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## Distributive Property

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**The Distributive Property-When two addends are multiplied by**a factor, the product is the same as if each addend was by the factor and those products were addedExample: a x (b+c) = (a x b) + (a x c) or 4 x 13 = 4 x (10 + 3) = (4 x 10) + (4 x 3)**This is how we distribute**• 5 x (20 + 3) • 5 x 20 = 5 x 3 = • 100 + 15 = 115 • Try the four on your notes**The distributive property is mental math strategy that can**be used when multiplying. 43 x 5 =?**Break apart the double-digit number.**43 x 5 =? 40 3 +**Then multiply each part by 5.**43 x 5 =? 40 3 + x 5x 5**Then multiply each part by 5.**43 x 5 =? 40 3 + x 5x 5 200 15**Finally, sum your two products**43 x 5 =215 40 3 + x 5x 5 200 15 + = 215**Let’s look at another example.**53 x 6 = ?**Break apart the double-digit number.**53 x 6 = ?**Break apart the double-digit number.**53 x 6 = ? 50 3 +**Multiply each part by 6.**53 x 6 = ? 50 3 + x 6x 6**Multiply each part by 6.**53 x 6 = ? 50 3 + x 6x 6 300 18**Sum the two products.**53 x 6 = 318 50 3 + x 6x 6 300 + 18 = 318**There are three steps to the distributive property.**4 x 28 =**There are three steps to the distributive property.**4 x 28 = 1) Break apart the double-digit number.**There are three steps to the distributive property.**4 x 28 = 4 x (20 + 8) 1) Break apart the double-digit number.**There are three steps to the distributive property.**4 x 28 = 4 x (20 + 8) • Break apart the double-digit number. • Multiply each part by 4. (distribute the 4)**There are three steps to the distributive property.**4 x 28 = 4 x (20 + 8) = (4 x 20) + (4 x 8) • Break apart the double-digit number. • Multiply each part by 4. (distribute the 4)**There are three steps to the distributive property.**4 x 28 = 4 x (20 + 8) = (4 x 20) + (4 x 8) • Break apart the double-digit number. • Multiply each part by 4. (distribute the 4) • Sum the two products.**There are three steps to the distributive property.**4 x 28 = 4 x (20 + 8) = 80 + (4 x 8) • Break apart the double-digit number. • Multiply each part by 4. (distribute the 4) • Sum the two products.**There are three steps to the distributive property.**4 x 28 = 4 x (20 + 8) = 80 + 32 • Break apart the double-digit number. • Multiply each part by 4. (distribute the 4) • Sum the two products.**There are three steps to the distributive property.**4 x 28 = 4 x (20 + 8) = 80 + 32 = 112 • Break apart the double-digit number. • Multiply each part by 4. (distribute the 4) • Sum the two products.**In this example, the 5 was distributed.**5 x 38 = 5 x (30 + 8) = (5 x 30) + (5 x 8)**In this example, the 7 was distributed.**7 x 46 = 7 x (40 + 6) = (7 x 40) + (7 x 6)**1) Which of the following expressions shows the distributive**property for 5 x (3 + 7)? (5 + 3) x (5 + 7) (5 x 3) x (5 x 7) (5 x 3) + (5 x 7)**1) Which of the following expressions shows the distributive**property for 5 x (3 + 7)? Correct! (5 x 3) + (5 x 7)**2) Which of the following expressions shows the distributive**property for 3 x (9 + 4) ? (3 x 9) + (3 x 4) (3 + 9) + (3 + 4) (3 + 9) x (3 + 4)**2) Which of the following expressions shows the distributive**property for 3 x (9 + 4) ? (3 x 9) + (3 x 4) Correct!**5) Which of the following expressions is equivalent to:(5 x**9) + (5 x 3) ? 3 x (9 + 5) 5 x (9 + 3) 9 x (3 + 5)