possible Answers:

$\frac{1}{5}$

Correct answer:

Explanation:

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.

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Example Question #92 : Algebraic Concepts

Which of the following numbers is divisible by 60?

Possible Answers:

3,606

3,500

3,700

3,600

Correct answer:

3,600

Explanation:

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.

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Example Question #93 : Algebraic Concepts

Simplify the following expression:

$\frac{6x5y2z}{3x}$

Possible Answers:

The expression is already reduced.

$\frac{2*5yz}{x}$

20yz

10y

2x5y2z

Correct answer:

20yz

Explanation:

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

$\frac{6x}{3x}=2$ .

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

2*5y*2z=20yz .

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Example Question #94 : Variables

Simplify the following expression:

$\frac{t^4x^5p^{26}}{t^2x^4p^{20}}$

Possible Answers:

t^2xp^6

$t^2x^{10}p^6$

$\frac{1}{t^2xp^6}$

tx^3p^6

Correct answer:

t^2xp^6

Explanation:

Simplify the following expression:

$\frac{t^4x^5p^{26}}{t^2x^4p^{20}}$

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:

$t^4-t^2=t^{4-2}=t^2$

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

$\frac{t^4x^5p^{26}}{t^2x^4p^{20}}=t^2xp^6$

Making our answer:

t^2xp^6

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Example Question #95 : Variables

Reduce the expression:

$\frac{4x^{3}y^{2}}{2x}$

Possible Answers:

$2x^{2}y^{2}$

$2y^{2}$

Cannot be reduced

$y^{5}$

Correct answer:

$2x^{2}y^{2}$

Explanation:

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

You will divide the constants and then divide the variables.

$4\div2=2$

and then

$x^{3}\div x=x^{2}$

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

The variable remains unchanged and your answer is,

$2x^{2}y^{2}$ .

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Example Question #94 : Algebraic Concepts

$7^{4} \div (18-11) =$

Possible Answers:

343

Correct answer:

343

Explanation:

To solve

$7^{4} \div (18-11) =$

First, use the order of operations.

$7^{4} \div 7 =$

When dividing with variables and the coefficients are the same, subtract the exponents.

$7^{4} \div 7^{1} = 7^{4-1}$

$7^{4-1} = 7^{3}$ $7^{3} = 7\times 7\times 7 = 343$

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Example Question #95 : Algebraic Concepts

$\frac{x^{8}}{x^{2}}$

Possible Answers:

$x^{10}$

$x^{4}$

$x^{6}$

$x^{\frac{1}{4}}$

Correct answer:

$x^{6}$

Explanation:

To solve, subtract the exponents

$\frac{x^{8}}{x^{2}} = x^{8-2}$

$x^{6}$

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Example Question #96 : Algebraic Concepts

$\frac{n^{3}}{n^{6}}$

Possible Answers:

$n^{\frac{1}{2}}$

$n^{9}$

$\frac{1}{n^{3}}$

$n^{3}$

Correct answer:

$\frac{1}{n^{3}}$

Explanation:

To solve $\frac{n^{3}}{n^{6}}$ subtract the exponents

$n^{3-6} = n^{-3}$

$n^{-3} = n\div -3 =$

$\frac{1}{n^{3}}$

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Example Question #97 : Algebraic Concepts

The area (A) of a rectangle is $36ab^{3}$ square units. The length is 6ab units. What is the width of this rectangle?

Possible Answers:

$6b^{2$ units

$216ab^{2}$ units

$6a^{2}b^{2}$ units

$216a^{2}b^{4}$ units

Correct answer:

$6b^{2$ units

Explanation:

The formula for the Area of a rectangle is:

A - length x width

Is this problem, you are given the amount of total area or A, which is $36ab^{3}$ square units, and you are given the measurement of the length, which is 6ab . In order to solve for the measurement of the width, divide. When dividing, exponents are subtracted.

$36\div6 =6$

$\frac{a^{1}}{a^{1}} = a^{1-1} = a^{0} = 1$

$\frac{b^{3}}{b^{1}} = b^{3-1} = b^{2}$

$6 (1) \times b^{2} = 6b^{2}$ units

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Example Question #98 : Algebraic Concepts

$\frac{9x^{4}y^{6}}{3x^{2}y^{2}} =$

Possible Answers:

$6x^{2}y^{4}$ $3x^{2}y^{3}$

$3x^{2}y^{4}$

$6x^{8}y^{12}$

Correct answer:

$3x^{2}y^{4}$

Explanation:

To solve $\frac{9x^{4}y^{6}}{3x^{2}y^{2}}$ separate each part of the terms and divide. When dividing variables with exponents, subtract the exponents.

$9\div 3 = 3$

$\frac{x^{4}}{x^{2}}=x^{4-2} =x^{2}$

$\frac{y^{6}}{y^{2}}=y^{6-2} =y^{4}$

$3x^{2}y^{4}$

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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 #91 : Algebraic Concepts

Example Question #92 : Algebraic Concepts

Example Question #93 : Algebraic Concepts

Example Question #94 : Variables

Example Question #95 : Variables

Example Question #94 : Algebraic Concepts

Example Question #95 : Algebraic Concepts

Example Question #96 : Algebraic Concepts

Example Question #97 : Algebraic Concepts

Example Question #98 : Algebraic Concepts

All ISEE Middle Level Math Resources

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