What is the Distributive Property?
The distributive property helps us multiply a number by a group of numbers added together.
It tells us that multiplying a number by a sum is the same as multiplying the number by each addend and then adding the products. In math language: \( a \times (b + c) = a \times b + a \times c \)
How Does It Work?
1️⃣ Break apart one of the numbers into easier parts (like tens and ones)
2️⃣ Multiply the other number by each part separately
3️⃣ Add all the products together to get your final answer
Let's Try Some Examples!
Example 1: Cookie Boxes
You have 4 boxes, and each box has 12 cookies. How many cookies total?
Instead of calculating 4 × 12, let's break it down:
12 = 10 + 2, so:
4 × (10 + 2) = (4 × 10) + (4 × 2) = 40 + 8 = 48 cookies!
See how we have 4 rows of 12 cookies? That's the same as 4 rows of 10 plus 4 rows of 2!
Example 2: Interactive Practice
Let's solve 5 × 13 using the distributive property:
First, break 13 into parts: 13 = ___ + ___
13 = 10 + 3
Now calculate: 5 × (10 + 3) = (5 × 10) + (5 × 3) = ___ + ___ = ___
50 + 15 = 65
Great job! You just used the distributive property!
Parent Tips 🌟
- Use real objects: Show the property with blocks or snacks - group them to demonstrate breaking numbers apart.
- Make it a game: Challenge your child to find different ways to break numbers (like 12 as 7+5 or 8+4) and see they all give the same result.
- Connect to mental math: Show how this method makes mental calculations easier (like calculating 6×15 as 6×10 + 6×5 = 60+30=90).