SSAT Middle 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 Middle Level

Q1 Medium

Of the following fractions, which is closest to 63%?

\frac{1}{2}

\frac{3}{5}

\frac{5}{8}

\frac{2}{3}

\frac{7}{10}

Show Solution

To find the closest fraction, convert each answer choice to a percentage or decimal:

(A) $\frac{1}{2} = 50%$ (13% away from 63%)
(B) $\frac{3}{5} = 60%$ (3% away)
(C) $\frac{5}{8} = 62.5%$ (0.5% away)
(D) $\frac{2}{3} \approx 66.7%$ (3.7% away)
(E) $\frac{7}{10} = 70%$ (7% away)
The closest value to 63% is 62.5%, which corresponds to $\frac{5}{8}$ .

Answer: C

Q2 Medium

Which of the following is equivalent to

\frac{3}{15} + 0.45

A 0.25

B 0.48

C 0.65

D 0.75

E 1.25

Show Solution

First, simplify the fraction $\frac{3}{15}$ by dividing the numerator and denominator by 3, which gives $\frac{1}{5}$ . Next, convert $\frac{1}{5}$ into a decimal to make it easier to add to 0.45. Since $\frac{1}{5} = \frac{2}{10}$ , it is equivalent to 0.20. Finally, add the two decimals together: $0.20 + 0.45 = 0.65$ .

Answer: C

Q3 Medium

The square in the number

0. □ 7

represents a digit from 0 through 9. Which of the following fractions is equivalent to

0. □ 7

\frac{□ + 7}{100}

\frac{( 10 \times □ ) + 7}{10}

\frac{( 10 \times □ ) + 7}{100}

\frac{( 100 \times □ ) + 7}{100}

\frac{10 \times ( □ + 7 )}{100}

Show Solution

A decimal with two places represents a fraction out of 100. The number $0. □ 7$ has $□$ in the tenths place and 7 in the hundredths place. As a two-digit whole number in the numerator over 100, the digits are $□ 7$ . To write this two-digit number mathematically, you multiply the tens digit by 10 and add the units digit, which yields $(10 \times □) + 7$ . Therefore, the equivalent fraction is $\frac{( 10 \times □ ) + 7}{100}$ .

Answer: C

Q4 Medium

Which of the following values is the greatest?

\frac{3}{5}

B 0.65

C 62%

\frac{2}{3}

\frac{5}{8}

Show Solution

Convert all the options to decimals to easily compare them:

(A) $\frac{3}{5} = 0.60$
(B) 0.65
(C) 62% = 0.62
(D) $\frac{2}{3} \approx 0.666...$
(E) $\frac{5}{8} = 0.625$
Comparing these values, 0.666... is the greatest decimal, which corresponds to $\frac{2}{3}$ .

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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