Same Math › Grades 3–4 › Break apart to multiply
What is the break apart strategy?
Break apart turns a hard multiplication fact into two easy ones. To find 7 × 8, split the 8 into 5 + 3, multiply 7 × 5 and 7 × 3, then add. The formal name is the distributive property.
- Split 8 into 5 + 3, two numbers that are easy to multiply.
- Multiply each part: 7 × 5 = 35 and 7 × 3 = 21.
- Add them: 35 + 21 = 56, so 7 × 8 = 56
Why schools teach it
Kids don't get stuck on a fact they've forgotten
Third graders are expected to use properties of operations as strategies, and the standards give this exact example: 8 × 7 = 8 × (5 + 2) = 40 + 14 = 56 (3.OA.B.5). A child who forgets 7 × 8 can still work it out from facts they know.
It's also the idea behind the area model and partial products. 23 × 4 is just 20 × 4 plus 3 × 4. Later, the same property shows up in algebra as a(b + c) = ab + ac.
At the kitchen table
What to say, and what to skip
Say this
Which facts do you already know that could help?
Fives and tens are the usual favorites.Can you split the 8 into two easier numbers?
Show me on the dots where you split it.
Drawing a line through an array makes the idea visible.Is there another way to split it?
7 × 8 is also 7 × 4 + 7 × 4. Any split works.
Skip this
Just memorize it.
Fluency is the goal by the end of 3rd grade, but break apart is how many kids get there.- Splitting both numbers at once.7 × 8 is not 5 × 5 + 2 × 3. Only one number gets split, and both parts get multiplied by the other.
- Calling it a trick.It's a property of numbers, and it works every time.
See it in action
Solving 6 × 12 by breaking it apart
Split 12 into 10 + 2
6 × 12 = 6 × (10 + 2)Multiply each part by 6
6 × 10 = 60, 6 × 2 = 12Add the two products
60 + 12 = 72
Splitting off a 10 is the most useful move, because multiplying by 10 is easy.
Free practice sheet
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Parents also ask
Is break apart the same as the distributive property?
Yes. Break apart is the classroom name; distributive property is the math name.
Why does the split use 5s and 10s?
Most kids know their 5s and 10s first, so they make the easiest partial facts.
Is it the same as the area model?
Same idea. The area model draws the split as boxes; break apart writes it as two facts.
Can you split the first number instead?
Yes. 7 × 8 can be (5 + 2) × 8 = 40 + 16. Either factor can be split.