Top number
Numerator
How many pieces you have, or how many the question is talking about. Remember it this way: numerator tells the number of pieces.
ISEE LOWER PREP MASTERCLASS · Topic 4
Fractions & Decimals
You already share cookies and count change, so you already know this. Today we give those everyday skills their proper math names and point them at the ISEE.
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 ISEE.
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 us look at how they work on the ISEE.
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. Every fraction has two parts, separated by a line.
Top number
Bottom number
Denominator
How many pieces make up the entire whole. Remember it this way: the denominator sits down at the bottom.
Here is the pizza in action. 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 wearing a disguise. It is another way to show a part of a whole, but instead of a top and bottom number we use a decimal point, which is a little dot.
The easiest way to understand decimals is to think about money.
- One whole dollar is written as 1.00
- A dime is one tenth of a dollar, written as 0.10
- A penny is one hundredth of a dollar, written as 0.01
So if you have 3 dimes and 5 pennies, you have 35 cents, and we write that as the decimal 0.35.
Connecting fractions and decimals
Fractions and decimals are two ways of writing the exact same thing, so you need to know how they match up. These are the most important pairs to memorize for the ISEE.
| Fraction | Decimal | Money you already know |
|---|---|---|
| $\frac{1}{2}$ (one half) | 0.50 | Half of a dollar, which is 50 cents |
| $\frac{1}{4}$ (one quarter) | 0.25 | A real quarter coin, which is 25 cents |
ISEE tip: read carefully!
The ISEE loves to play a little trick with fractions. A question might say, “A cake has 8 slices. Leo eats 3 slices. What fraction of the cake is left?”
If you are not paying attention, you might answer $\frac{3}{8}$. But the question did not ask what Leo ate. It asked what was left over. Always read the very last sentence of a math problem twice.
Worked examples
Worked example 1: The shared 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?
- First find the bottom number, the denominator. The whole bar has 10 pieces, so the bottom number is 10.
- Next figure out how many pieces are left. Maya started with 10 and gave away 4, so $10 – 4 = 6$.
- Put the number of pieces left on top, as the numerator. The fraction is $\frac{6}{10}$.
The trap
$\frac{4}{10}$
This is the part Maya gave away. It is the number your eyes grab first, and it is not what the question asked for.
The answer
$\frac{6}{10}$
This is the part Maya still has. The question asked what is left, so this is the one to bubble in.
Takeaway
Maya has $\frac{6}{10}$ of the chocolate bar left.
By reading the question carefully we realized we needed to count the remaining pieces (6) instead of the pieces she gave away (4).
Worked example 2: Which one is bigger?
Scenario. Which number is larger, $\frac{1}{2}$ or 0.35?
- Comparing a fraction against a decimal can feel tricky, so turn them both into money.
- We know $\frac{1}{2}$ is half of a dollar, which is 50 cents, written as 0.50.
- The decimal 0.35 is like having 35 cents.
- Now the question is easy: which is more money, 50 cents or 35 cents?
Takeaway
$\frac{1}{2}$ is larger than 0.35, because $0.50 > 0.35$.
Turning fractions and decimals into money makes it much easier for your brain to compare their sizes.
Worked example 3: The shaded circle
Scenario. Sam is looking at a shape on his test. It is a circle divided into 4 equal pieces, and only 1 of the pieces is shaded in with a pencil. The test asks, “What decimal represents the shaded part of the circle?”
- First write what you see as a fraction. One piece is shaded out of 4 total pieces, so the fraction is $\frac{1}{4}$.
- Notice that 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.
Sam read the picture as a fraction first, then used what he knows about money to change that fraction into a decimal.
Short review
Key points covered
- Fractions show a part of a whole. The numerator sits on top (the number of pieces) and the denominator sits on the bottom (the total pieces in the whole).
- Decimals are fractions 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 reminder
Always double check what the question is actually asking. Does it want to know what was eaten, or what was left over?
Study tip
Whenever you see decimals on the ISEE, pretend they are money. It makes adding, subtracting, and comparing sizes much easier.
Great job!
You have finished your first official math lesson and you are training your brain perfectly. When you are ready, click the “Mark Complete” button below to move forward.