SSAT Middle Level

Comparing & Ordering

Q: How do I remember which way the greater than/less than sign goes?

The alligator mouth always eats the bigger number! `0.8 > 0.5` means the hungry alligator wants the `0.8`.

Comparing fractions, decimals, and percents on a number line

Generate Unlimited Practice Questions

Learn This Topic

Have you ever tried to compare different things, like whether a slice of pizza is better than a scoop of ice cream? It’s tough because they are so different! 🍕🍦 On the SSAT, comparing fractions, decimals, and percents can feel just as tricky. Imagine a test question asks: which is bigger, $\frac{3}{4}$ , $0.80$ , or $75%$ ? To solve this, you need a secret translator ring!

The best trick for comparing and ordering these numbers is to turn them all into the same language. Usually, turning everything into decimals makes comparing them as easy as counting money! Think of decimals as dollars and cents. For example, $0.75$ is just 75 cents. What about $75%$ ? Percents are out of 100, so that's exactly 75 cents too! And $\frac{3}{4}$ of a dollar is... you guessed it, 3 quarters, which is 75 cents! 💰

If a tricky SSAT question throws a fraction like $\frac{4}{5}$ at you, just translate it. Since $\frac{1}{5}$ is 20 cents, $\frac{4}{5}$ is 80 cents, or $0.80$ . Suddenly, it's super easy to see that $0.80$ is bigger than $0.75$ . By turning everything into "money" (decimals), you can line them up on a number line without breaking a sweat. You've got this! 🚀

Key Formula

To compare different forms, convert them all to decimals! For fractions, divide the top by the bottom:

\frac{a}{b} = a \div b

. For percents, divide by 100:

x % = \frac{x}{100}

Practice Questions

4 practice questions for SSAT Middle Level

Q1 Medium

5,_32

The _ in the number above represents a digit from 0 through 9. If the number is less than 5,510, what is the greatest possible value for _?

A 3

B 4

C 5

D 6

E 9

Show Solution

To find the greatest possible value for the missing digit, test the choices starting from the greatest to the least, or evaluate the place value. The number 5,_32 must be less than 5,510. If the missing hundreds digit is 5, the number becomes 5,532, which is greater than 5,510. If the missing digit is 4, the number becomes 5,432, which is less than 5,510. Therefore, 4 is the greatest possible value for the missing digit.

Answer: B

Q2 Medium

Which of the following fractions has the greatest value?

\frac{5}{8}

\frac{2}{3}

\frac{7}{12}

\frac{3}{5}

\frac{11}{15}

Show Solution

To compare the fractions, you can convert them to decimals or find a common denominator. Converting to decimals:

$\frac{5}{8} = 0.625$
$\frac{2}{3} \approx 0.667$
$\frac{7}{12} \approx 0.583$
$\frac{3}{5} = 0.60$
$\frac{11}{15} \approx 0.733$
Comparing the decimal values, 0.733 is the largest, meaning $\frac{11}{15}$ has the greatest value.

Answer: E

Q3 Medium

45%, 0.48,

\frac{1}{2}

\frac{2}{5}

, 0.52

Which of the following expresses the list above in order from least to greatest?

\frac{2}{5}

, 45%, 0.48,

\frac{1}{2}

, 0.52

\frac{2}{5}

, 0.48, 45%,

\frac{1}{2}

, 0.52

C 45%,

\frac{2}{5}

, 0.48, 0.52,

\frac{1}{2}

\frac{1}{2}

, 0.52, 0.48, 45%,

\frac{2}{5}

E 45%,

\frac{2}{5}

\frac{1}{2}

, 0.48, 0.52

Show Solution

To order the list, convert all the numbers to decimals:

45% = 0.45
0.48 = 0.48
$\frac{1}{2}$ = 0.50
$\frac{2}{5}$ = 0.40
0.52 = 0.52
Now, arrange the decimals from least to greatest: 0.40, 0.45, 0.48, 0.50, 0.52. Finally, substitute the original values back into this order: $\frac{2}{5}$ , 45%, 0.48, $\frac{1}{2}$ , 0.52.

Answer: A

Q4 Medium

Five friends are reading the same book for a class assignment. Alice has read

\frac{2}{3}

of the book, Ben has read 65%, Carlos has read 0.68, Diana has read

\frac{5}{8}

, and Evan has read

\frac{7}{10}

. Which friend has read the LEAST portion of the book?

A Alice

B Ben

C Carlos

D Diana

E Evan

Show Solution

Convert the portion each friend has read into a decimal to easily compare them:

Alice: $\frac{2}{3} \approx 0.667$
Ben: 65% = 0.65
Carlos: 0.68
Diana: $\frac{5}{8} = 0.625$
Evan: $\frac{7}{10} = 0.70$
Comparing the decimal values, 0.625 is the smallest number. Therefore, Diana has read the least portion of the book.

Answer: D

Tips & Strategies

Memorize common fraction-to-decimal conversions! Knowing $\frac{1}{3} \approx 0.33$ , $\frac{1}{4} = 0.25$ , and $\frac{1}{5} = 0.20$ saves tons of time on the SSAT.
When comparing decimals, add zeros to the end so they all have the same number of digits. Comparing $0.7$ and $0.68$ is much easier if you write it as $0.70$ vs $0.68$ .
Use benchmark fractions! If you know $\frac{1}{2}$ is $0.50$ , you can quickly tell that $\frac{4}{9}$ is less than $0.50$ (since half of 9 is 4.5), and $\frac{5}{8}$ is more than $0.50$ .

Common Mistakes

Watch out for negative numbers! $- \frac{1}{2}$ is actually GREATER than $- 0.8$ . Think of it like owing money: owing 50 cents is better than owing 80 cents!
Don't compare denominators without looking at numerators. Just because 8 is bigger than 3 doesn't mean $\frac{1}{8}$ is bigger than $\frac{1}{3}$ (a slice of an 8-slice pizza is much smaller!).

Frequently Asked Questions

Do I always have to convert to decimals?

Nope! Sometimes finding a common denominator for all the fractions is faster, especially if the numbers are small like 2, 3, and 4.

How do I remember which way the greater than/less than sign goes?

The alligator mouth always eats the bigger number! $0.8 > 0.5$ means the hungry alligator wants the $0.8$ .

What if I forget how to turn a fraction into a decimal during the test?

Just treat the fraction bar like a division symbol. Divide the top number by the bottom number using long division.

Will I get scratch paper on the SSAT to do my long division?

You can write directly in your test booklet! Use the blank space around the questions to do your long division or line up your decimals.

Generate Unlimited Practice Questions

Learn This Topic

Practice Questions

Tips & Strategies

Common Mistakes

Frequently Asked Questions

Related Topics

More Fractions, Decimals, Ratios & Percents

Other Levels

Browse

Generate Unlimited Practice Questions