If a bag holds an unknown number of marbles, call it n. Two bags hold 2n.
Variable is a letter standing for a number that can change or is not yet known.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
The multiplication sign disappears
2 × n is written 2n. The number always goes in front of the letter.
Substituting
If n is 7, then 2n + 3 is 2 × 7 + 3, which is 17.
An expression is not an equation
2n + 3 has no equals sign. It is a recipe for a number, not a statement about one.
A letter is a name for a number
In 3n + 5, the n stands for a number that is not yet known or that can vary. It is not a mystery symbol and it is not an abbreviation for a word. Read 3n as "three times n", since the multiplication sign is left out by convention.
Substituting a value
If n = 4, then 3n + 5 = 3 × 4 + 5 = 17. Substitution replaces the letter with a number and evaluates as usual. Writing the multiplication sign back in while you substitute prevents the common slip of reading 3n as 34.
The writing conventions
We write 3n rather than n3, and n/2 rather than n ÷ 2. A number multiplying a letter goes in front and is called the coefficient. These conventions exist so that everyone reads an expression the same way.
Why letters are worth the trouble
A letter lets you state a rule once instead of every case: the perimeter of any square is 4s. It also lets you describe a relationship before knowing any of the numbers, which is what makes algebra a tool for solving rather than just recording.
Step 2: Try It Yourself
Tap and try it out.
One bag and Another bag
7
7
Together
14
7 and 7 make 14.
Step 3: Watch an Example
One step at a time.
Watch Leo Write an Expression
Leo is told: three more than five times a number.
- Step 1
He calls the unknown number n.
Step 4: Your Turn
Practice makes it stick.
Substituting
Problem 1 of 2
If n = 6, what is 3n + 2?
The Perimeter
Problem 2 of 2
A square has side s. If s = 9, what is 4s?
Put the Number In
1 of 4
If x = 4, what is 5x?
2 of 4
If x = 5, what is 2x + 7?
3 of 4
If y = 3, what is y²?
4 of 4
If n = 10, what is 3n − 4?
Step 5: Quick Check
Show what you know.
Question 1 of 2
If a = 8, what is 4a − 5?
Question 2 of 2
What does 2n mean?
What You Learned
- A variable is a letter standing for a number.
- 2n means 2 multiplied by n.
- Substituting puts a value in and works the expression out.