Words to Equations

Learn how to turn a sentence into a math equation using the variable \( x \).

ISEE Lower Level

What is a Variable?

A variable is a letter that stands for a number we do not know yet. We often use the letter \( x \). When a word problem says "a number," we can name that number \( x \).

What is an Equation?

An equation is a math sentence with an equals sign (\( = \)). It says the two sides are worth the same amount, like a balanced scale.

Why This Matters

Many math problems are written in words, not numbers. If you can change the words into an equation, the problem becomes much easier to solve.

Step 1

Read the words carefully.

Step 2

Write the equation.

Step 3

Solve for \( x \).

Key Words = Math Signs

Certain words always tell you which operation to use. Learn these "signal words":

Words	Sign
sum, plus, more than, added to	\( + \)
difference, minus, less than, fewer	\( - \)
product, times, of, twice	\( \times \)
quotient, divided by, per	\( \div \)
is, equals, will be, total	\( = \)

The Translation Rule

Watch the Word Order

For "less than" and "subtracted from," the order flips! These tricky words put the second number first.

Words	Equation
5 more than a number	\( x + 5 \)
5 less than a number	\( x - 5 \)
5 subtracted from a number	\( x - 5 \)

Steps to Translate

1

Name the unknown. Let \( x \) stand for the mystery number.

2

Find the signal words. Circle words like "sum," "times," or "is."

3

Replace words with signs. Turn each part into math symbols.

4

Write the equation. Connect both sides with the \( = \) sign.

Example 1: Addition

"The sum of a number and 8 is 15." Write the equation.

Example 2: Multiplication

"Three times a number is 21." Write the equation.

Example 3: Less Than

"4 less than a number is 10." Write the equation.

Common Mistakes

✕ Flipping subtraction

Writing "5 less than \( x \)" as \( 5 - x \). It should be \( x - 5 \).

✕ Missing the equals

Forgetting that "is" or "equals" needs an \( = \) sign in the equation.

✕ Wrong operation

Using \( + \) when the word "product" or "times" means \( \times \).

Quick Summary

Words	Equation
The sum of a number and 6 is 10	\( x + 6 = 10 \)
7 less than a number is 2	\( x - 7 = 2 \)
Twice a number is 18	\( 2x = 18 \)
A number divided by 4 is 5	\( x \div 4 = 5 \)

Question 1 of 5

"The sum of a number and 9 is 14." Which equation is correct?

"Sum" means add, so \( x + 9 \), and "is" means \( = 14 \).

Question 2 of 5

"Five times a number is 30." Which equation is correct?

"Times" means multiply, so \( 5 \times x = 5x \), giving \( 5x = 30 \).

Question 3 of 5

"6 less than a number is 11." Which equation is correct?

"Less than" flips the order: the number \( x \) comes first, so \( x - 6 = 11 \).

Question 4 of 5

"A number divided by 3 is 8." Which equation is correct?

"Divided by" means \( \div \), so the number \( x \div 3 = 8 \).

Question 5 of 5

"Twice a number, plus 1, is 13." Which equation is correct?

"Twice a number" is \( 2x \), "plus 1" adds 1, and "is 13" gives \( 2x + 1 = 13 \).

You Can Translate!

Great work! You now know how to turn words into equations using a variable and signal words.

Name it

Use \( x \) for the unknown.

Spot signals

Sum, times, less than, is.

Write it

Connect with \( = \).

Keep Practicing!

Every word problem is just an equation waiting to be written. You've got this!