How Do You Know When to Add or Subtract When Using the Distributive Property of Multiplication
The Distributive Property
Learning Objective(due south)
· Simplify using the distributive property of multiplication over add-on.
· Simplify using the distributive property of multiplication over subtraction.
Introduction
The distributive property of multiplication is a very useful property that lets you simplify expressions in which you are multiplying a number by a sum or divergence. The property states that the production of a sum or deviation, such as 6(5 – 2), is equal to the sum or difference of the products – in this example, vi(5) – 6(2).
Remember that in that location are several ways to write multiplication. 3 10 6 = 3(vi) = iii • six.
3 • (2 + 4) = 3 • six = eighteen.
Distributive Property of Multiplication over Addition
The distributive holding of multiplication over addition tin can be used when you multiply a number by a sum. For example, suppose you want to multiply three by the sum of 10 + 2.
3(ten + 2) = ?
Co-ordinate to this property, you tin can add the numbers and and then multiply by 3.
3(10 + 2) = 3(12) = 36. Or, you can first multiply each addend by the 3. (This is chosen distributing the 3.) Then, you can add the products.
The multiplication of iii(ten) and three(2) will each be done before you add.
iii(x) + iii(2) = 30 + half-dozen = 36. Note that the answer is the same as before.
Yous probably use this belongings without knowing that you are using it. When a grouping (let's say v of y'all) order food, and order the same thing (let'south say you each order a hamburger for $three each and a coke for $one each), you tin can compute the beak (without tax) in ii ways. Yous can figure out how much each of you needs to pay and multiply the sum times the number of you. So, y'all each pay (3 + 1) and then multiply times 5. That'southward 5(3 + 1) = five(iv) = 20. Or, you can effigy out how much the v hamburgers will cost and the 5 cokes and then detect the total. That's 5(3) + 5(i) = xv + 5 = 20. Either way, the answer is the aforementioned, $20.
The 2 methods are represented by the equations below. On the left side, nosotros add 10 and 2, and then multiply past 3. The expression is rewritten using the distributive property on the right side, where we distribute the three, then multiply each by iii and add the results. Notice that the issue is the same in each example.
The same procedure works if the three is on the other side of the parentheses, every bit in the instance below.
| Instance | ||
| Trouble | Rewrite the expression 5(8 + 4) using the distributive property of multiplication over addition. Then simplify the result. | |
| 40 + xx = 60 | In the original expression, the 8 and the four are grouped in parentheses. Using arrows, you lot can run into how the v is distributed to each addend. The 8 and four are each multiplied by 5. The resulting products are added together, resulting in a sum of threescore. | |
| Answer 5(8 + four) = v(eight) + five(4) = 60 | ||
Rewrite the expression 30(two + 4) using the distributive property of add-on.
A) 30(2 + iv) + thirty(two + 4)
B) xxx(2) + 30(iv)
C) xxx(half dozen)
D) 30(24)
Show/Hide Answer
A) xxx(2 + 4) + 30(two + 4)
Incorrect. This would be doubling your original value. To distribute the thirty, multiply the 2 by 30 and the iv past 30. The right answer is 30(2) + 30(four).
B) thirty(2) + 30(4)
Correct. The number thirty is distributed to both the 2 and the 4, and so that both two and 4 are multiplied by thirty.
C) 30(half dozen)
Incorrect. The number 30 is non distributed in this answer. To distribute the 30, multiply the 2 by xxx and the 4 past 30. The correct reply is xxx(2) + 30(4).
D) xxx(24)
Incorrect. The digits 2 and 4 should non be combined to form 24 because the addition process is incorrect. The number 30 is non distributed in this answer. To distribute the 30, multiply the 2 past 30 and the 4 past xxx. The correct reply is thirty(2) + 30(4).
Distributive Property of Multiplication over Subtraction
The distributive property of multiplication over subtraction is like the distributive property of multiplication over add-on. You tin can subtract the numbers and then multiply, or you can multiply and and then subtract as shown below. This is chosen "distributing the multiplier."
The same number works if the 5 is on the other side of the parentheses, as in the case beneath.
In both cases, you tin can so simplify the distributed expression to get in at your answer. The instance beneath, in which 5 is the outside multiplier, demonstrates that this is true. The expression on the right, which is simplified using the distributive property, is shown to be equal to 15, which is the resulting value on the left equally well.
| Example | ||
| Problem | Rewrite the expression 20(nine – ii) using the distributive holding of multiplication over subtraction. And then simplify. | |
| 180 – 40 = 140 | In the original expression, the 9 and the 2 are grouped in parentheses. Using arrows, yous tin see how the xx is distributed to each number so that the ix and ii are both multiplied by 20 individually. Here, the resulting product of 40 is subtracted from the product of 180, resulting in an respond of 140. | |
| Answer 20(ix – 2) = 20(nine) – twenty(ii) = 140 | ||
Rewrite the expression ten(xv – six) using the distributive property of subtraction.
A) 10(6) – 10(15)
B) 10(9)
C) 10(half-dozen –fifteen)
D) 10(fifteen) – 10(six)
Bear witness/Hibernate Answer
A) 10(6) – 10(xv)
Wrong. Here a greater number would be subtracted from a lesser number, and the answer would non exist a whole number. The correct answer is 10(fifteen) – x(six).
B) 10(9)
Incorrect. The numbers in parentheses were subtracted before the number x could be distributed. The correct respond is 10(15) – 10(half-dozen).
C) x(vi –fifteen)
Incorrect. Yous probably used the commutative law instead of the distributive property. The correct reply is x(15) – 10(half-dozen).
D) 10(15) – 10(6)
Correct. The 10 is correctly distributed so that information technology is used to multiply the 15 and the 6 separately.
Summary
The distributive properties of improver and subtraction can be used to rewrite expressions for a variety of purposes. When you are multiplying a number by a sum, you can add and and then multiply. You can also multiply each addend first so add the products. This can be done with subtraction every bit well, multiplying each number in the difference before subtracting. In each case, you are distributing the outside multiplier to each number in the parentheses, so that multiplication occurs with each number before addition or subtraction occurs. The distributive property will be useful in hereafter math courses, so understanding information technology now will help you lot build a solid math foundation.
Source: http://www.montereyinstitute.org/courses/DevelopmentalMath/COURSE_TEXT_RESOURCE/U01_L4_T2_text_final.html
0 Response to "How Do You Know When to Add or Subtract When Using the Distributive Property of Multiplication"
Post a Comment