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SSAT Middle Level Prep Masterclass · Topic 4

Fractions & Decimals

Two golden rules, five benchmark conversions, and the misaligned-decimal trap the SSAT loves to set.

Quantitative sections
50 math questions
Common denominators

Lesson summary

Welcome to the Math section of your SSAT Middle Level course! Today, we are mastering two of the most important concepts on the exam: fractions and decimals. You will learn the golden rules for adding and subtracting them, discover how to quickly convert between the two, and see how the SSAT tries to trick you with misaligned numbers. By the end of this lesson, you will be able to slice through fraction and decimal problems with total confidence.

Direct instruction

Welcome to Middle Level math!

Hello, Brain Athlete! On the SSAT Middle Level exam, the Quantitative sections are a big part of your score. You will see 50 math questions in total, spread across two sections.

A huge chunk of these questions will involve fractions and decimals. Because you are in 5th, 6th, or 7th grade, the test makers expect you to do more than just know what a fraction is. They want to see if you can add, subtract, and compare them without getting tricked!

The golden rule of fractions: common denominators

A fraction has a numerator (top number) and a denominator (bottom number). When you multiply or divide fractions, you can just go straight across. But when you add or subtract fractions, you must follow the golden rule:

The denominators must be exactly the same before you add or subtract.

$$\frac{1}{3} + \frac{1}{4}$$

You cannot just add the bottom numbers together. You have to find a common denominator, which is a number that both $3$ and $4$ can multiply into. In this case, that number is $12$.

The golden rule of decimals: line up the dot!

Decimals are just fractions written in a different format based on place value: tenths, hundredths, thousandths. When adding or subtracting decimals on the SSAT, the test will often write the problem horizontally to trick your eyes, like this:

$$4.2 + 1.35$$

If you try to add this in your head, you might accidentally add the $2$ and the $5$. Your golden rule is to rewrite the problem vertically on your scratch paper and line up the decimal points. You can add a placeholder zero to the end of a decimal to make them the same length, so $4.2$ becomes $4.20$.

$$\begin{array}{r} 4.20 \\ +\;1.35 \\ \hline 5.55 \end{array}$$

Connecting fractions and decimals

To save time on the test, you should memorize a few benchmark conversions. If you know these by heart, you won’t have to do the long division on test day!

Fraction Decimal Say it out loud
$\frac{1}{2}$ $0.5$ One half
$\frac{1}{4}$ $0.25$ One quarter
$\frac{3}{4}$ $0.75$ Three quarters
$\frac{1}{5}$ $0.2$ One fifth
$\frac{1}{10}$ $0.1$ One tenth

SSAT tip: mixing formats

The SSAT loves to give you a problem that contains both a fraction and a decimal, like $\frac{1}{4} + 0.5$. You cannot do math with two different formats!

Your first step is always to convert one of them so they match. You can change them both to fractions, or both to decimals, whichever feels easier for your brain.

Worked examples

1
Worked example

Adding two unlike fractions

Scenario

Solve the following: $\frac{2}{5} + \frac{1}{3}$

Step by step

  1. First, we check the denominators. They are $5$ and $3$. Because we are adding, we must find a common denominator!
  2. We list the multiples of $5$ ($5, 10, 15, 20$) and the multiples of $3$ ($3, 6, 9, 12, 15$). The smallest number they share is $15$.
  3. We convert $\frac{2}{5}$ by multiplying the top and bottom by $3$, which gives us $\frac{6}{15}$.
  4. We convert $\frac{1}{3}$ by multiplying the top and bottom by $5$, which gives us $\frac{5}{15}$.
  5. Now we add the numerators: $6 + 5 = 11$. The denominator stays the same.
$$\frac{6}{15} + \frac{5}{15} = \frac{11}{15}$$
Takeaway

The answer is $\frac{11}{15}$.

Why this is correct

By finding a common denominator first, we made sure the pieces we were adding were the exact same size.

2
Worked example

Marcus lines up the dot

Scenario

Marcus sees this problem on his test: $12.5 – 3.42$. He has to calculate the difference.

Step by step

  1. Marcus remembers the golden rule of decimals: line up the dot!
  2. He writes the problem vertically on his scratch paper, putting $12.5$ on top and $3.42$ underneath it, making sure the decimal points are stacked right on top of each other.
  3. He notices a blank space above the $2$. He adds a placeholder zero to the top number, making it $12.50$.
  4. Now he subtracts normally.
$$\begin{array}{r} 12.50 \\ -\;3.42 \\ \hline 9.08 \end{array}$$
Takeaway

The difference is $9.08$.

Why this is correct

Using a placeholder zero lets you borrow correctly. If you don’t line up the decimals and add the zero, it is very easy to mistakenly bring the $2$ straight down and get the wrong answer!

3
Worked example

Chloe compares a fraction and a decimal

Scenario

Chloe is asked to compare two numbers to see which one is larger. The test asks: which is greater, $\frac{3}{5}$ or $0.55$?

Step by step

  1. Chloe sees that the problem mixes a fraction and a decimal. She knows she needs to make them match.
  2. She decides to turn the fraction into a decimal.
  3. She remembers her benchmark fractions: $\frac{1}{5} = 0.2$.
  4. Since she has $\frac{3}{5}$, she multiplies $0.2 \times 3 = 0.6$, which she can also write as $0.60$.
  5. Now she compares her two decimals: $0.60$ and $0.55$. Sixty hundredths is greater than fifty-five hundredths.
Takeaway

The fraction $\frac{3}{5}$ is greater than $0.55$.

Why this is correct

You can never accurately compare a fraction and a decimal just by looking at them. By converting the fraction into a decimal first, Chloe created an easy, apples-to-apples comparison!

Short review

Key points covered

  • Fractions: you must find a common denominator before you add or subtract!
  • Decimals: always rewrite the problem vertically and line up the decimal points. Use placeholder zeros to make the numbers the same length.
  • Conversions: memorizing benchmark fractions like $\frac{1}{4} = 0.25$ and $\frac{1}{5} = 0.2$ saves you valuable time.

Important reminders

  • If a problem has both a fraction and a decimal, convert one of them immediately so they are in the same format before you do any math.
  • Do not try to solve decimal subtraction in your head. The SSAT designs these questions to trick mental-math users. Always use your scratch paper!

Study tips

  • Write down the five benchmark fractions from this lesson on a sticky note and put it on your bathroom mirror. Read them out loud every time you brush your teeth, and you will have them memorized by test day!

Excellent work tackling some of the most important math on the SSAT!

When you are ready for your next challenge, click the Mark Complete button below.

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