➕Addition

You have 3 candies in your pocket and a friend hands you 5 more. How many now? $3 + 5 = 8$ — you just performed the oldest operation people learn: addition.

Addition does exactly one thing: combine two groups into one. Simple as it looks, it is the foundation for subtraction, multiplication and, eventually, algebra.

Combine, then count

Pour 3 candies and 5 candies into the same bowl, count again, and you get 8. The result of addition is called the sum.

The friendliest fact about addition: you may swap the order.

• $3 + 5 = 5 + 3 = 8$ — that is the commutative law;
• A room with 4 rows of 6 seats holds the same 24 people as one with 6 rows of 4.

When adding several numbers, pair them any way you like: for $27 + 48 + 2$, work out $48 + 2 = 50$ first and the answer appears instantly. Pairing to make tens is the first speed trick, and it works because of the associative law.

7 + 15 = ?

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Column addition: carry past ten

For big numbers, line the digits up in columns and start from the ones. Here is $358 + 467$:

	Hundreds	Tens	Ones
	3	5	8
+	4	6	7
	8	2	5

• Ones: $8 + 7 = 15$ — write 5, carry 1 to the tens;
• Tens: $5 + 6 + 1 = 12$ — write 2, carry 1 again;
• Hundreds: $3 + 4 + 1 = 8$.

The answer is 825. Every step is "carry when you hit ten" — the same rule that runs place value.

Estimate before you compute

Before computing, say a rough number out loud: 358 is near 360, 467 is near 470, so $360 + 470 = 830$. The exact answer is 825, close to 830 — nothing went wrong. If you get 425 or 1525, you know instantly that something did.

Estimating never replaces exact work, but it is a free safety check. You can train it fully in the estimation lesson.

Addition words in word problems

These phrases usually signal addition: in all, altogether, total, combined, "some more arrive".

Watch one exception: "Ming has 34 cards and Amy has 8 more than him." To find Amy's cards you add: $34 + 8 = 42$. Seeing "more" does not always mean subtract — first ask who is growing.

Check yourself

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Quick quiz

↺ Try again

1. 1. 358 + 467 = ?

   815825925

2. 2. Which statement is always true?

   a + b = b + aa + b > aa + b = a − b

3. 3. Estimate first: 396 + 505 is closest to which number?

   8009001000