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Learn how to find a missing number in an equation like a math detective!
People have been solving for missing numbers for thousands of years! Long ago, farmers needed to figure out things like: "I had some sheep. 5 ran away. Now I have 7. How many did I start with?" That's really just solving an equation!
An equation is a math sentence that uses an equals sign (=). It says two sides are the same amount. Let's see how this idea grew over time.
Today, you use equations all the time! When you figure out how much more money you need to buy a toy, you're solving an equation. Let's learn how to do it step by step.
Before we start solving, let's learn a few important ideas. These are like the rules of the game!
Let's picture the equation n + 3 = 8 as a balance scale. The left side and right side must weigh the same!
Notice how we always check our answer at the end. Plug 5 back in: 5 + 3 = 8. It works! Always check by putting your answer back into the original equation.
Here's the big secret to solving equations: use the opposite operation to get the unknown all by itself. Addition and subtraction are opposites. Multiplication and division are opposites.
On the ISEE, you'll see different kinds of equations. The unknown might show up in different spots. Let's look at all four types and how to handle each one.
Sometimes the ISEE puts the unknown in a different spot. For example: 15 − □ = 9. That's okay! You can still think: "What number do I subtract from 15 to get 9?" The answer is 15 − 9 = 6. So □ = 6.
Let's solve a problem together, just like you'd see on the ISEE. Follow each step carefully!
There are different strategies you can use to find the unknown. Each one works great! Let's compare them so you can pick your favorite.
| Strategy | How It Works | Best For |
|---|---|---|
| Opposite Operation | Undo what's done to the unknown. If the equation has + 5, subtract 5. | All equation types. This is the fastest method! |
| Backsolving | Try each answer choice in the equation. The one that makes both sides equal is correct. | When you're not sure how to solve. Great ISEE strategy! |
| Fact Families | Think of related facts. If 7 + 5 = 12, then 12 − 5 = 7 and 12 − 7 = 5. | Addition and subtraction problems with smaller numbers. |
Right now you're solving one-step equations. That means you only need one step to find the answer. As you grow as a math student, equations will get a little bigger — but the same rules apply!
| What You Know Now | What Comes Next |
|---|---|
| n + 5 = 12 (one step) | 2 × n + 5 = 17 (two steps) |
| The unknown is shown as □ or n | The unknown uses letters like x and y |
| Use opposite operations | Still use opposite operations — same idea! |
| Check by plugging in your answer | Still check by plugging in — always works! |
The awesome thing is that the opposite operation trick you're learning right now will be used all the way through high school and college math. You're building a super important skill!
Time to practice! Try each problem on your own first. Remember: find the operation, use the opposite, then check. You've got this!
An equation is a math sentence with an equals sign. The unknown is the missing number you need to find. To solve, use the opposite operation: addition undoes subtraction, and multiplication undoes division. Think of the equation like a balanced seesaw — both sides must always stay equal.
Always check your answer by plugging it back into the original equation. On the ISEE, you can also try backsolving — test each answer choice to see which one makes the equation true. Remember, there's no penalty for guessing, so always pick an answer!