AI Tutor
Imagine you need to buy 6 tickets to a theme park, and each ticket costs 24.Youdonotneedpaperoracalculatortomultiply24. You do not need paper or a calculator to multiply 6 \times 24$ if you know how to break numbers apart.

The Area Model and Splitting Numbers

Over 2,300 years ago, Greek mathematicians like Euclid showed that multiplying two numbers is the same as finding the area of a rectangle. When a rectangle is wide, you can split it into smaller pieces and add their areas together.
This rule is the distributive property, which states that multiplying a factor by a sum gives the same result as multiplying that factor by each addend separately: a×(b+c)=(a×b)+(a×c)a \times (b + c) = (a \times b) + (a \times c).
To decompose a number means to break it down into friendlier parts, such as tens and ones.
When we rewrite 6×246 \times 24 as (6×20)+(6×4)(6 \times 20) + (6 \times 4), we are expanding the product.

Decomposing Over Addition

Let's look at another calculation: 7×537 \times 53. Decompose 53 into tens and ones as (50+3)(50 + 3).
7×53=7×(50+3)=(7×50)+(7×3)7 \times 53 = 7 \times (50 + 3) = (7 \times 50) + (7 \times 3)
Since 7×50=3507 \times 50 = 350 and 7×3=217 \times 3 = 21, we add the two partial products: 350+21=371350 + 21 = 371.
What if a factor is extremely close to an easy benchmark number like 50 or 100, but just a little below it?

Distributing Over Subtraction