Short Multiplication — Multiplying by a Single Digit
Short multiplication is used when one number is a single digit. Write the numbers in columns, multiply each digit of the larger number by the single digit working right to left, and carry any tens to the next column.
Estimation check: \(347 \times 6 \approx 350 \times 6 = 2100\). Our answer 2082 is close — reasonable!
Checking with the inverse operation: is \(347 \times 6 = 2082\) correct?
Step 1
Multiplication and division are inverse (opposite) operations — one undoes the other. If \(347 \times 6 = 2082\), then \(2082 \div 6\) should give back 347.
Step 2
\(2082 \div 6 = 347\) ✓ — matches the original number, so the multiplication is confirmed correct.
💡 Estimation vs inverse checking: estimation only tells you the answer is roughly right (a wrong answer close to the estimate would slip through). The inverse-operation check is exact — dividing the product by one factor must give back the other factor precisely, with no rounding.
✓ Quick Check 1 — Short Multiplication
Question 1 of 10
Long Multiplication — Multiplying by Two or More Digits
When multiplying by a two-digit number, use the grid method or traditional column method. Both split the calculation into manageable parts and then add the partial products.
Example 3 — Calculate \(347 \times 23\) using the column method
Step 1
Multiply \(347 \times 3\) (the ones digit of 23): \(= 1041\).
Step 2
Multiply \(347 \times 20\) (the tens digit of 23): write a 0 placeholder, then \(347 \times 2 = 694\), giving \(6940\).
Step 3
Add the partial products: \(1041 + 6940 = \mathbf{7981}\).
Example 4 — Calculate \(56 \times 48\) using the grid method
Common mistake: Forgetting the 0 placeholder when multiplying by the tens digit. \(347 \times 2\) (for the tens) is really \(347 \times 20\) — the 0 shifts every digit one place to the left.
✓ Quick Check 2 — Long Multiplication
Question 1 of 10
Real-Life Multiplication — Unit Rates, Wages and Scaling
Real-life multiplication problems often involve unit rates (price per item, pay per hour) or scaling up (double a recipe, cost of multiple items). Identify what is being multiplied and what the multiplier is.
Example 5 — Wages calculation
Step 1
A worker earns £12 per hour and works 38 hours. Total = \(38 \times 12\).
A box holds 24 items. There are 37 boxes. How many items in total?
4
145 × 6
5
312 × 15
6
327 × 5
7
46 × 19
8
A crate holds 18 bottles. There are 45 crates. How many bottles in total?
9
218 × 7
10
129 × 22
⚠ Things to Watch Out For
Forgetting to add the carry in short multiplication: In 347 × 6, after 7×6=42, write 2 and carry 4. Then 4×6=24, plus the 4 carried = 28. The carry must be added AFTER multiplying.
Long multiplication — forgetting to indent: When multiplying by the tens digit, shift the second row ONE place to the left (or add a zero placeholder). Forgetting this makes the answer ten times too small.
Partial products order: In 347 × 23, multiply by 3 first (units), then by 2 (tens, indented). Then add the two rows.
Multiplying by zero: Any number × 0 = 0. But 0 in long multiplication is a placeholder — don't skip that row, write zeros and continue.
Not estimating first: Estimate before calculating: 347 × 23 ≈ 350 × 20 = 7,000. If your answer is 798 or 79,810, you know something went wrong.