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Arithmetic Calculator

Step-by-step column arithmetic — see exactly how to add, subtract, multiply or divide any two numbers. Every carry, borrow and partial product is shown so you understand the method, not just the answer.

ARITHMETIC CALCULATOR

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ARITHMETIC CALCULATOR — STEP BY STEP

Addition — step by step

Arithmetic Calculator Explained

Core concepts, classroom applications, and plain-English explanations for all audiences.

When do you actually use this?

At a supermarket, you're mentally adding up whether £3.49 + £1.75 + £4.20 stays under a tenner. At a café, you're dividing a £28.80 bill between four people. These four operations — add, subtract, multiply, divide — run every financial decision you'll ever make.

Worked example

"You buy 3 items at £4.75 each and pay with £20. How much change?"

Step 1: 3 × £4.75 = £14.25 (multiplication)

Step 2: £20.00 − £14.25

Borrow from tens: £20.00 − £14.25

Result: £5.75 change

Quick check: 3 × £5 = £15, so change should be just over £5. ✓

One mistake to avoid

  • ✗ Skipping the estimate: Always ask "does this answer feel roughly right?" before accepting it. 247 × 36 should be around 250 × 36 = 9,000 — if your answer is 89,892 something went wrong.

The column method works on any size number

Whether you're adding 47 + 38 or 4,700 + 3,800, the same column process applies. The digits just shift left by place value.

The methods explained

How column arithmetic works

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Addition: column method with carrying
Line up the digits by place value (units under units, tens under tens). Add each column from right to left. If the sum is 10 or more, write the units digit and carry the tens digit to the next column.
2 4 7
+ 1 8 6
─────
4 3 3

Units: 7+6=13 → write 3, carry 1
Tens: 4+8+1=13 → write 3, carry 1
Hundreds: 2+1+1=4
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Subtraction: column method with borrowing
Line up digits by place value. Subtract each column from right to left. If the top digit is too small, borrow from the next column to the left — add 10 to the current column and reduce the column to the left by 1.
4 5 2
- 1 8 7
─────
2 6 5

Units: 2<7 → borrow → 12-7=5
Tens: 5-1-8<0 → borrow → 15-1-8=6
Hundreds: 4-1-1=2
×
Multiplication: long multiplication
Multiply the top number by each digit of the bottom number separately, keeping track of place value (shift one position left for each digit). Then add all the partial products together. Each partial product uses carrying just like addition.
247
× 36
────
1482 (247 × 6)
+ 7410 (247 × 30)
────
8892
÷
Division: long division
Work through the dividend digit by digit from left to right. At each step, ask how many times the divisor fits into the current number. Multiply, subtract, then bring down the next digit. Any leftover after all digits is the remainder.
247 ÷ 8

8 into 2: 0 — bring in next digit
8 into 24: 3 (3×8=24), rem 0
8 into 07: 0 (0×8=0), rem 7

Result: 30 remainder 7
As decimal: 30.875