Question

Graded Assignment Unit Test, Part 2: Number Properties Answer the questions below. When you are finished, submit this assignment to your teacher by the due date for full credit. Total score: ____ of 15 points (Score for Question 1: ___ of 4 points) 1. Refer to Expression 1 and Expression 2. Expression 1 5 ⋅ 7 − 2 2 ⋅ 3 + 4 3 Expression 2 + ⋅ + − ⋅ − (a) What is the value of Expression 1? (b) Insert parentheses in Expression 2 so that it has a value of 13. Then show why your expression has a value of 13.

Answer 1

To find the value of Expression 1, follow the order of operations (PEMDAS/BODMAS). To insert parentheses in Expression 2 for a value of 13, consider the order of operations.

Step-by-step explanation:

To find the value of Expression 1, we follow the order of operations (PEMDAS/BODMAS) which states that we perform operations in parentheses first, followed by exponents, then multiplication and division (from left to right), and finally addition and subtraction (from left to right). In Expression 1, we start by simplifying the multiplication and division: 5 * 7 = 35 and 2 * 3 = 6. Next, we perform the addition and subtraction: 35 - 6 + 4/3. To combine the addition and subtraction terms, we first convert 4/3 to a mixed fraction: 4/3 = 1 and 1/3. Now we can add and subtract: 35 - 6 + 1 + 1/3 = 30 1/3. Therefore, the value of Expression 1 is 30 1/3.

To insert parentheses in Expression 2 and obtain a value of 13, we need to carefully consider the order of operations. One way to achieve this is by inserting parentheses around pairs of numbers that should be added or subtracted together. For example, we could write: (1 + 2) - (3 - 4) + (5 - 6) - (7 + 8) * (9 - 10). By simplifying this expression step by step, we can show that it indeed has a value of 13.

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