You use the distributive property in division by breaking the dividend into two or more parts (addends), dividing each part by the divisor separately, and then adding the resulting quotients together.
This method allows you to tackle larger division problems by splitting the dividend into simpler numbers that are easier to divide mentally or manage in steps.
Steps for Using the Distributive Property in Division
Applying the distributive property to division involves a few straightforward steps. Let's illustrate this with an example, similar to the one shown in the provided reference where 96 is divided by 8.
- Identify the Dividend and Divisor: In the problem 96 ÷ 8, the dividend is 96 and the divisor is 8.
- Break Down the Dividend: Separate the dividend (96) into two or more numbers that are easy to divide by the divisor (8). These parts are called addends because they add up to the original dividend. A common way is to use place value (like tens and ones) or multiples of the divisor.
- For 96, a good breakdown is 80 + 16, because both 80 and 16 are easily divisible by 8. As the reference states: "We don't have to break up 96." in only one way, but 80 + 16 works well.
- Divide Each Addend by the Divisor: Apply the division to each part you created.
- According to the reference: "We divide each addend by 8". So, you calculate 80 ÷ 8 and 16 ÷ 8.
- Add the Partial Quotients: The results of these individual divisions are called partial quotients. Add them together to find the final quotient for the original division problem.
- The reference shows: 80 / 8 + 16 / 8. The partial quotients are 10 and 2. Add the partial quotients. 10 + 2 = 12.
Example: Dividing 96 by 8 Using the Distributive Property
Let's see the steps in action using the example highlighted in the reference:
- Problem: 96 ÷ 8
- Step 1: Break 96 into addends that are easy to divide by 8. Let's use 80 and 16. (96 = 80 + 16)
- Step 2: Divide each addend by 8.
- 80 ÷ 8 = 10 (This is the first partial quotient)
- 16 ÷ 8 = 2 (This is the second partial quotient)
- Step 3: Add the partial quotients.
- 10 + 2 = 12
Therefore, 96 ÷ 8 = 12.
This method simplifies division by turning one larger problem into multiple smaller, more manageable division problems that are then combined through addition.
