Expressions: replace the letter, keep the rules

A letter stands for a value

An expression can use a letter to stand for a number. Our example says x is five and asks for the value of three x plus four. Here, three x means three times x. It does not mean a new two-digit number made by sticking three beside five.

Substitute before calculating

Substitute means put the given value where the letter appears. Replace x with five, keeping the operations. Now we have three times five plus four. Writing that step helps you avoid skipping a multiplication or accidentally changing the expression while you work.

Multiplication before addition

Multiply three by five first to get fifteen. Then add four to get nineteen. Adding five and four first would create a different expression with parentheses. Operation order keeps readers working from the same instructions. Otherwise every calculator would be having its own little argument.

Parentheses change the first job

Compare three times the quantity x plus four. The parentheses tell us to add inside first. With x equal to five, five plus four is nine, then three times nine is twenty-seven. This is different from the diagram's expression, three x plus four, which gives nineteen.

Pause with a new expression

Pause and evaluate two times the quantity n plus three when n is four. Write the substitution, solve inside the parentheses, and then multiply. Say which operation you did first and why. The letter has changed, but the method has not.

Check each step

Replace n with four. Inside the parentheses, four plus three is seven. Multiply two by seven to get fourteen. Two times four plus three, without the parentheses, would give eleven. Those are different instructions, so different answers are exactly what we should expect.

One value need not identify a rule

Fun fact: two different expressions can give the same output for one input. When x is two, x plus two and two x both give four. But when x is three, they give five and six. One matching result does not make the rules identical.

Replace, calculate, check

Continue to the expressions worksheet. Write the given value in place of each letter, preserve the parentheses, and follow operation order. Check your arithmetic one step at a time. You are evaluating an expression with a supplied value, not guessing a missing value or solving an equation.