SSAT Upper Level

Conversions

Q: Do I really need to memorize fraction conversions for the SSAT?

Yes! Memorizing common ones like `\frac{1}{4}`, `\frac{3}{4}`, and `\frac{1}{8}` is like having a secret shortcut. It saves you precious minutes on the test.

Converting between fractions, decimals, and percents

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Imagine you're playing a video game, and your health bar shows $50%$ . Then you look at your pizza, and you've eaten $\frac{1}{2}$ of it. Later, you find $0.50$ dollars (50 cents) in your pocket. Guess what? Those are all the exact same amount! 🍕🎮

Fractions, decimals, and percents are just three different languages for saying the exact same thing. It's like saying "Hello" in English, "Hola" in Spanish, and "Bonjour" in French. On the SSAT, you'll need to be an awesome translator who can switch between these three math languages super fast!

Here's the secret: "Percent" literally means "out of 100." So, $50%$ is just $\frac{50}{100}$ . Decimals are also based on tens and hundreds, so $0.50$ means 50 hundredths, or $\frac{50}{100}$ . Once you get them into a fraction, you just shrink them down (simplify) to their smallest form, like $\frac{1}{2}$ .

Sometimes the SSAT will give you a tricky math problem with decimals, but it's actually much easier to solve if you turn them into fractions first. Or they might ask you to compare a list of numbers to see which is biggest. If you turn them all into percents, it becomes a piece of cake! 🍰 Being able to change a fraction to a decimal, or a percent to a fraction, is a super-powered cheat code for the SSAT. Let's learn how to translate! 🦸‍♂️✨

Key Formula

To turn a decimal into a fraction, count the decimal places! Three places means thousandths:

0. x y z = \frac{x y z}{1000}

. For percents, just put the number over 100:

x % = \frac{x}{100}

Practice Questions

4 practice questions for SSAT Upper Level

Q1 Hard

Express

0.41 \overline{6}

as a fraction in simplest form.

\frac{1}{24}

\frac{5}{12}

\frac{41}{100}

\frac{416}{1000}

\frac{13}{30}

Show Solution

Let $x = 0.41 \overline{6}$ .

First, multiply $x$ by a power of 10 to move the non-repeating part to the left of the decimal point:
$100 x = 41.666...$
Next, multiply $x$ by a power of 10 to move one full repeating block to the left of the decimal point:
$1000 x = 416.666...$
Subtract the first equation from the second to eliminate the repeating part:
$1000 x - 100 x = 416.666... - 41.666...$
$900 x = 375$
Now, solve for $x$ :
$x = \frac{375}{900}$
To simplify the fraction, find the greatest common divisor (GCD). Both 375 and 900 are divisible by 25:
$375 \div 25 = 15$
$900 \div 25 = 36$
So, $x = \frac{15}{36}$
Both 15 and 36 are divisible by 3:
$15 \div 3 = 5$
$36 \div 3 = 12$
Thus, $x = \frac{5}{12}$ in simplest form.

Answer: B

Q2 Hard

A clothing store sells two types of shirts, Type A and Type B.

37.5%

of the shirts sold are Type A. Of the Type A shirts,

\frac{2}{5}

are blue. Of the Type B shirts,

\frac{3}{8}

are blue. What percentage of all shirts sold are blue?

\frac{3}{8} %

37.5%

38 \frac{7}{16} %

42.5%

48 \frac{3}{4} %

Show Solution

Let the total number of shirts sold be $T$ .

First, convert $37.5%$ to a fraction: $37.5% = \frac{37.5}{100} = \frac{375}{1000} = \frac{3}{8}$ .
So, Type A shirts $= \frac{3}{8}$ of $T$ .
This means Type B shirts $= 1 - \frac{3}{8} = \frac{5}{8}$ of $T$ .
Calculate the fraction of blue shirts from Type A:
Blue Type A shirts $= (\frac{2}{5}) \times (\frac{3}{8})$ of $T = \frac{6}{40}$ of $T = \frac{3}{20}$ of $T$ .
Calculate the fraction of blue shirts from Type B:
Blue Type B shirts $= (\frac{3}{8}) \times (\frac{5}{8})$ of $T = \frac{15}{64}$ of $T$ .
Now, add these fractions to find the total fraction of blue shirts:
Total blue shirts $= \frac{3}{20} + \frac{15}{64}$ .
To add these fractions, find a common denominator for 20 and 64. The least common multiple (LCM) of 20 ( $2^{2} \times 5$ ) and 64 ( $2^{6}$ ) is $2^{6} \times 5 = 320$ .
$\frac{3}{20} = (3 \times 16) / (20 \times 16) = \frac{48}{320}$
$\frac{15}{64} = (15 \times 5) / (64 \times 5) = \frac{75}{320}$
Total blue shirts $= \frac{48}{320} + \frac{75}{320} = \frac{123}{320}$ .
Finally, convert this fraction to a percentage:
$(\frac{123}{320}) \times 100% = (123 \times 100) /320% = \frac{12300}{320} % = \frac{1230}{32} % = \frac{615}{16} %$ .
To express this as a mixed number percentage:
$615 \div 16$
$615 = 16 \times 38 + 7$
So, $\frac{615}{16} % = 38 \frac{7}{16} %$ .

Answer: C

Q3 Hard

A number

x

\frac{1}{3}

more than

0.6

. What percentage of

x

\frac{1}{5}

10%

14 \frac{2}{7} %

20%

21 \frac{3}{7} %

25%

Show Solution

First, find the value of $x$ .

