BUS-BOOK55-05 · Lesson 3 · 13 clock hours · lab
Formulas, Arithmetic Operators, and Cell References
Objective. Students write formulas using arithmetic operators and distinguish between relative, absolute, and mixed cell references to build a reusable expense-tracking template that recalculates correctly when copied across rows and columns.
⚠ Pending professional review
This lesson, its worked examples and its practice questions has not yet been verified by a credentialed professional in the field or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.
VoTechWorks program approval and accreditation are still in progress. Credentials are issued only by the certifying bodies named in each program, after their own exams.
Why Formulas Matter in Bookkeeping
Every bookkeeping task—tracking expenses, comparing budgets to actuals, calculating payroll totals—depends on accurate arithmetic. Excel lets you write formulas that do that arithmetic automatically and update instantly when the underlying numbers change. One changed budget figure can ripple through an entire spreadsheet in seconds, with no risk of the manual addition errors that plague paper ledgers. Understanding how formulas work is therefore a core skill for any bookkeeper or office administrator.
Arithmetic Operators
Excel uses five arithmetic operators inside formulas:
| Symbol | Operation | Example |
|--------|-----------|----------|
| `+` | Addition | `=A1+B1` |
| `-` | Subtraction | `=A1-B1` |
| `` | Multiplication | `=A1B1` |
| `/` | Division | `=A1/B1` |
| `^` | Exponentiation | `=A1^2` |
Every formula begins with an equals sign (`=`). Without it, Excel treats your entry as plain text.
Order of Operations
Excel follows standard mathematical order of operations, often remembered as PEMDAS:
1. Parentheses
2. Exponents
3. Multiplication and Division (left to right)
4. Addition and Subtraction (left to right)
This means `=2+34` returns 14, not 20, because multiplication happens before addition. To force addition first, use parentheses: `=(2+3)4` returns 20. In bookkeeping templates, misplaced parentheses are a common source of silent errors—your spreadsheet will calculate something, just not what you intended. Always predict results on paper before trusting a formula.
Cell References: Relative, Absolute, and Mixed
Cell references tell Excel where to find the values a formula needs. There are three types, and choosing the right one is the key to building templates you can copy without breaking.
Relative References
A relative reference such as `B3` adjusts automatically when you copy the formula to another location. If `=B3-B2` is in cell B4 and you copy it to C4, it becomes `=C3-C2`. This is exactly what you want for row-by-row or column-by-column repetition.
Absolute References
An absolute reference such as `$B$2` never changes when copied. The dollar signs lock both the column letter and the row number. Use absolute references when every copy of a formula must point to the same cell—for example, a single annual budget figure that all six monthly percentages divide by.
Mixed References
A mixed reference locks either the column or the row, but not both: `$B2` locks the column; `B$2` locks the row. Mixed references are useful in two-dimensional tables where one dimension should stay fixed and the other should shift.
Keyboard shortcut: While editing a formula, press F4 to cycle a cell reference through all four states: `B2` → `$B$2` → `B$2` → `$B2` → back to `B2`.
Building the Six-Month Expense Tracker
The expense tracker you will build in the lab uses all three reference types working together:
- Row 2 holds monthly budget figures (B2 through G2).
- Row 3 holds actual spending figures (B3 through G3).
- Row 4 calculates variance: `=B3-B2`. Copied across, the relative references shift correctly for each month.
- Row 5 calculates percent of budget: `=B3/$B$2`. The denominator is locked with `$B$2` only if a single master budget cell is used; if each month has its own budget, the formula becomes `=B3/B2` (both relative). Verify which design your template uses before copying.
- Row 6 accumulates a year-to-date total using a fixed annual budget cell with an absolute reference.
Copying formulas across all six columns and then changing a single budget value is how you confirm everything is wired correctly—all dependent cells should update simultaneously.
Common Formula Errors and How to Trace Them
Excel displays error codes when a formula cannot produce a valid result:
- #REF! — The formula points to a cell that no longer exists, usually because a row or column was deleted.
- #DIV/0! — The formula tries to divide by zero or by an empty cell.
- #VALUE! — The formula attempts arithmetic on a cell containing text instead of a number.
Finding errors: Go to Formulas → Error Checking to step through errors one at a time. Use Trace Precedents to draw blue arrows showing which cells feed into the selected formula, and Trace Dependents to show which cells depend on it. These tools make it fast to spot a broken reference or an empty divisor cell without reading through every formula manually.
Document every error you find in your lab log: note the cell address, the error code, the cause, and the correction you made. This habit mirrors professional practice—audit trails are expected in bookkeeping environments.
Data Integrity and Workplace Safety
In an office setting, the main risks around spreadsheet work are data-entry errors and file loss, not physical hazards. Protect your work:
- Save frequently with Ctrl+S and keep a backup copy, following your employer's file-naming and version-control policy.
- Never share a workbook containing sensitive financial figures via unsecured email or personal cloud storage.
