Question

Perform the indicated operations. Give exact answers. \(8.17-3.05=\) ______

Short answer

The exact answer is 5.12.

Step-by-step solution

Identify the Operation

The operation you need to perform is subtraction. You have the expression \(8.17 - 3.05\).

Align for Subtraction

Write down the numbers you are subtracting, aligning them by their decimal points:\[\begin{array}{c} 8.17 \- 3.05 \\hlinetime\end{array}\]

Subtract the Hundredths Place

Subtract the digits in the hundredths place: \(7 - 5 = 2\). Write 2 in the hundredths place in the result.

Subtract the Tenths Place

Subtract the digits in the tenths place: \(1 - 0 = 1\). Write 1 in the tenths place in the result.

Subtract the Units Place

Subtract the digits in the units place: \(8 - 3 = 5\). Write 5 in the units place in the result.

Write Down the Final Result

Combine the results from each place value to get the final result: \(8.17 - 3.05 = 5.12\).

Key concepts

Decimal Subtraction

Decimal subtraction is an essential skill in mathematics that involves subtracting one decimal number from another. Decimals are numbers that have a whole number part and a fractional part separated by a decimal point. When performing decimal subtraction, aligning numbers by their decimal points is crucial. This alignment ensures that digits in corresponding place values such as tenths, hundredths, and units are correctly subtracted. To perform decimal subtraction effectively, follow these steps:

• Align the decimal points of the numbers vertically.
• Subtract each digit starting from the rightmost side (hundredths place) to the left (units place).
• Borrow from the next higher digit if needed, just like in whole number subtraction.

Decimal subtraction requires practice to master, but with systematic alignment and subtraction, it can be executed smoothly.

Step-by-Step Solution

A step-by-step solution is a methodical approach to solving mathematical problems. It involves breaking down a problem into smaller, manageable parts or steps. Let’s examine how this approach applies to subtracting decimals like in the exercise with the expression \(8.17 - 3.05\).

Steps to Subtract Decimals

• Identify the Operation: Recognize that subtraction is needed.
• Align the Numbers: Make sure to write the numbers one below the other, aligning their decimal points.
• Subtract Digit by Digit: Begin subtracting from the rightmost digits to the left, handling each decimal place (hundredths, tenths, units) separately.
• Write the Result: After subtracting each digit, combine the remaining numbers into your final answer.

This step-by-step guide reinforces a logical procedure, allowing for accuracy and a firm understanding of decimal operations.

Mathematics Education

Mathematics education plays a vital role in developing critical thinking and problem-solving skills. It is not just about learning numbers but also about understanding their applications and implications in real life. Among these fundamental skills, learning operations with decimals, such as addition, subtraction, multiplication, and division, is crucial. Decimals are used daily in activities like handling money, measuring quantities, and more, making decimal operations a foundational concept. Teachers and educational resources focus on clear explanations and repetitive practice to instill confidence and comprehension in students. Exposing learners to varied exercises and step-by-step problem-solving encourages exploration and understanding. Ultimately, the goal of mathematics education is to equip students with skills that are not only academically beneficial but also applicable in their everyday lives, ensuring they can solve problems efficiently and accurately.