Problem 70 - Algebra 1

Question

Evaluate the expression. Use estimation to check your answer. $$ -15.7+0.01+(-34.44) $$

Step-by-Step Solution

Answer

-50.13

Step 1: Add the negative numbers

Start by adding the negative numbers together. -15.7 and -34.44 together yields -50.14. It's important to align the decimal points when adding these numbers.

Step 2: Add the positive number

Next, add the positive number 0.01 to -50.14. This results in -50.13. This is the final answer since there are no more numbers to add.

Step 3: Estimation

An estimation can be done by rounding the numbers to the nearest integers, i.e., -16 + 0 + (-34), which yields -50. Comparing this with the actual result of -50.13 shows that our result is reasonable.

Key Concepts

Estimation

Making an estimation can be a powerful tool in mathematics. It allows us to quickly gauge the reasonableness of our answers.
In algebraic expressions, estimation involves simplifying numbers by rounding them to their nearest whole number or to another simpler form. This makes them easier to add or subtract.

In our exercise, we rounded the numbers

• -15.7 rounded to -16
• 0.01 rounded to 0
• -34.44 rounded to -34

Adding these rounded numbers gives us an estimated result of -50. Though not exact, this estimate is close to the actual result of -50.13, verifying the accuracy of our calculations. Estimation is especially useful when you're solving problems in real-life situations where quick judgments are necessary.

Negative Numbers

Dealing with negative numbers might seem tricky at first, but it's all about understanding that these are numbers less than zero.
When you add negative numbers together, it's like combining debts: the more you add, the larger the debt gets.

In the step-by-step solution, we first added the two negative numbers:

• -15.7
• -34.44

The addition results in -50.14.
Remember that when both numbers have the same sign (both negative in this case), you simply add their absolute values (15.7 + 34.44) and keep the negative sign for the result. Negative numbers are fundamental in math because they enable representation and calculation of many real-world quantities, such as temperatures below freezing or financial losses.

Decimal Addition

Adding decimals means you need to pay closer attention to the placement of the decimal point. Always align the decimals before adding to ensure accuracy. This method helps you keep track of place values, similar to lining up columns in whole-number addition.

In our problem, the operation included decimals:

• -15.7
• 0.01
• -34.44

When adding these, we first calculate i.e.,\(-15.7 + (-34.44) = -50.14\).

Then, we add 0.01, resulting in -50.13.
Keeping the decimal points aligned allows for correct addition of the values in each place, reinforcing the precision of the operation. Decimal addition is key in many measurements and financial calculations, making it a necessary skill for algebraic proficiency.