ISEE Middle Level Math : Operations

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

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Example Questions

Example Question #121 : Variables

Suppose you know the values of all variables in the expression 

\displaystyle t - w \cdot k + n

and you want to evaluate the expression.

In which order will you carry out the operations?

Possible Answers:

Subtracting, adding, multiplying

Subtracting, multiplying, adding

Multiplying, adding, subtracting

Multiplying, subtracting, adding

Adding, subtracting, multiplying

Correct answer:

Multiplying, subtracting, adding

Explanation:

By the order of operations, in the absence of grouping symbols, multiplication takes precedence over addition and subtraction. Addition and subtraction are then carried out with equal priority, but from left to right, so the subtraction is performed second and the addition last.

Example Question #93 : Variables

Which of the following phrases can be written as the algebraic expression \displaystyle 7 + x ^{2} ?

Possible Answers:

The square of a number added to seven

Twice a number added to seven

Twice the sum of seven and a number

The square of the product of seven and a number

The square of the sum of seven and a number

Correct answer:

The square of a number added to seven

Explanation:

\displaystyle 7 + x^{2} is \displaystyle x^{2} added to seven; \displaystyle x^{2} is the square of a number.

\displaystyle 7 + x^{2} is subsequently "the square of a number added to seven".

Example Question #21 : How To Subtract Variables

Solve.

\displaystyle 0.4 +\frac{5}{10}-4.67

Possible Answers:

None of these

\displaystyle 4.07

\displaystyle -4.07

\displaystyle 4.67

\displaystyle -4.61

Correct answer:

\displaystyle -4.07

Explanation:

The first step to solving is to convert all the numbers to a common form. We will convert to decimals, since this form is used in the answer choices. 

\displaystyle \frac{5}{10}=5\div10=0.20

Plug this value into the original equation and solve.

\displaystyle 0.4 +0.2-4.67

\displaystyle 0.6-4.67

\displaystyle -4.07

Our final answer is \displaystyle -4.07.

Example Question #96 : Variables

If \displaystyle R is an odd number, which of the following must also be odd?

Possible Answers:

\displaystyle 4R-8

\displaystyle R+3

\displaystyle R+1

\displaystyle R-4

\displaystyle 6R

Correct answer:

\displaystyle R-4

Explanation:

The easiest way to solve this problem is to pick an odd number (we can use 3 for example), and plug it into each answer choice. 

The only answer choice that gives us an odd result is:

\displaystyle R-4

\displaystyle 3-4=-1

As a rule of thumb, an even number subtracted from an odd number will always result in an odd number.

Example Question #21 : How To Subtract Variables

Philip had a glass containing 16 ounces of water. He drank 2 ounces. His brother then drank half of what remained. How many ounces of water are now in the glass?

Possible Answers:

\displaystyle 8

\displaystyle 7

\displaystyle 2

\displaystyle 6

\displaystyle 5

Correct answer:

\displaystyle 7

Explanation:

If there were 16 ounces of water to start, this amount decreased to 14 ounces when Philip drank 2 ounces. 

\displaystyle 16-2=14

With 14 ounces remaining, his brother drank half. This would be equal to 7 ounces.

\displaystyle 14\div2=7

This left the other half of the water, which was also 7 ounces; thus, 7 ounces in the amount of water that remained.

Example Question #98 : Variables

If \displaystyle 17 minus two times another number equals \displaystyle 3, what is the other number?

Possible Answers:

\displaystyle 14

\displaystyle 10

\displaystyle 12

\displaystyle 7

Correct answer:

\displaystyle 7

Explanation:

The first step is to transfer \displaystyle 17 minus two times another number equals \displaystyle 3 into mathematical terms. Doing so gives us:

\displaystyle 17-2x=3

Next, 17 is subtracted from each side. 

\displaystyle -2x=-14

Each side is now divided by \displaystyle -2

\displaystyle x=7

Therefore, \displaystyle 7 is the correct answer. 

Example Question #101 : Operations

Jim and Jack are having tea together. There are 10 sugar cubes on a small tray. Jim takes 1 cube for his tea, and Jack takes twice as many cubes as Jim. How many sugar cubes remain?

Possible Answers:

\displaystyle 8

\displaystyle 3

\displaystyle 7

\displaystyle 6

Correct answer:

\displaystyle 7

Explanation:

The first step is to convert the following into a mathematical equation:

There are 10 sugar cubes on a small tray. Jim takes 1 cube for his tea, and Jack takes twice as many cubes as Jim.

The equation for the remaining cubes would be:

\displaystyle 10-1-2*1=7

Therefore, 7 is the correct answer. 

Example Question #102 : Operations

There are 9 cats in a shelter. Bob adopts 2 of the cats. Anita then adopts more cats than Bob adopted, but fewer than the majority of the cats remaining. How many cats did Anita adopt?

Possible Answers:

\displaystyle 3

\displaystyle 5

\displaystyle 2

\displaystyle 4

Correct answer:

\displaystyle 3

Explanation:

If Anita adopted more cats than Bob, then she adopted more than 2 cats. 

Given that Bob adopted 2 cats, there are 7 cats remaining. A majority of the remaining cats would be 4. 

Given that Anita adopted more than 2 cats, but less than 4, she must have adopted 3 cats; therefore, 3 is the correct answer. 

Example Question #103 : Operations

Tom has 8 pretzel sticks. He gives one stick to his sister, and then breaks what remains in half. Tom eats 5 of the half-pretzel sticks. How many half-pretzel sticks remain?

Possible Answers:

\displaystyle 7

\displaystyle 9

\displaystyle 10

\displaystyle 8

Correct answer:

\displaystyle 9

Explanation:

If Tom has 8 pretzel sticks and gives one stick to his sister, then he will have 7 pretzel sticks remaining. If he then breaks what remains in half, he will have 14 half-pretzel sticks. If Tom eats 5 of the half-pretzel sticks, 9 half-pretzel sticks will therefore remain. 

Example Question #1302 : Hspt Mathematics

\displaystyle 14s - 3s=

Possible Answers:

\displaystyle 21s

\displaystyle 17s

\displaystyle 11s

\displaystyle 42s

Correct answer:

\displaystyle 11s

Explanation:

Subtract the numbers and keep the variable:

\displaystyle 14s-3s=11s

Answer: \displaystyle 11s

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