Translate number and integer word problems into equations and solve step-by-step. Covers consecutive integers, number relationships, and two-digit digit problems.
| Word / Phrase | Operation | Example |
|---|---|---|
| "more than" / "increased by" | + | "5 more than n" → n + 5 |
| "less than" / "decreased by" | − | "3 less than n" → n − 3 |
| "times" / "of" / "multiplied by" | × | "4 times n" → 4n |
| "twice" / "double" | 2 × | "twice the number" → 2n |
| "half of" / "divided by 2" | ÷ 2 | "half of n" → n/2 |
| "is" / "equals" / "the result is" | = | "the sum is 21" → = 21 |
| "sum" / "total" / "together" | + | "sum of x and y" → x + y |
| "difference" / "exceeds by" | − | "x exceeds y by 4" → x − y = 4 |
| "product" | × | "product of x and y" → x · y |
| "quotient" | ÷ | "quotient of n and 3" → n / 3 |
| "square of" / "squared" | ² | "square of n" → n² |
| "consecutive integers" | n, n+1, n+2 | three consecutive → n, n+1, n+2 |
| "consecutive even/odd" | n, n+2, n+4 | two consecutive even → n, n+2 |
| "tens digit a, units digit b" | 10a + b | two-digit number → 10a + b |
| "reversed digits" | 10b + a | reversed → 10b + a |
Word phrase → Algebraic expression
Step 1 — Define: Pick a variable for the unknown. If there are two unknowns, express the second one in terms of the first using the relationship given in the problem.
Step 2 — Translate: Use the table above to convert each word phrase into arithmetic. "More than" means add; "less than" means subtract; "times" means multiply; "is" means equals.
Step 3 — Solve: Solve the equation (or system) using substitution or the quadratic formula if needed.
Step 4 — Check: Substitute your answers back into the original word problem to confirm every condition is satisfied.
Integers: n, n+1, n+2, n+3, …
Even / Odd: n, n+2, n+4, n+6, …
For consecutive integers, each term is 1 more than the previous. Let the first integer = n, then the next are n+1, n+2, etc.
For consecutive even or odd integers, each term is 2 more than the previous — the gap is always 2. Use n, n+2, n+4 regardless of whether the problem says "even" or "odd." The starting value of n determines which type you get.
Sum of three consecutive integers = 3n + 3 = 3(n+1). The middle integer is always the average of the sum.
One-on-one tutoring builds the translation skill — we decode the words together, set up the equation, and practice until the pattern clicks. Book a session on Wyzant.