Problem 101 Simplify. $$ -31+(-28)-(-14)... [FREE SOLUTION]

Chapter 1: Problem 101

Simplify. $$ -31+(-28)-(-14)-17 $$

Short Answer

Expert verified

-62

Step by step solution

- Remove Parentheses

The first step is to rewrite the expression by removing the parentheses. Recall that subtracting a negative is the same as adding a positive. So, -31 + (-28) - (-14) - 17 becomes -31 + (-28) + 14 - 17.

- Combine Negatives

Now, combine all the negative numbers first. Add -31 + (-28) + 14 - 17. Start by adding -31 + (-28) = -59.

- Add Positive Numbers

Next, add the positive numbers to the result. So, add 14 to -59: -59 + 14 = -45.

- Subtract the Remaining Number

Finally, subtract 17 from -45: -45 - 17 = -62.

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Key Concepts

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

Removing Parentheses

When simplifying expressions with parentheses, the first step is to remove the parentheses properly. This means understanding the rules for negative and positive signs. If you see a negative sign right before a parenthesis, you need to distribute it to each term inside. For instance, -31 + (-28) - (-14) - 17becomes-31 + (-28) + 14 - 17. Notice how - (-14) turned into +14 because subtracting a negative is the same as adding a positive. Always change - (-x) to +x and + (-x) to -x. This simple rule helps to clear up the expression and makes it easier to manage the next steps.

Combining Negative Numbers

After removing the parentheses, the next step is combining the negative numbers together. Negative numbers have a minus sign in front of them. In this example, we have -31 + (-28) + 14 - 17. We start by adding the negative numbers. Calculate -31 + (-28): -31 + (-28) = -59. Now we have-59 + 14 - 17. When combining negative numbers, treat it like regular addition but keep the minus sign in front. Think of the negative sign as a direction on a number line. Combining negatives always gives you a larger negative number, moving you further away from zero.

Addition and Subtraction

Once the negative numbers are combined, the next step involves simple addition and subtraction. Let's continue with our example, -59 + 14 - 17. We first add 14 to -59, which is like moving 14 steps to the right on the number line from -59, resulting in -45. So, we have: -59 + 14 = -45. Lastly, subtract 17 from -45, which means moving 17 steps to the left on the number line from -45: -45 - 17 = -62. Therefore, the simplified expression is -62. As a quick tip, always perform addition first if you have both addition and subtraction in an expression. This approach helps keep the numbers manageable and reduces the potential for errors.

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91影视

Simplify. $$ -31+(-28)-(-14)-17 $$

Short Answer

Step by step solution

- Remove Parentheses

- Combine Negatives

- Add Positive Numbers

- Subtract the Remaining Number

Key Concepts

Removing Parentheses

Combining Negative Numbers

Addition and Subtraction

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