Use the properties of operation in rules for multiplying and dividing to solve
To solve problems using the properties of operations in rules for multiplying and dividing, we need to understand the following rules:
1. Multiplicative Identity Rule: The product of any number and 1 is equal to that number.
2. Associative Property Rule: The product of three or more numbers remains the same regardless of their grouping.
3. Distributive Property Rule: The product of a number and the sum or difference of two numbers is equal to the sum or difference of their individual products.
Now, let's solve an example problem using these properties:
Problem: Solve the expression 5 * (3 + 2).
Solution: We can use the distributive property rule to simplify the expression. According to the rule, the product of a number and the sum of two numbers is equal to the sum of the individual products.
So, we can rewrite the expression as (5 * 3) + (5 * 2).
Now, using the multiplication operation, we can solve each individual product:
(5 * 3) = 15
(5 * 2) = 10
Finally, we add the individual products:
15 + 10 = 25
Therefore, the solution to the expression 5 * (3 + 2) is 25.
To solve a problem using the properties of operations for multiplication and division, you can follow these steps:
1. Identify the problem: Read the problem carefully to understand what you need to solve for.
2. Determine the appropriate operation: Determine whether you need to multiply or divide to solve the problem. Look for keywords such as "times," "multiplied by," "product," "divided by," or "quotient" to determine the operation.
3. Apply the properties of multiplication and division: Use the appropriate properties of multiplication and division to simplify the problem and find the solution. Here are some key properties:
- Multiplicative Identity Property: Any number multiplied by 1 equals the original number. For example, 5 x 1 = 5.
- Zero Property of Multiplication: Any number multiplied by 0 equals 0. For example, 7 x 0 = 0.
- Commutative Property: The order of multiplication doesn't affect the result. For example, 3 x 4 = 4 x 3.
- Associative Property: The grouping of numbers being multiplied together doesn't affect the result. For example, (2 x 3) x 4 = 2 x (3 x 4).
- Division Property: Multiplying a number by its reciprocal (or multiplicative inverse) equals 1. For example, 3 x (1/3) = 1. This property can be used to simplify division problems.
4. Solve the equation step-by-step: Apply the relevant properties to simplify the equation or expression one step at a time until you find the solution.
5. Check your answer: Once you have found a solution, check the result by substituting it back into the original problem. Make sure the answer satisfies all the conditions given in the problem.
By following these steps and using the properties of multiplication and division, you can solve problems efficiently and accurately.
To use the properties of multiplication and division to solve equations, you need to understand the following rules:
1. Multiplicative Identity Rule: The product of any number and 1 is equal to the original number. For example, 5 x 1 = 5.
2. Multiplicative Property of Zero: The product of any number and 0 is equal to 0. For example, 7 x 0 = 0.
3. Multiplicative Inverse Rule: For any non-zero number, there exists a reciprocal (multiplicative inverse) such that when multiplied together, they equal 1. For example, the reciprocal of 2 is 1/2 because 2 x 1/2 = 1.
4. Division Property of Equality: If you divide both sides of an equation by the same non-zero number, the equality is preserved. For example, if 4x = 12, dividing both sides by 4 gives you x = 3.
Now let's see how these properties can be applied to solve equations:
Example 1:
Solve the equation: 2x = 8
To isolate x, we need to get rid of the coefficient 2. We can do this by dividing both sides of the equation by 2 because the Division Property of Equality states that we can divide both sides by the same non-zero number.
2x / 2 = 8 / 2
Simplifying, we get:
x = 4
So the solution to the equation 2x = 8 is x = 4.
Example 2:
Solve the equation: 3(x + 2) = 15
To solve this equation, we first need to apply the Distributive Property.
3(x + 2) = 15
3*x + 3*2 = 15
3x + 6 = 15
Now, we can isolate x by subtracting 6 from both sides:
3x + 6 - 6 = 15 - 6
3x = 9
Finally, we divide both sides by 3 to find the value of x:
3x / 3 = 9 / 3
x = 3
Therefore, the solution to the equation 3(x + 2) = 15 is x = 3.
By using the properties of multiplication and division, you can manipulate equations to solve for the unknown variable. Remember to apply these rules while performing the same operations on both sides of the equation to maintain equality.