- Lock formula cells (using worksheet protection under the Review tab) so that other users cannot accidentally overwrite them—this is a standard internal-control practice aligned with good bookkeeping procedure.
- Maintain good ergonomic posture and take short breaks to prevent repetitive-strain injury during extended data-entry sessions.
Key terms10
FormulaAn expression entered in a cell, beginning with =, that tells Excel to perform a calculation and display the result.
Arithmetic operatorA symbol (+, -, *, /, ^) that specifies the mathematical operation to perform between two values in a formula.
Order of operationsThe sequence Excel uses to evaluate parts of a formula: parentheses first, then exponents, then multiplication and division, then addition and subtraction.
Relative referenceA cell address such as B3 that automatically adjusts its column and row when the formula is copied to a new location.
Absolute referenceA cell address such as $B$2 that is locked with dollar signs so it does not change when the formula is copied.
Mixed referenceA cell address that locks either the column ($B2) or the row (B$2) but not both, allowing one dimension to shift when copied.
#REF! errorAn error code Excel displays when a formula references a cell that has been deleted or moved out of the valid range.
#DIV/0! errorAn error code Excel displays when a formula attempts to divide by zero or by an empty cell.
Trace PrecedentsAn Excel auditing tool found on the Formulas tab that draws arrows pointing from the cells that supply values to the selected formula cell.
VarianceThe difference between an actual figure and a budgeted figure, calculated by subtracting the budget from the actual (Actual − Budget).
Worked examples4
1. Predict the result of the formula =4+6/2*3 before entering it in Excel.
- Identify the operators: addition (+), division (/), multiplication (*).
- Apply order of operations: division and multiplication are evaluated left to right before addition.
- Divide first: 6/2 = 3.
- Multiply next: 3*3 = 9.
- Add last: 4+9 = 13.
Answer: 13
2. Cell B2 contains the monthly budget $1,200. Cell B3 contains actual spending $1,380. Write the variance formula for cell B4 and calculate the result.
- Variance = Actual − Budget, so the formula is =B3-B2.
- Substitute values: 1380 − 1200.
- Calculate: 1380 − 1200 = 180.
Answer: =B3-B2 returns 180, meaning spending exceeded budget by $180.
3. Using the same tracker, cell H1 holds the fixed annual budget of $14,400. Write a percent-of-annual-budget formula in B5 that can be copied to C5 through G5 without the annual budget reference shifting.
- The actual monthly figure is in B3 (relative — should shift to C3, D3, etc. when copied).
- The annual budget in H1 must not shift, so lock it with dollar signs: $H$1.
- Write the formula: =B3/$H$1.
- When copied to C5, Excel adjusts B3 to C3 but keeps $H$1 fixed, giving =C3/$H$1.
- Verify with numbers: =1380/14400 ≈ 0.0958, or about 9.58% of the annual budget used in January.
Answer: =B3/$H$1 (relative numerator, absolute denominator); January result ≈ 9.58%.
4. A formula in cell C10 reads =C8/C9. Cell C9 is empty. What error appears and how do you fix it?
- An empty cell has a value of zero in arithmetic context.
- Dividing by zero causes Excel to display the #DIV/0! error in C10.
- Use Formulas → Error Checking or Trace Precedents to confirm C9 is the divisor and that it is empty.
- Fix: enter the correct divisor value in C9, or wrap the formula with an IFERROR function if zero is a legitimate possibility: =IFERROR(C8/C9,0).
Answer: #DIV/0! error; fix by populating C9 with the correct value or handling the zero case with IFERROR.
The math in this lesson2
Learners compute budget variance as actual minus budget in cell formulas.
7.NS.3A-SSE.1
In class: Instructor presents the order-of-operations rules with three projected examples; students then manually predict formula results on a paper worksheet before entering the same formulas in Excel and comparing their predictions to actual outputs. · Students build a six-month expense tracker: they enter monthly budget figures in row 2 and actual figures in row 3, then write formulas for variance (=B3-B2), percent of budget (=B3/$B$2), and year-to-date total using absolute references for a fixed annual budget cell; they copy formulas across all six months and verify recalculation. · Error-tracing drill: instructor provides a pre-built workbook containing five broken formulas (#REF!, #DIV/0!, #VALUE! errors); students use Formulas > Error Checking and Trace Precedents/Dependents arrows to identify and fix each error, documenting the cause and fix in a lab log entry.
Materials: Excel, paper prediction worksheet, pre-built error-tracing workbook file, lab log template
Check: Expense tracker: all six months recalculate correctly after instructor changes one budget value (pass = correct values in all variance and percentage cells); error-tracing log: all five errors correctly identified with cause described (pass = 5/5).
Practice check8
Answer each question, then check it. Nothing is recorded; this is your own practice.
Record this lesson on my transcript. Sign in with your key and enrollment email to record lessons (enroll free if you have no key). This page stays open to read and practise.