Arithmetic FAQs – Your Questions Answered
Below are answers to the questions learners ask most often. Each answer is clear and direct — no jargon, no confusion.
General Questions
What are the four arithmetic operations?
Addition (+), subtraction (−), multiplication (×), and division (÷). Together they are the building blocks of all mathematics.
What does BODMAS / PEMDAS mean?
These are mnemonics for the order of operations: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (left to right), Addition and Subtraction (left to right). Always follow this order in any expression.
Is division the same as multiplication?
They are inverse operations. Dividing by 4 gives the same result as multiplying by 1/4. They undo each other.
Addition and Subtraction
Can I add numbers in any order?
Yes — addition is commutative: a + b = b + a. Subtraction is not: a − b ≠ b − a.
What is carrying in addition?
When a column total exceeds 9, the tens digit is carried to the next column. Example: 7 + 8 = 15, write 5 carry 1.
What is borrowing in subtraction?
When the top digit is smaller, you borrow 10 from the column to the left, reducing that digit by 1 and adding 10 to the current column.
Multiplication and Division
Why is anything multiplied by zero equal to zero?
Multiplication means repeated addition. Zero groups of anything is nothing.
Why can't you divide by zero?
Because no number multiplied by zero can ever equal a non-zero value. The result is undefined — not infinity, not zero, just undefined.
How do I divide fractions?
Use Keep-Change-Flip (KCF): keep the first fraction, change ÷ to ×, flip the second. Example: 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
Decimals and Fractions
How do I add decimals?
Line up the decimal points. Pad with zeros if needed. Then add as normal whole numbers.
How do I multiply decimals?
Ignore the decimal points and multiply as whole numbers. Count total decimal places in both numbers and insert the point that many places from the right of the answer.
What is a mixed number?
A number with a whole part and a fraction part, e.g. 3¼. Convert to an improper fraction to multiply or divide: 3¼ = 13/4.
Negative Numbers
What is a negative times a negative?
Positive. The rule: same signs → positive product; different signs → negative product.
What is −5 − −3?
−5 − (−3) = −5 + 3 = −2. Subtracting a negative is the same as adding.
Key Takeaways
- BODMAS/PEMDAS determines the order of operations.
- Division by zero is undefined.
- Inverse operations undo each other — use this to check answers.
- Negative × negative = positive; negative × positive = negative.
- For fractions: keep denominators the same for + and −; multiply straight across for ×; use KCF for ÷.