Top number
Numerator
This tells you how many pieces you have or are talking about. Think: Numerator = Number of pieces.
SSAT Elementary Prep Masterclass · Topic 3
Fractions & Decimals
Chop up some imaginary pizzas, then learn the money trick that makes decimals easy.
Lesson summary
Welcome to your first math lesson in this section! Today, we are going to chop up some imaginary pizzas and chocolate bars to understand fractions. Then, we will look at decimals, which are just another fun way to write fractions using a little dot. You will learn the secret to remembering the top and bottom numbers of a fraction, how to count decimals using money, and how to avoid the tricky traps on the SSAT!
Direct instruction
Welcome to math!
Hello again, Brain Athlete! Are you ready to dive into some math? Today, we are talking about fractions and decimals. Sometimes, kids think these sound scary, but here is a secret: you already use them every single day! If you have ever shared half a cookie with a friend or counted your change to buy a toy, you are already a fraction and decimal expert. Let’s look at how they work on the SSAT.
What is a fraction?
A fraction is simply a way to describe a part of a whole. Imagine a giant, delicious pizza. If you cut it into slices, a fraction tells you how many slices you have compared to the whole pizza.
$$\frac{1}{4} \qquad = \qquad \frac{\text{pieces you have}}{\text{total pieces in the whole}}$$
Fractions have two parts, separated by a line:
Top number
Bottom number
Denominator
This tells you how many pieces make up the entire whole. Think: Denominator = Down at the bottom.
Example
If a pizza is cut into 4 slices, and you eat 1 slice, you ate $\frac{1}{4}$ of the pizza!
What is a decimal?
A decimal is just a fraction dressed up in a disguise! It is another way to show a part of a whole, but instead of using a top and bottom number, we use a decimal point (a little dot).
The easiest way to understand decimals is to think about money!
$1.00
One whole dollar
One whole dollar
This is the whole thing, all of it.
$0.10
One dime
One dime
A dime is one tenth of a dollar.
$0.01
One penny
One penny
A penny is one hundredth of a dollar.
If you have 3 dimes and 5 pennies, you have 35 cents, which we write as a decimal: $0.35.
Connecting fractions and decimals
Because fractions and decimals are just two ways of writing the exact same thing, you will need to know how they match up. Here are the most important ones to memorize for the SSAT:
| Name | Fraction | Decimal | Think of it as |
|---|---|---|---|
| One half | $\frac{1}{2}$ | $0.50$ | Half of a dollar, or 50 cents |
| One quarter | $\frac{1}{4}$ | $0.25$ | A real quarter coin, which is 25 cents |
SSAT tip: read carefully!
The SSAT loves to play a little trick with fractions. They might say: “A cake has 8 slices. Leo eats 3 slices. What fraction of the cake is left?”
If you aren’t paying attention, you might say $\frac{3}{8}$. But the question didn’t ask what Leo ate; it asked what was left over! Always read the very last sentence of a math problem twice.
Worked examples
1
Worked example
Maya’s chocolate bar
Scenario
A chocolate bar is broken into 10 equal pieces. Maya shares 4 pieces with her little brother. What fraction of the chocolate bar does Maya have left?
Step by step
- First, we find the bottom number (denominator). The whole bar has 10 pieces, so the bottom number is 10.
- Next, we figure out how many pieces are left. Maya started with 10 and gave away 4, so $10 – 4 = 6$.
- We put the number of pieces left on top (numerator). The fraction is $\frac{6}{10}$.
Takeaway
Maya has $\frac{6}{10}$ of the chocolate bar left.
Why this is correct
By reading the question carefully, we realized we needed to count the remaining pieces (6) instead of the pieces she gave away (4).
2
Worked example
Which number is larger?
Scenario
Which number is larger: $\frac{1}{2}$ or $0.35$?
Step by step
- Comparing fractions and decimals can be tricky, so let’s turn them both into “money” to make it easy!
- We know that $\frac{1}{2}$ is the same as half a dollar, which is written as $0.50$, or 50 cents.
- The decimal $0.35$ is like having 35 cents.
- Now we just ask: which is more money, 50 cents or 35 cents?
Takeaway
$\frac{1}{2}$ is larger than $0.35$.
Why this is correct
Converting fractions and decimals into money makes it super easy for our brains to compare their sizes. $0.50$ is greater than $0.35$!
3
Worked example
Sam’s shaded circle
Scenario
Sam is looking at a shape on his test. It is a circle divided into 4 equal pieces. Only 1 of the pieces is shaded in with a pencil. The test asks: “What decimal represents the shaded part of the circle?”
Step by step
- First, let’s write what we see as a fraction. 1 piece is shaded out of 4 total pieces, so the fraction is $\frac{1}{4}$.
- The question asks for a decimal, not a fraction!
- Sam remembers that $\frac{1}{4}$ is a “quarter.”
- A quarter in money is written as $0.25$.
Takeaway
The shaded part of the circle is $0.25$.
Why this is correct
Sam correctly identified the fraction visually, and then used his knowledge of money to change that fraction into a decimal!
Short review
Key points covered
- Fractions show a part of a whole. The numerator is on top (number of pieces) and the denominator is on the bottom (total pieces in the whole).
- Decimals are just fractions written with a dot instead of a line.
- Fractions and decimals are best friends: $\frac{1}{2} = 0.50$ and $\frac{1}{4} = 0.25$.
Important reminders
- Always double-check what the question is asking! Does it want to know what was eaten or what was left over?
Study tips
- Whenever you see decimals on the SSAT, pretend it is money! It will make addition, subtraction, and comparing sizes much easier.
Great job completing your first official math lesson!
You are training your brain perfectly. When you are ready, click the Mark Complete button below to move forward!