Alphabet Arithmetic Practice Test Worksheets
Build confidence with printable alphabet arithmetic worksheets and focused mental maths practice tests. Students substitute letter values, apply BIDMAS operator precedence, and convert final totals back into letter keys.
For students who can handle basic arithmetic, but need targeted practice with letter substitution, operator order, and mental algebra.
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What Do Alphabet Arithmetic Questions Look Like?
Students are given a letter-to-number key and an arithmetic expression made of letters. They must substitute each letter with its value, evaluate the expression following the order of operations (BIDMAS), and match the final total back to a letter in the key. Here is a worked example.
Linear Addition & Subtraction
Question: Use BIDMAS to evaluate the calculation and convert your answer to a letter using the key.
A = 7, B = 4, C = 6, D = 22, E = 2, F = 24
B + D − E = [ ? ]
Worked Method
What it's testing: Rule 1 & Rule 3 — direct value substitution and left-to-right calculation.
Step-by-step evaluation:
- Substitute values: B = 4, D = 22, E = 2.
- Expression: 4 + 22 − 2
- Evaluate left to right: 4 + 22 = 26, then 26 − 2 = 24.
- Reverse Key Lookup: 24 corresponds to F.
Answer: F
Tip: Addition and subtraction have equal priority, so process them strictly from left to right.
Rules to Help You Solve Alphabet Arithmetic Questions
As shown in the worked example above, solving alphabet arithmetic questions requires careful substitution, strict order of operations, and a final reverse lookup. Use these core rules to avoid common BIDMAS traps.
Key for all four rules: A = 4, B = 23, C = 25, D = 15, E = 2, F = 9.
🔤 Rule 1: Direct Letter Value Substitution
Locate each letter in the provided key and replace it with its exact integer value before carrying out any arithmetic operations. Letter values can change between questions, so always use the key supplied for the current question.
Example: Given D = 15, A = 4, E = 2: D + A × E → 15 + 4 × 2.
⚡ Rule 2: Follow the Order of Operations
Work out brackets first, then powers (indices), when present. Next evaluate multiplication (×) and division (÷), then addition (+) and subtraction (−). Work from left to right within each equal-priority pair of operations.
Example: 15 + 4 × 2 → 15 + 8 = 23 (NOT 19 × 2 = 38).
↔️ Rule 3: Left-to-Right Equal Precedence
When operators have equal precedence (Addition and Subtraction, or Multiplication and Division), process them strictly from left to right.
Example: C − A + E = 25 − 4 + 2 = 21 + 2 = 23, giving answer B.
Adding 4 + 2 first would incorrectly turn the expression into 25 − (4 + 2) = 19. Addition does not take priority over subtraction.
🔑 Rule 4: Target Key Reverse Lookup
Calculate the final numerical total, then match that exact number to the letter key to write the final letter answer.
Example: Numerical result = 23. Key specifies B = 23 → Final Answer = B.
Two More Worked Examples
Practise applying BIDMAS when multiplication appears on the left, then see how to avoid the common trap when multiplication appears on the right.
Standard Multiplication BIDMAS
Question: Use BIDMAS to evaluate the calculation and convert your answer to a letter using the key.
D = 23, F = 2, I = 3, P = 19, U = 13, W = 8
I × F + U = [ ? ]
Worked Method
What it's testing: Rule 2 — applying multiplication before addition according to BIDMAS.
Step-by-step evaluation:
- Substitute values: I = 3, F = 2, U = 13.
- Expression: 3 × 2 + 13
- Apply BIDMAS: Perform multiplication first → 3 × 2 = 6.
- Add remaining value: 6 + 13 = 19.
- Reverse Key Lookup: 19 corresponds to P.
Answer: P
Tip: Always highlight multiplication or division terms before starting calculation steps.
Right-Side Multiplication BIDMAS Precedence
Question: Use BIDMAS to evaluate the calculation and convert your answer to a letter using the key.
A = 4, B = 23, C = 25, D = 15, E = 2, F = 9
D + A × E = [ ? ]
Worked Method
What students do wrong: They read left-to-right and perform addition first (15 + 4 = 19), then multiply by 2 to get 38 (which is wrong!).
The correct method:
- Substitute values: D = 15, A = 4, E = 2.
- Expression: 15 + 4 × 2
- Apply BIDMAS precedence: There are no brackets or powers here, so perform multiplication before addition: 4 × 2 = 8.
- Perform addition: 15 + 8 = 23.
- Reverse Key Lookup: 23 corresponds to B.
Answer: B
Tip: After dealing with any brackets and powers, calculate multiplication and division before addition and subtraction. Work left to right only among operations with equal priority.
