Start by naming what you do not know. "Let n be the number of pencils."
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Translate piece by piece
"Three more than n" is n + 3. "Three times n" is 3n.
Order matters twice
"Three less than n" is n − 3, not 3 − n. Subtraction and division are not reversible.
When to use brackets
"Double the sum of n and 4" is 2(n + 4). Without brackets, 2n + 4 doubles only the n.
Translating phrase by phrase
"Five more than three times a number" becomes 3n + 5. Work through the phrase in pieces: "a number" is n, "three times" gives 3n, "five more than" adds 5. Translating in order usually works, but not always.
Where word order misleads
"Five less than a number" is n − 5, not 5 − n. The words come in the opposite order to the symbols. Subtraction and division are not commutative, so getting the order wrong changes the meaning entirely.
Say what your letter means
Write "let n be the number of apples" before using n. Without that, an expression is uninterpretable, and in a multi-step problem you will lose track of which letter is which. Defining variables is a habit that pays off increasingly as problems grow.
Test with a number
Substitute a value into your expression and check the answer against the words. If a number is 10, "five less than the number" is 5, and n − 5 gives 5 — correct. This catches a reversed subtraction instantly.
Step 2: Try It Yourself
Tap and try it out.
n and added on
12
3
n + 3
?
The hatched bar is the piece the story is asking for.
Step 3: Watch an Example
One step at a time.
Watch Leo Translate a Sentence
"Five less than double a number."
- Step 1
He names the number: let it be n.
Step 4: Your Turn
Practice makes it stick.
The Pencils
Problem 1 of 2
n pencils, and 4 more are bought. Evaluate the expression when n is 10.
The Boxes
Problem 2 of 2
Each box holds n pens, and there are 6 boxes. Evaluate when n is 8.
Sentence into Symbols
1 of 4
Which is "four less than n"?
2 of 4
Which is "double the sum of n and 5"?
3 of 4
Evaluate 3n + 2 when n is 5.
4 of 4
Evaluate 2(n + 4) when n is 3.
Step 5: Quick Check
Show what you know.
Question 1 of 1
Evaluate 4n − 3 when n is 5.
What You Learned
- Name the unknown before you write anything.
- "Less than" and "divided by" reverse the order you hear them in.
- Brackets say that a whole sum is being multiplied, not just one part.