Multiplying by 1
7 × 1 means one group of 7. So the answer is 7. Nothing changed.
Step 1: Let's Learn
Read it, or press Listen and follow the words.
Multiplying by 0
7 × 0 means seven groups with nothing in them. Seven lots of nothing is still nothing.
And the other way round
0 × 7 means no groups at all. Also nothing.
Dividing by 1
7 ÷ 1 means sharing 7 between one person. They get all 7.
Why zero and one behave oddly
7 × 0 means seven groups with nothing in each, so the total is nothing: 0. And 0 × 7 means no groups of seven at all, which is also 0. Meanwhile 7 × 1 means seven groups of one, which is 7, and 1 × 7 means one group of seven, also 7.
What these two are called
One is the identity for multiplication — multiplying by it changes nothing. Zero is the annihilator: multiplying by it destroys everything and leaves zero. You do not need those words yet, but the behaviours are worth recognising as rules rather than facts to memorise one at a time.
The confusion with addition
Adding zero changes nothing, but multiplying by zero wipes everything out. Many mistakes come from carrying the addition habit into multiplication and writing 7 × 0 = 7. Say the meaning out loud — "seven groups of nothing" — and the answer is obvious.
Step 2: Try It Yourself
Tap and try it out.
1 + 1 + 1 + 1 + 1 + 1 + 1 = 7
7 × 1 = 7
7 rows of 1 makes 7.
Step 3: Watch an Example
One step at a time.
Watch Ana Explain Zero
Ana is asked why 6 × 0 is 0.
- Step 1
She reads it as six groups of nothing.
Step 4: Your Turn
Practice makes it stick.
Empty Plates
Problem 1 of 2
5 plates have no biscuits on them. How many biscuits are there?
biscuits
One Bag
Problem 2 of 2
One bag holds 9 marbles. How many marbles in all?
marbles
Zero and One
1 of 4
8 × 1 = ?
2 of 4
8 × 0 = ?
3 of 4
0 × 6 = ?
4 of 4
9 ÷ 1 = ?
Step 5: Quick Check
Show what you know.
Question 1 of 2
7 × 0 = ?
Question 2 of 2
Why does 6 × 1 = 6?
What You Learned
- Multiplying by 1 leaves a number alone.
- Multiplying by 0 always gives 0.
- Reading it as "groups of" explains both.