SSAT Upper 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

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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 Upper Level

Q1 Hard

Which of the following lists of numbers is ordered from least to greatest?

0.37, \frac{11}{30}, \frac{3}{8}, 37.7%

\frac{11}{30}, 0.37, \frac{3}{8}, 37.7%

0.37, \frac{3}{8}, \frac{11}{30}, 37.7%

\frac{11}{30}, \frac{3}{8}, 0.37, 37.7%

37.7%, \frac{3}{8}, 0.37, \frac{11}{30}

Show Solution

To order these numbers, convert them all to their decimal equivalents:

• $\frac{3}{8} = 0.375$
• $0.37 = 0.370$
• $37.7% = 37.7 \div 100 = 0.377$
• $\frac{11}{30} = 11 \div 30 = 0.3666...$ (approximately $0.367$ )
Now, compare the decimal values:
• $0.3666...$ ( $\frac{11}{30}$ )
• $0.370$ ( $0.37$ )
• $0.375$ ( $\frac{3}{8}$ )
• $0.377$ ( $37.7%$ )
Arranged from least to greatest, the order is $\frac{11}{30}, 0.37, \frac{3}{8}, 37.7%$ .

Answer: B

Q2 Hard

Three investment options offer different annual return rates. Option P has a return of

\frac{5}{16}

. Option Q has a return of

31.5%

. Option R has a return of

0.31

. Which option offers the highest annual return?

A Option P

B Option Q

C Option R

D Options P and Q offer the same highest return.

E All options offer the same return.

Show Solution

To determine which option offers the highest return, convert all return rates to their decimal equivalents:

• Option P: $\frac{5}{16}$ . To convert the fraction to a decimal, divide 5 by 16: $5 \div 16 = 0.3125$ .
• Option Q: $31.5%$ . To convert a percentage to a decimal, divide by 100: $31.5 \div 100 = 0.315$ .
• Option R: $0.31$ . This is already in decimal form.
Now, compare the decimal values:
• Option P: $0.3125$
• Option Q: $0.3150$
• Option R: $0.3100$
Comparing these values, $0.3150$ is the largest. Therefore, Option Q offers the highest annual return.

Answer: B

Q3 Hard

Which of the following numbers is closest to

\frac{2}{3}

on a number line?

0.66

\frac{13}{20}

67%

\frac{5}{7}

0.665

Show Solution

First, convert $\frac{2}{3}$ to its decimal approximation: $\frac{2}{3} = 0.6666...$ (repeating).

Now, convert each answer choice to a decimal and find the absolute difference between it and $0.6666...$ .
• A) $0.66$ : Difference: $∣0.6666... - 0.66∣ = 0.0066...$
• B) $\frac{13}{20}$ : $13 \div 20 = 0.65$ . Difference: $∣0.6666... - 0.65∣ = 0.0166...$
• C) $67%$ : $67 \div 100 = 0.67$ . Difference: $∣0.6666... - 0.67∣ = ∣ - 0.0033...∣ = 0.0033...$
• D) $\frac{5}{7}$ : $5 \div 7 \approx 0.71428$ . Difference: $∣0.6666... - 0.71428∣ \approx ∣ - 0.0476∣ = 0.0476$
• E) $0.665$ : Difference: $∣0.6666... - 0.665∣ = 0.0016...$
Comparing the differences, $0.0016...$ (Choice E) is the smallest. Therefore, $0.665$ is closest to $\frac{2}{3}$ .

Answer: E

Q4 Hard

Four students are reading the same book. Alex has read

\frac{5}{8}

of the book. Ben has read

0.63

of the book. Carla has read

62.5%

of the book. David has read

\frac{13}{20}

of the book. Which student has read the second greatest portion of the book?

A Alex

B Ben

C Carla

D David

E Alex and Carla

Show Solution

To compare the portions of the book read by each student, convert all values to their decimal equivalents:

• Alex: $\frac{5}{8}$ . To convert the fraction to a decimal, divide 5 by 8: $5 \div 8 = 0.625$ .
• Ben: $0.63$ . This is already in decimal form.
• Carla: $62.5%$ . To convert a percentage to a decimal, divide by 100: $62.5 \div 100 = 0.625$ .
• David: $\frac{13}{20}$ . To convert the fraction to a decimal, divide 13 by 20: $13 \div 20 = 0.65$ .
Now, list the decimal values:
• Alex: $0.625$
• Ben: $0.63$
• Carla: $0.625$
• David: $0.65$
Order these values from least to greatest:
1. $0.625$ (Alex and Carla - they read the same amount)
2. $0.63$ (Ben)
3. $0.65$ (David)

The greatest portion is $0.65$ (David).
The second greatest portion is $0.63$ (Ben).

Answer: B

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.

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