Explain how to use mental math to simplify the expression.
a.) 8 * 3 * 2
b.) 8 * 2 + 3
c.) 5 + 8 + 3
d.) 10 * 3 -4
I have to include what properties (associative, distributive etc.) I used to simplify the problems.
a.) To simplify the expression 8 * 3 * 2:
Step 1: Apply the associative property of multiplication. This states that the grouping of numbers being multiplied does not affect the product. In this case, it means we can choose any pair of numbers to multiply first. Let's start by multiplying 8 * 3.
8 * 3 = 24
Step 2: Multiply the result obtained from the previous step by 2.
24 * 2 = 48.
So, the simplified expression is 48.
Properties used: Associative property of multiplication.
b.) To simplify the expression 8 * 2 + 3:
Step 1: Multiply 8 by 2.
8 * 2 = 16.
Step 2: Add the result from the previous step to 3.
16 + 3 = 19.
So, the simplified expression is 19.
Properties used: Multiplication and addition properties.
c.) To simplify the expression 5 + 8 + 3:
Step 1: Add 5 and 8.
5 + 8 = 13.
Step 2: Add the result obtained from the previous step to 3.
13 + 3 = 16.
So, the simplified expression is 16.
Properties used: Addition property.
d.) To simplify the expression 10 * 3 - 4:
Step 1: Multiply 10 by 3.
10 * 3 = 30.
Step 2: Subtract 4 from the result obtained from the previous step.
30 - 4 = 26.
So, the simplified expression is 26.
Properties used: Multiplication and subtraction properties.
To simplify expressions using mental math, you can apply various properties and strategies. Let's go through each expression along with the properties you can use:
a.) 8 * 3 * 2:
When multiplying numbers, you can use the associative property to rearrange the order of multiplication. First, perform the multiplication of any two numbers. In this case, let's multiply 8 and 3: 8 * 3 = 24. Then, multiply the result by the remaining number: 24 * 2 = 48. So, the simplified expression is 48. Property used: associative property.
b.) 8 * 2 + 3:
For this expression, simplify multiplication first. Multiply 8 and 2: 8 * 2 = 16. Then, add the resulting product with 3: 16 + 3 = 19. So, the simplified expression is 19. No specific property used here.
c.) 5 + 8 + 3:
Simply add all the numbers together: 5 + 8 + 3 = 16. So, the simplified expression is 16. No specific property used here.
d.) 10 * 3 - 4:
Again, simplify multiplication before subtraction. Multiply 10 and 3: 10 * 3 = 30. Then, subtract 4 from the result: 30 - 4 = 26. So, the simplified expression is 26. No specific property used here.
Remember, mental math simplification relies on properties like the associative property for rearranging multiplication and maintaining the order of operations (multiplication before addition/subtraction). Additionally, be sure to follow the usual rules for simplifying expressions by performing operations in the correct order.