Prerequisites
Arithmetic | 15 of 17
Prerequisites: Order of Operations. Enables: None.
Use this checklist for most arithmetic problems.
Step 1: Identify the goal
Decide what the problem asks for.
Examples:
Sum
Difference
Product
Quotient
Percent
Ratio
Missing value
Estimate
Step 2: List knowns and unknowns
Write the given values.
Assign a symbol for the unknown quantity if needed.
Example:
Step 3: Choose the operation
Use the wording and structure of the problem.
| Wording | Common operation |
|---|---|
| total, altogether, combined | Addition |
| difference, left, fewer, how much more | Subtraction |
| groups of, times, product, area | Multiplication |
| per, each, quotient, shared equally | Division |
| out of 100, discount, markup, tax | Percent |
| same ratio, scale, equivalent rates | Proportion |
Step 4: Set up the expression
Write the expression before calculating.
Example:
A $15\%$ tip on a $\$42$ bill is:
Step 5: Calculate carefully
Follow order of operations.
Line up place values when adding or subtracting.
Use common denominators for fraction addition or subtraction.
Step 6: Check units and meaning
Ask:
Does the answer need units?
Should the answer be positive?
Is the result larger or smaller than the starting value?
Is the estimate close to the exact answer?
Step 7: Verify with an inverse operation
Use the inverse operation when possible.
Examples:
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