Answer:

1. C. 7/10

2. B. 10

3. C. 6 8/15

4. D. 4 11/24

5. A. 3

Step-by-step explanation:

Hope it helps

Answer:      

Rewrite the expression 10(15 – 6) using the distributive property of subtraction.

A) 10(6) – 10(15)

B) 10(9)

C) 10(6 –15)

D) 10(15) – 10(6)

Step-by-step explanation:

According to this property, you can add the numbers and then multiply by 3.

3(10 + 2) = 3(12) = 36. Or, you can first multiply each addend by the 3. (This is called distributing the 3.) Then, you can add the products.

U01_L4_T2_text_image1.png

The multiplication of 3(10) and 3(2) will each be done before you add.

3(10) + 3(2) = 30 + 6 = 36. Note that the answer is the same as before.

You probably use this property without knowing that you are using it. When a group (let’s say 5 of you) order food, and order the same thing (let’s say you each order a hamburger for $3 each and a coke for $1 each), you can compute the bill (without tax) in two ways. You can figure out how much each of you needs to pay and multiply the sum times the number of you. So, you each pay (3 + 1) and then multiply times 5. That’s 5(3 + 1) = 5(4) = 20. Or, you can figure out how much the 5 hamburgers will cost and the 5 cokes and then find the total. That’s 5(3) + 5(1) = 15 + 5 = 20. Either way, the answer is the same, $20.

The two methods are represented by the equations below. On the left side, we add 10 and 2, and then multiply by 3. The expression is rewritten using the distributive property on the right side, where we distribute the 3, then multiply each by 3 and add the results. Notice that the result is the same in each case.

The same process works if the 3 is on the other side of the parentheses, as in the example below.

U01_L4_T2_text_image2.png

Example

Problem

Rewrite the expression 5(8 + 4) using the distributive property of multiplication over addition. Then simplify the result.

40 + 20 = 60

In the original expression, the 8 and the 4 are grouped in parentheses. Using arrows, you can see how the 5 is distributed to each addend. The 8 and 4 are each multiplied by 5.

The resulting products are added together, resulting in a sum of 60.

Answer             5(8 + 4) = 5(8) + 5(4) = 60