Show Formula$a \times (b-c)$ $\,=\,$ $a \times b -a \times c$ An arithmetic property that distributes the multiplication across the subtraction is called the distributive property of multiplication over subtraction. Introduction$a$, $b$ and $c$ are three literals and denote three terms in algebraic form. The product of the term $a$ and the difference of the terms $b$ and $c$ can be written in the following mathematical form. $a \times (b-c)$ The product of them can be calculated by distributing the multiplication over the subtraction. $\implies$ $a \times (b-c)$ $\,=\,$ $a \times b -a \times c$ ProofLearn how to prove the distributive property of multiplication across subtraction in algebraic form by geometrical method. Verification$3$, $4$ and $7$ are three numbers. Find the product of number $2$ and subtraction of $4$ from $7$. $3 \times (7-4)$ Now, calculate the value of the arithmetic expression. $\implies$ $3 \times (7-4)$ $\,=\,$ $3 \times 3$ $\implies$ $3 \times (7-4) \,=\, 9$ Now, find the difference of the products of $3$ and $4$, and $3$ and $7$. $3 \times 7 -3 \times 4$ $\,=\,$ $21-12$ $\implies$ $3 \times 7 -3 \times 4$ $\,=\,$ $9$ Now, compare the results of both the arithmetic expressions. Numerically, they are equal. $\,\,\, \therefore \,\,\,\,\,\,$ $3 \times (7-4)$ $\,=\,$ $3 \times 7 -3 \times 4$ $\,=\,$ $9$ The Distributive Property Learning Objective(s) · Simplify using the distributive property of multiplication over addition. · 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 difference. The property states that the product of a sum or difference, such as 6(5 – 2), is equal to the sum or difference of the products – in this case, 6(5) – 6(2). Remember that there are several ways to write multiplication. 3 x 6 = 3(6) = 3 • 6. 3 • (2 + 4) = 3 • 6 = 18. Distributive Property of Multiplication over Addition The distributive property of multiplication over addition can be used when you multiply a number by a sum. For example, suppose you want to multiply 3 by the sum of 10 + 2. 3(10 + 2) = ? 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. 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.
Rewrite the expression 30(2 + 4) using the distributive property of addition. A) 30(2 + 4) + 30(2 + 4) B) 30(2) + 30(4) C) 30(6) D) 30(24) Distributive Property of Multiplication over Subtraction The distributive property of multiplication over subtraction is like the distributive property of multiplication over addition. You can subtract the numbers and then multiply, or you can multiply and then subtract as shown below. This is called “distributing the multiplier.” The same number works if the 5 is on the other side of the parentheses, as in the example below. In both cases, you can then simplify the distributed expression to arrive at your answer. The example below, 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 as well.
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) Summary The distributive properties of addition 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 then multiply. You can also multiply each addend first and then add the products. This can be done with subtraction as 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 future math courses, so understanding it now will help you build a solid math foundation. What is distributive property with example?The distributive property of multiplication over addition is applied when you multiply a value by a sum. For example, you want to multiply 5 by the sum of 10 + 3. As we have like terms, we usually first add the numbers and then multiply by 5. But, according to the property, you can first multiply every addend by 5.
What is example of distributive property of multiplication?According to the distributive property 2 × (3 + 5) will be equal to 2 × 3 + 2 × 5. Let's check to see if this is true. 2 × (3 + 5) = 2 × 8 = 16. 2 × 3 + 2 × 5 = 6 + 10 = 16. In both cases we get the same result, 16, and therefore we can show that the distributive property of multiplication is correct.
What is distributive property of division over subtraction?The distributive property states that an expression which is given in form of A (B + C) can be solved as A × (B + C) = AB + AC. This distributive law is also applicable to subtraction and is expressed as, A (B - C) = AB - AC.
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