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High School Math : How to compare integers in pre-algebra

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Example Questions

Example Question #1 : How To Compare Integers In Pre Algebra

Which of the following numbers is the greatest?

Possible Answers:

$\displaystyle -8$

$\displaystyle -10$

-1.8 $\displaystyle -1.8$

$\displaystyle -5$

$\displaystyle -1$

Correct answer:

$\displaystyle -1$

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 $\displaystyle -10$ 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 $\displaystyle -1$.

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

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Example Question #1 : How To Compare Integers In Pre Algebra

Given that $\displaystyle s$ is an odd integer, which of the following must produce an even integer?

Possible Answers:

s/2 $\displaystyle s/2$

5s+4 $\displaystyle 5s+4$

s-2 $\displaystyle s-2$

$\displaystyle 4s$

s+2 $\displaystyle s+2$

Correct answer:

$\displaystyle 4s$

Explanation:

An easy way to solve this problem is to define $\displaystyle s$ as 1, which is an odd integer. Plugging in 1 into each answer yields $\displaystyle 4s$ as the correct answer, since $\displaystyle 4(1) = 4.$

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

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Example Question #2 : How To Compare Integers In Pre Algebra

Which number is greater?

$\displaystyle -6$ or $\displaystyle -8$

Possible Answers:

$\displaystyle -6$

It cannot be determined from the information provided.

They are equivalent.

$\displaystyle -8$

Correct answer:

$\displaystyle -6$

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 $\displaystyle -6$.

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Example Question #3 : How To Compare Integers In Pre Algebra

Which of $\displaystyle -2$ and $\displaystyle -8$ is larger?

Possible Answers:

Neither

$\displaystyle -2$

$\displaystyle -8$

Correct answer:

$\displaystyle -2$

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 8 > 2 $\displaystyle 8 > 2$, we have that -8 < -2 $\displaystyle -8 < -2$.

Therefore $\displaystyle -2$ is larger.

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Example Question #5 : How To Compare Integers In Pre Algebra

Place in order from smallest to largest:

$\frac{1}{5},\; \frac{1}{8},\; \frac{3}{10},\; \frac{3}{4},\; \frac{1}{2}$ $\displaystyle \frac{1}{5},\; \frac{1}{8},\; \frac{3}{10},\; \frac{3}{4},\; \frac{1}{2}$

Possible Answers:

$\frac{1}{5},\; \frac{1}{8},\; \frac{1}{2},\; \frac{3}{10},\; \frac{3}{4}$ $\displaystyle \frac{1}{5},\; \frac{1}{8},\; \frac{1}{2},\; \frac{3}{10},\; \frac{3}{4}$

$\frac{3}{10},\; \frac{1}{5},\; \frac{1}{8},\; \frac{3}{4},\; \frac{1}{2}$ $\displaystyle \frac{3}{10},\; \frac{1}{5},\; \frac{1}{8},\; \frac{3}{4},\; \frac{1}{2}$

$\frac{1}{8},\; \frac{1}{5},\; \frac{3}{10},\; \frac{1}{2},\; \frac{3}{4}$ $\displaystyle \frac{1}{8},\; \frac{1}{5},\; \frac{3}{10},\; \frac{1}{2},\; \frac{3}{4}$

$\frac{3}{4},\; \frac{1}{8},\; \frac{1}{2},\; \frac{1}{5},\; \frac{3}{10}$ $\displaystyle \frac{3}{4},\; \frac{1}{8},\; \frac{1}{2},\; \frac{1}{5},\; \frac{3}{10}$

$\frac{1}{2},\; \frac{3}{4},\; \frac{1}{5},\; \frac{1}{8},\; \frac{3}{10}$ $\displaystyle \frac{1}{2},\; \frac{3}{4},\; \frac{1}{5},\; \frac{1}{8},\; \frac{3}{10}$

Correct answer:

$\frac{1}{8},\; \frac{1}{5},\; \frac{3}{10},\; \frac{1}{2},\; \frac{3}{4}$ $\displaystyle \frac{1}{8},\; \frac{1}{5},\; \frac{3}{10},\; \frac{1}{2},\; \frac{3}{4}$

Explanation:

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

$\frac{1}{5}=\frac{8}{40}$ $\displaystyle \frac{1}{5}=\frac{8}{40}$

$\frac{1}{8}=\frac{5}{40}$ $\displaystyle \frac{1}{8}=\frac{5}{40}$

$\frac{3}{10}=\frac{12}{40}$ $\displaystyle \frac{3}{10}=\frac{12}{40}$

$\frac{3}{4}=\frac{30}{40}$ $\displaystyle \frac{3}{4}=\frac{30}{40}$

$\frac{1}{2}=\frac{20}{40}$ $\displaystyle \frac{1}{2}=\frac{20}{40}$

So the correct order from smallest to largest is

$\frac{1}{8},\; \frac{1}{5},\; \frac{3}{10},\; \frac{1}{2},\; \frac{3}{4}$ $\displaystyle \frac{1}{8},\; \frac{1}{5},\; \frac{3}{10},\; \frac{1}{2},\; \frac{3}{4}$

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High School Math : How to compare integers in pre-algebra

Study concepts, example questions & explanations for High School Math

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Example Questions

Example Question #1 : How To Compare Integers In Pre Algebra

Example Question #1 : How To Compare Integers In Pre Algebra

Example Question #2 : How To Compare Integers In Pre Algebra

Example Question #3 : How To Compare Integers In Pre Algebra

Example Question #5 : How To Compare Integers In Pre Algebra

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