Question

1. explain how to evaluate the expression.

10 × 4 × (12 − 8)

1. write and evaluate two equivalent numerical expressions using brackets or braces that show the distributive property.

1. you have 12 blue sticky notes, 8 purple sticky notes, 5 green sticky notes, and 5 red sticky notes. you keep 2 sticky notes, and then divide the rest equally between 4 friends. how many sticky notes does each friend receive?

_____ sticky notes

Explanation:

Question 18

Step1: Evaluate innermost parentheses

First, calculate the expression inside the innermost parentheses: \(12 - 8 = 4\).

Step2: Evaluate the brackets

Next, use the result from Step 1 to evaluate the expression inside the brackets: \(4\times4 = 16\).

Step3: Evaluate the final multiplication

Finally, multiply the result from Step 2 by 10: \(10\times16 = 160\).

The Distributive Property states that \(a\times(b + c)=a\times b + a\times c\) (or \(a\times(b - c)=a\times b - a\times c\)). We can create two equivalent expressions using this property.

Example 1: Using addition
Let \(a = 5\), \(b = 3\), \(c = 2\).

• Original expression (using brackets to show grouping): \(5\times(3 + 2)\)
• Distributive form: \(5\times3 + 5\times2\)

Evaluate both:

• \(5\times(3 + 2)=5\times5 = 25\)
• \(5\times3 + 5\times2 = 15 + 10 = 25\)

Example 2: Using subtraction
Let \(a = 7\), \(b = 6\), \(c = 4\).

• Original expression (using braces to show grouping): \(7\times(6 - 4)\)
• Distributive form: \(7\times6 - 7\times4\)

Evaluate both:

• \(7\times(6 - 4)=7\times2 = 14\)
• \(7\times6 - 7\times4 = 42 - 28 = 14\)

Question 22

Step1: Calculate total sticky notes

First, find the total number of sticky notes: \(12 + 8 + 5 + 5 = 30\).

Step2: Subtract the kept notes

Subtract the 2 sticky notes you kept: \(30 - 2 = 28\).

Step3: Divide by the number of friends

Divide the remaining notes by 4 friends: \(28\div4 = 7\).

Answer:

To evaluate \(10\times[4\times(12 - 8)]\), follow the order of operations (PEMDAS/BODMAS):

1. Innermost parentheses: \(12 - 8 = 4\)
2. Brackets: \(4\times4 = 16\)
3. Final multiplication: \(10\times16 = 160\)

Question 20