ISEE Upper Level Math : How to multiply variables

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

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Example Questions

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Example Question #1 : How To Multiply Variables

Machine A can produce 4 buttons in 2 days.  Machine B can produce 20 buttons in 4 days.  How many buttons can Machine A and B, working together, produce in 40 days?

Possible Answers:

\dpi{100} 7

\dpi{100} 280

\dpi{100} 70

\dpi{100} 200

Correct answer:

\dpi{100} 280

Explanation:

First determine how many buttons each machine can produce in a day.

Machine A: \dpi{100} \frac{4}{2}=2\ buttons\ per\ day

Machine B: \dpi{100} \frac{20}{4}=5\ buttons\ per\ day

Machine A and B can produce 7 buttons per day when they are working together.

\dpi{100} 7\times 40=280\ buttons

Example Question #2 : How To Multiply Variables

Brian has 3 siblings.  When his family orders pizza, each of the 4 children is given \dpi{100} \frac{1}{4} of the pizza.  Brian does not feel well so he only finishes \dpi{100} \frac{1}{3} of his pizza.  If the original pizza consisted of 12 slices of pizza, how many slices did Brian eat?

Possible Answers:

\dpi{100} 3

\dpi{100} 1

\dpi{100} 6

\dpi{100} 4

Correct answer:

\dpi{100} 1

Explanation:

Brian eats \dpi{100} \frac{1}{3}\times \frac{1}{4}\times 12\ slices\ of\ pizza.

So Brian eats

\dpi{100} \frac{1}{12}\cdot 12=1\ slice\ of\ pizza.

Example Question #3 : How To Multiply Variables

Solve for \dpi{100} x:

\dpi{100} 4x^{2}=256

Possible Answers:

\dpi{100} \pm 2

\dpi{100} 4

\dpi{100} \pm 8

\dpi{100} \pm 4

Correct answer:

\dpi{100} \pm 8

Explanation:

\dpi{100} 4x^{2}=256

\dpi{100} \frac{4x^{2}}{4}=\frac{256}{4}

\dpi{100} x^{2}=64

\dpi{100} \sqrt{x^{2}}=\sqrt{64}

\dpi{100} x=\pm 8

Example Question #4 : How To Multiply Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

This can be solved using the pattern for the square of a sum:

Example Question #5 : How To Multiply Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

This can be solved using the pattern for the square of a difference:

Example Question #6 : How To Multiply Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

This can be solved using the pattern for the square of a sum:

Example Question #7 : How To Multiply Variables

Multiply:

Possible Answers:

Correct answer:

Explanation:

Example Question #8 : How To Multiply Variables

Multiply:

Possible Answers:

Correct answer:

Explanation:

Use the FOIL method:

Example Question #9 : How To Multiply Variables

Define 

What is  ?

Possible Answers:

Correct answer:

Explanation:

Substitute  for :

Example Question #10 : How To Multiply Variables

Simplify:

Possible Answers:

Correct answer:

Explanation:

First, recognize that raising the fraction to a negative power is the same as raising the inverted fraction to a positive power.

Apply the exponent within the parentheses and simplify. Remember that fractional exponents can be written as roots.

Simplify by taking the roots and canceling common factors.

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