The distributive property of multiplication on subtraction is similar to the distributive property of multiplication on addition, except for the operation of addition and subtraction. Consider an example of the distributive property of multiplication on subtraction. The distributive property of multiplication over addition is applied when we need to multiply a number by the sum of two numbers. For example, let`s multiply 7 by the sum of 20 + 3. Mathematically, we can represent this as 7 (20 + 3). The distributive property is applied to variables in the same way as to numbers. For example, we find the value of `x` in the equation -4(x – 3) = 8 with the distributive property. We first multiply -4 by x, then by -3. This means -4(x – 3) = 8 ⇒ -4x + 12 = 8. So the value of x = 1. The distributive property of addition is another name for the distributive property of multiplication over addition. This is expressed as follows: a × (b + c) = (a × b) + (a × c). In mathematics, the distributive law, also called distributive property, the law of multiplication and addition operations, symbolically expressed by A(b + C) = ab + ac; That is, monomial factor A is distributed at each term of binomial factor B + C or applied separately, resulting in the product AB + AC.
From this law it is easy to show that the result of the first addition of several numbers and the subsequent multiplication of the sum by a number is the same as first multiplying each individually by the number, and then adding the products. See also Associations Act; Commutative law. If we use the formula for distributive properties, we multiply the external term by the bracketed terms, and then add the terms to get the solution. For example, let`s solve 15 (4 + 3). We first multiply 15 by 4, then we multiply 15 by 3 and then we add the products to get the answer. This means 15 × (4 + 3) = (15 × 4) + (15 × 3) = 60 + 45 = 105. The distributive property is used when adding, subtracting, multiplying, and dividing large numbers. By grouping numbers together, we can create smaller parts, regardless of order, to solve larger equations.
It makes calculations easier and faster. For example, division 24 ÷ 6 with the distributive property of the division. Solution: We can write 24 as 18 + 6 24 ÷ 6 = (18 + 6) ÷ 6 Now let`s distribute the division operation for each factor (18 and 6) in parentheses. ⇒ (18 ÷ 6) + (6 ÷ 6) ⇒ 3 + 1 Therefore, the answer is 4. Using the distributive property formula a × (b + c) = (a × b) + (a × c), we multiply the outer term by the two terms in parentheses. This means 2(m + 2) = 22 ⇒ 2m + 4 = 22. Now the value of `m` can be calculated. That is, 2m = 22 – 4, which can be solved further, m = 9. Example: Solving expression 2(4 – 1) with the distributive law of multiplication over subtraction. Solution: 2(4 – 1) = (2 × 4) – (2 × 1) ⇒ 8 – 2 = 6 The distributive property is applicable to fractions in the same way as numbers and variables.
For example, let`s solve the expression 1/3(2/6 + 4/6) with the distributive property. We first multiply 1/3 by 2/6, then by 4/6. That is, 1/3(2/6 + 4/6) ⇒ (1/3 × 2/6) + (1/3 × 4/6) = 2/18 + 4/18 = 6/18 = 1/3. Distributive property of subtraction: The distributive law of multiplication over subtraction is expressed by A × (B – C) = AB – AC. Let`s check this with an example. We can show the division of the largest numbers using the distributive property by decomposing the larger number into two or more smaller factors. Let`s understand this with an example. Solution: Using the distributive property of multiplication, we can solve the expression as follows: 7 × (20 – 3) = (7 × 20) – (7 × 3) = 140 – 21 = 119 The distributive property of multiplication is used when we need to multiply a number by the sum of two or more additions.
The distributive property of multiplication is applicable to the addition and subtraction of two or more numbers. It is used to solve expressions simply by dividing a number among the numbers given in parentheses. For example, if we apply the distributive property of multiplication to solve the expression 4(2 + 4), we will solve it as follows: 4(2 + 4) = (4 × 2) + (4 × 4) = 8 + 16 = 24. The distributive property states that if p, q and r are three rational numbers, then the relation between the three is given as follows: p × (q + r) = (p × q) + (p × r). Example: 1/3(1/2 + 1/5) = (1/3 × 1/2) + (1/3 × 1/5) = 7/30. The formula for the distributive property is expressed as follows× (b + c) = (a × b) + (a × c); where a, b and c are the operands. Here, the number outside the parentheses is multiplied by each term in parentheses, and then the products are added. Solution: If we solve the expression 7(20 + 3) with the distributive property, we first multiply each addition by 7. This is called the distribution of number 7 between the two addends and then we can add the products. This means that the multiplication of 7(20) and 7(3) is done before addition. This results in 7(20) + 7(3) = 140 + 21 = 161. We multiply the outer term by the two terms in parentheses.
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