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Chapter 2: Problem 19

Write as an equivalent addition; then evaluate. $$35-(-10)$$

Short Answer

Expert verified
Question: Rewrite the expression 35 - (-10) as an equivalent addition and evaluate it. Answer: The equivalent addition expression for 35 - (-10) is 35 + 10. The evaluated result is 45.

Step by step solution

01

Rewrite as an equivalent addition

To rewrite the subtraction problem as an equivalent addition, we can change the sign of the second number (simply meaning, change -10 to 10) and use addition instead of subtraction: $$35-(-10)=35+10$$
02

Evaluate the expression

Now, we need to perform the addition in the transformed expression: $$35+10$$ The answer is $$45.$$

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Equivalent Addition
When we talk about equivalent addition, we're focusing on rewriting subtraction problems into a form that makes addition easier to handle. The key is to understand that subtracting a negative number is like adding a positive one. For instance, if you see a problem like \(35 - (-10)\), it might look complicated at first, but you can transform it. Here鈥檚 how:
  • Take the negative sign away from the second number, turning it from \(-10\) to \(+10\).
  • Replace the subtraction symbol with an addition symbol.
This changes \(35 - (-10)\) into \(35 + 10\). Equivalent addition simplifies calculations and helps to keep track of signs easily. As you practice, translating subtraction into equivalent addition becomes second nature.
Evaluating Expressions Simplified
Evaluating expressions involves calculating the value of a mathematical phrase. Once you have your expression written as an equivalent addition, like \(35 + 10\), the next step is straightforward. Just perform the addition:
  • Add the numbers together: \(35 + 10\).
  • This equals \(45\).
Evaluating expressions can be fun and is crucial for solving math problems correctly. Remember, take it step by step. Break down the problem into smaller parts, transform where necessary, like rewriting to addition, then solve steadily.
Handling Negative Numbers
Negative numbers can be tricky, but understanding them is crucial to mastering math problems involving addition and subtraction. A negative number is essentially a number below zero. When dealing with operations involving negatives:
  • "Subtracting a negative" turns into "adding a positive." For instance, \(-(-10)\) becomes \(+10\).
  • The signs dictate the direction you move along a number line鈥攍eft for negative, right for positive.
The transition to positive when subtracting a negative is a specific rule that streamlines calculations and clarifies the manipulation of these numbers. Always watch the signs closely, as they determine the whole course of your computation.

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Most popular questions from this chapter

For Exercises \(1-74,\) simplify. $$(5-7)^{2} \div(-2)-(-3) \div 3$$

Prep Exercise 8 For the following equation, complete the related division equation used to solve the equation. \(3 x=-15\) \(x=\) ____ solve and check. $$(-9)(-1)(2) w=-90$$

Prep Exercise 9 Every positive integer has two square roots, a ____ square root and a ____ square root. Prep Exercise 10 A negative number has ____ real square roots. find all square roots of each number. $$49$$

Simplify. $$|-18|$$

Prep Exercise 9 Every positive integer has two square roots, a ____ square root and a ____ square root. Prep Exercise 10 A negative number has ____ real square roots. find all square roots of each number. $$36$$
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