Lesson 9: The Distributive Property, Part 1

The Distributive Property, Part 1

Student Summary

When we need to do mental calculations, we often come up with ways to make the calculation easier to do mentally.

Suppose we are grocery shopping and need to know how much it will cost to buy 5 cans of beans at 79 cents a can. We may calculate mentally in this way:

$5 \boldcdot 79\\ 5 \boldcdot (70+9)\\ 5 \boldcdot 70 + 5 \boldcdot 9\\ 350 + 45\\ 395$

When we think, “79 is the same as $70 + 9$ . I can just multiply $5 \boldcdot 70$ and $5 \boldcdot 9$ and add the products together” we are using the distributive property.

In general, when we multiply two factors, we can break up one of the factors into parts, multiply each part by the other factor, and then add the products. The result will be the same as the product of the two original factors. When we break up one of the factors and multiply the parts we are using the distributive property of multiplication.

The distributive property also works with subtraction. Here is another way to find $5 \boldcdot 79$ :

$5 \boldcdot 79\\ 5 \boldcdot (80-1)\\ 5 \boldcdot 80 - 5 \boldcdot 1\\ 400 - 5\\ 395$

Visual / Anchor Chart

Standards

Building On

3.MD.7.c

Relate area to the operations of multiplication and addition.

4.NBT.5

Multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers.

5.NBT.7

Add, subtract, multiply, and divide decimals to hundredths.

Addressing

6.NS.4

Find the greatest common factor of two whole numbers less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor other than 1.

Building Toward

6.EE.3

Apply the properties of operations to generate equivalent expressions.

6.EE.4

Identify when two expressions are equivalent.

6.NS.4