Math Problem Statement

Perform the indicated operations: (a) 35 - (-7), (b) 35 + (-7), (c) 35 * (-7).

Solution

Let's analyze the image step by step:

The problem asks to perform the indicated operations. The expressions are as follows:

Part 1 of 4: 35(7)35 - (-7)

Using the rule that subtracting a negative number is equivalent to adding: 35(7)=35+7=4235 - (-7) = 35 + 7 = 42 Answer: 42


Part 2 of 4: 35+(7)35 + (-7)

Adding a negative number is equivalent to subtraction: 35+(7)=357=2835 + (-7) = 35 - 7 = 28 Answer: 28


Part 3 of 4: 35(7)35 \cdot (-7)

Multiplying a positive number by a negative number results in a negative product: 35(7)=24535 \cdot (-7) = -245 Answer: -245

Would you like detailed explanations of these rules? Here are some related questions for practice:

  1. What is 12(3)12 - (-3)?
  2. Simplify 15+(10)-15 + (-10).
  3. Solve 8(2)8 \cdot (-2).
  4. Perform 501550 - 15.
  5. Explain why subtracting a negative number is the same as adding.

Tip: When dealing with operations involving negative numbers, visualize the movement on a number line—it helps reinforce the concept!

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Math Problem Analysis

Mathematical Concepts

Arithmetic operations
Negative numbers
Multiplication and subtraction of integers

Formulas

a - (-b) = a + b
a + (-b) = a - b
a * (-b) = - (a * b)

Theorems

Rules for operations with negative numbers

Suitable Grade Level

Grades 6-8