Finding Unknown Numbers in Equations

Sometimes in math, an equation has a missing number. This missing piece might be shown as a blank space ($\_\_$), a question mark ($?$), or a letter like $n$ or $x$. Your goal is to figure out what number belongs there to make the equation true!

The Magic of Opposite Operations

The best trick for finding an unknown number is to use opposite operations (also called inverse operations).

• The opposite of addition is subtraction.
• The opposite of multiplication is division.

When you read an equation with a missing part, you can often work backward using the opposite operation to solve it.

Addition and Subtraction Examples

Problem: $\_\_ + 345 = 812$

To find the missing number, use the opposite of addition. Subtract $345$ from $812$: $812 - 345 = 467$ So, the unknown number is $467$. Let's check it: $467 + 345 = 812$. It works!

Multiplication and Division Examples

Problem: $\_\_ \times 6 = 42$

Here, a number multiplied by $6$ equals $42$. Use the opposite operation, which is division: $42 \div 6 = 7$ The missing number is $7$. Check your work: $7 \times 6 = 42$.

Problem: $56 \div n = 8$

In this division problem, $n$ is our unknown number. You can use fact families to help. If $56$ divided by $n$ is $8$, then $8$ times $n$ must be $56$: $8 \times n = 56$ Since we know our multiplication facts, we know $8 \times 7 = 56$. Therefore, $n = 7$.

Quick Tip

Always double-check your answer by plugging it back into the original equation. If both sides match, you've found the correct unknown number!