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.

Fractions have two parts, separated by a line:

Numerator (The Top Number): This tells you how many pieces you have or are talking about. (Think: Numerator = Number of pieces).

Denominator (The Bottom Number): 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 14\frac{1}{4} 41​ 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!

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.

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:

One Half: 12\frac{1}{2} 21​ is the exact same as $0.50$ (like half of a dollar, or $50$ cents).

One Quarter: 14\frac{1}{4} 41​ is the exact same as $0.25$ (like 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 38\frac{3}{8} 83​. 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 Example 1

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 explanation:

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 $4$. $10–4=6$.

We put the number of pieces left on top (Numerator). The fraction is 610\frac{6}{10} 106​.

Final answer or takeaway: Maya has 610\frac{6}{10} 106​ of the chocolate bar left.

Why the answer is correct: By reading the question carefully, we realized we needed to count the remaining pieces ($6$) instead of the pieces she gave away ($4$).

Worked Example 2

Scenario: Which number is larger: 12\frac{1}{2} 21​ or $0.35$?

Step-by-step explanation:

Comparing fractions and decimals can be tricky, so let’s turn them both into “money” to make it easy!

We know that 12\frac{1}{2} 21​ 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?

Final answer or takeaway: 12\frac{1}{2} 21​ is larger than $0.35$.

Why the answer is correct: Converting fractions and decimals into money makes it super easy for our brains to compare their sizes. $0.50$ is greater than $0.35$!

Worked Example 3

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 explanation:

First, let’s write what we see as a fraction. $1$ piece is shaded out of $4$ total pieces. The fraction is 14\frac{1}{4} 41​.

The question asks for a decimal, not a fraction!

Sam remembers that 14\frac{1}{4} 41​ is a “quarter.”

A quarter in money is written as $0.25$.

Final answer or takeaway: The shaded part of the circle is $0.25$.

Why the answer 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: 12=0.50\frac{1}{2} = 0.50 21​=0.50 and 14=0.25\frac{1}{4} = 0.25 41​=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!