Where Did Fractions Come From?
Have you ever split a pizza with friends? If so, you already know what a fraction is! A fraction is a part of a whole. People have been using fractions for thousands of years to share things fairly and measure things carefully.
Long ago, the ancient Egyptians needed fractions to divide land and food. Over time, people found smarter ways to work with parts of things. Let's look at how fractions grew up!
On the ISEE, you will see word problems that ask you to find a fraction of something (that means multiply!) or split something into equal fractional parts (that means divide!). Let's learn exactly how to do that.
Core Ideas You Need to Know
Before we jump into problems, let's review the big ideas. These four rules will help you tackle every fraction word problem on the ISEE.
"Of" Means Multiply
Multiply Straight Across
Divide by Flipping
Always Simplify
See It! Fractions in Pictures
Pictures make fractions much easier to understand. Let's look at what ½ × ⅔ really means. We start with a rectangle that represents one whole thing.
See how the picture matches the math? We multiplied the tops: 1 × 2 = 2. We multiplied the bottoms: 2 × 3 = 6. That gives us 2/6, which simplifies to ⅓. The picture and the math agree!
The Math Rules
Here are the two key formulas you need. Don't worry — they are simple once you practice them a few times!
Types of Fraction Word Problems
On the ISEE, fraction word problems come in a few common types. Learning to spot each type will help you pick the right operation fast. Let's look at them!
Here is a quick trick: if the problem asks you to find a smaller part of something, you usually multiply. If the problem asks you to split or share something, you usually divide.
Let's Solve One Together!
Here's a word problem just like one you might see on the ISEE. Let's work through it step by step.
ISEE Test-Taking Strategies
Knowing the math is great, but using smart strategies can help you even more. Here are some tips that work especially well on the ISEE.
| Strategy | How It Helps | Example |
|---|---|---|
| Look for "of" | The word "of" means multiply. Circle it when you see it! | "⅓ of 15" → ⅓ × 15 = 5 |
| Estimate first | Round the fraction to ½ or 1 to check which answer choice is close. | ⅜ of 24 ≈ ½ of 24 = 12, so answer is near 9. |
| Eliminate wrong answers | Cross out answers that are obviously too big or too small. | ½ of 10 can't be 15 (too big!) — cross it out. |
| Check with a picture | Draw a quick picture or number line to test your answer. | Draw a rectangle, split it, and shade to see the fraction. |
Connecting to Bigger Ideas
The skills you're learning now will keep helping you as math gets bigger. Multiplying and dividing fractions connects to many topics you'll study later.
| What You Know Now | What Comes Next |
|---|---|
| Multiplying fractions like ½ × ⅓ | Multiplying decimals like 0.5 × 0.33 |
| Dividing fractions using Keep-Change-Flip | Dividing decimals and solving equations |
| Finding ¾ of a number | Finding 75% of a number (percents!) |
| Fraction word problems | Ratio and proportion problems |
Did you know that fractions, decimals, and percents are all related? When you master fraction multiplication and division, you're also building skills for decimals and percents. You're getting a head start on future math!
Practice Problems
Time to practice! These problems go from easier to harder, just like the real ISEE. Try each one, then check the answer. You've got this!