High School Math : High School Math

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #71 : High School Math

Combine like terms for the simplest form:

Possible Answers:

Correct answer:

Explanation:

First multiply according to order of operations to get 6xy, and then see if there are like terms to be combined. In this case, there are not so the simplest form is 

Example Question #71 : High School Math

All of the following numbers are prime EXCEPT:

Possible Answers:

401

347

421

349

427

Correct answer:

427

Explanation:

A number is prime if it is divisible by only itself and one. Thus, if a number is divisible by anything else, it can't be prime. Of the answer choices, only 427 isn't prime, because it is divisible by 7.

To figure out which number is prime, one strategy you could employ is using your calculator and dividing each choice by 3, 7, 9, 11, and 13. Because all of the answer choices are odd, we know none of them will be divisible by 2, 4, 6, 8, or 10. Also, none of them have a 0 or 5 in the ones place, so they can't be divisible by 5. Thus, the best numbers to try would be 3, 7, 9, 11, and 13. When you divide 427 by 7, you will get a whole number. For all the other answer choices, when you divide by 3, 7, 9, 11, and 13, you will never get a whole number.

The answer is 427.

Example Question #73 : High School Math

Simplify the following expression. 

Possible Answers:

Correct answer:

Explanation:

Recall that the product of a negative number and a positive number is a negative number. Thus, we know that our answer will be a negative number. We then consider the product of the numbers, ignoring the sign. We know that . Then, we have that our final answer is 

Example Question #74 : High School Math

Simplify: 

Possible Answers:

Correct answer:

Explanation:

We know that dividing a positive integer and a negative integer will give us a negative integer. We thus consider the numbers themselves, without the sign. 

Add a negative sign to find our answer is .

Example Question #75 : High School Math

Find the product of  and 

Possible Answers:

Correct answer:

Explanation:

The word product indicates multiplication. Thus, we remember that when we multiply a positive number by a negative number we get a negative number.

Example Question #71 : High School Math

Which of the following numbers is the greatest? 

Possible Answers:

Correct answer:

Explanation:

When comparing negative numbers, it is important to remember that the numbers with the larger absolute value (greatest numerical term) are actually more negative. Though it seems that  would be the largest number in this case, it is actually the smallest, as it is the farthest down the number line in the negative direction. The greatest number is the one with the smallest absolute value, which is .

Remember, also, that zero is greater than any negative number!

Example Question #72 : High School Math

Given that  is an odd integer, which of the following must produce an even integer?

Possible Answers:

Correct answer:

Explanation:

An easy way to solve this problem is to define  as 1, which is an odd integer. Plugging in 1 into each answer yields  as the correct answer, since 

4 is an even integer, which is what we are looking for.

Example Question #78 : High School Math

Which number is greater? 

 or 

Possible Answers:

They are equivalent.

It cannot be determined from the information provided.

Correct answer:

Explanation:

When comparing negative numbers, recall the number line. Numbers that are "more negative", or negative with a large absolute value, are really very small. Thus, comparing negative numbers can sometimes seem counterintuitive. In this case, since we are comparing two negative numbers, the number with the larger absolute value is actually the smaller number. Therefore, the greater number is .

Example Question #79 : High School Math

Which of  and  is larger? 

Possible Answers:

Neither

Correct answer:

Explanation:

Recall that when comparing negative numbers, those numbers that are "more negative" are actually further to the left on the number line and thus are smaller. Therefore, even though , we have that 

Therefore  is larger. 

Example Question #73 : High School Math

Place in order from smallest to largest:

Possible Answers:

Correct answer:

Explanation:

Find the least common denominator (LCD) and convert all fractions to the LCD.  Then order the numerators from the smallest to the largest

So the correct order from smallest to largest is

 

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