$x$ is $\frac{1}{3}$ more than $0.6$ . Convert $0.6$ to a fraction: $0.6 = \frac{6}{10} = \frac{3}{5}$ .
So, $x = \frac{3}{5} + \frac{1}{3}$ .
To add these fractions, find a common denominator, which is 15.
$x = (3 \times 3) / (5 \times 3) + (1 \times 5) / (3 \times 5) = \frac{9}{15} + \frac{5}{15} = \frac{14}{15}$ .
Next, we need to find what percentage of $x$ is $\frac{1}{5}$ . This can be expressed as $((\frac{1}{5}) / x) \times 100%$ .
Substitute the value of $x$ :
$P er ce n t a g e = ((\frac{1}{5}) / (\frac{14}{15})) \times 100%$
To divide by a fraction, multiply by its reciprocal:
$P er ce n t a g e = (\frac{1}{5}) \times (\frac{15}{14}) \times 100%$
$P er ce n t a g e = (15/ (5 \times 14)) \times 100%$
$P er ce n t a g e = (\frac{15}{70}) \times 100%$
Simplify the fraction $\frac{15}{70}$ by dividing by 5:
$\frac{15}{70} = \frac{3}{14}$
So, $P er ce n t a g e = (\frac{3}{14}) \times 100%$
$P er ce n t a g e = \frac{300}{14} %$
Simplify the fraction by dividing by 2:
$P er ce n t a g e = \frac{150}{7} %$
Convert this improper fraction to a mixed number percentage:
$150 \div 7$
$150 = 7 \times 21 + 3$
So, $\frac{150}{7} % = 21 \frac{3}{7} %$ .

Answer: D

Q4 Hard

A company's total revenue is generated from three sources: X, Y, and Z. Source X contributes

\frac{1}{4}

of the total revenue, and Source Y contributes

45%

of the total revenue. The remaining revenue comes from Source Z. What fraction of Source Z's revenue is Source X's revenue? Express your answer as a fraction in simplest form.

\frac{1}{4}

\frac{3}{10}

\frac{5}{12}

\frac{5}{6}

\frac{7}{8}

Show Solution

Let the total revenue be represented by $1$ (or $100%$ ).

Source X's contribution: $\frac{1}{4}$ .
Convert $\frac{1}{4}$ to a percentage or decimal: $\frac{1}{4} = 0.25 = 25%$ .
Source Y's contribution: $45% = 0.45$ .
To find Source Z's contribution, subtract the contributions of X and Y from the total:
$S o u r ce Z = 1 - (S o u r ce X + S o u r ce Y)$
$S o u r ce Z = 1 - (\frac{1}{4} + 45%)$
It's easiest to work with decimals or fractions consistently. Let's use decimals first:
$S o u r ce Z = 1 - (0.25 + 0.45)$
$S o u r ce Z = 1 - 0.70$
$S o u r ce Z = 0.30$
Convert $0.30$ back to a fraction: $0.30 = \frac{30}{100} = \frac{3}{10}$ .
So, Source Z contributes $\frac{3}{10}$ of the total revenue.
Now, we need to find what fraction of Source Z's revenue is Source X's revenue. This means calculating $(S o u r ce X^{'} s R e v e n u e) / (S o u r ce Z^{'} s R e v e n u e)$ .
$F r a c t i o n = (\frac{1}{4}) / (\frac{3}{10})$
To divide by a fraction, multiply by its reciprocal:
$F r a c t i o n = (\frac{1}{4}) \times (\frac{10}{3})$
$F r a c t i o n = \frac{10}{12}$
Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2:
$F r a c t i o n = 10 \div \frac{2}{12} \div 2 = \frac{5}{6}$ .

Answer: D

Tips & Strategies

Memorize the 'Famous Fractions'! Knowing that $\frac{1}{2} = 0.50$ , $\frac{1}{4} = 0.25$ , $\frac{3}{4} = 0.75$ , and $\frac{1}{8} = 0.125$ saves you tons of time on the SSAT. ⏱️
When comparing a mix of fractions, decimals, and percents, change them ALL into decimals or percents first. It's much easier to see that $0.40$ is bigger than $0.35$ than to compare $\frac{2}{5}$ and $\frac{7}{20}$ in your head! 🧠

Common Mistakes

Watch out for simplifying only halfway! If you get $\frac{15}{40}$ , always ask yourself, 'Can I divide the top and bottom by another number?' If you stop too early, you might pick a trap answer!
Don't forget that $5%$ is $0.05$ , NOT $0.5$ . Since percent means 'out of 100', $5%$ is $\frac{5}{100}$ . $0.5$ is actually $50%$ ! 🚨

Frequently Asked Questions

Do I really need to memorize fraction conversions for the SSAT?

Yes! Memorizing common ones like $\frac{1}{4}$ , $\frac{3}{4}$ , and $\frac{1}{8}$ is like having a secret shortcut. It saves you precious minutes on the test.

How do I turn a fraction into a decimal if I don't have it memorized?

Just divide the top number (numerator) by the bottom number (denominator)! For example, for $\frac{3}{5}$ , you just calculate $3 \div 5 = 0.6$ .

What if I have a mixed number like

2 \frac{1}{2}

Treat the whole number and the fraction separately! Keep the 2, and change the $\frac{1}{2}$ to $0.5$ . Put them together to get $2.5$ .

Are calculators allowed on the SSAT?

Nope! That's why practicing these conversions by hand is so important. You get to be your own human calculator! 🧠⚡

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