Problem 50 - Algebra 1: Concepts and Skills

Question

Perform the indicated operation. $$ \frac{5.175}{1.15} $$

Step-by-Step Solution

Answer

The result of the division operation \(\frac{5.175}{1.15}\) is approximately \(4.50\) when rounded to two decimal places.

Step 1: Perform Division

Take the numerator \(5.175\) and divide it by the denominator \(1.15\). You can do this calculation using long division or a calculator.

Step 2: Rounding the Answer

It's not always necessary to round the answer. However, if the exercise requires it, make sure to round to the appropriate decimal place. In general, many exercises require rounding to two decimal places, which is common in real-world applications.

Key Concepts

Long Division

Long division is a method used to divide numbers into simpler, more understandable parts. It involves breaking down a larger number (the dividend) by a smaller number (the divisor). This method is very useful when dividing larger numbers or when you don't have access to a calculator. In the long division process, you first divide, then multiply, subtract, and finally bring down the next digit. This cycle repeats until all numbers have been used. For dividing decimals, it's important to keep track of the decimal point.

• Begin by aligning the numbers so the divisor is outside the division bracket and the dividend is inside.
• Adjust the numbers if the divisor is not a whole number. Multiply both the dividend and divisor by a power of 10 to make it whole.
• Continue the division, treating the decimal point in the dividend by bringing it straight up into the quotient of your result.

Long division with decimals might seem challenging, but with practice, it becomes a lot easier and helps build a strong foundation for tackling more complex math problems.

Rounding Numbers

Rounding numbers simplifies them while keeping their values close to what they were originally. This is especially useful in everyday life where exact precision isn't always needed. When rounding numbers after a division like in this exercise, especially if the answer is a decimal, you should often round to two decimal places.

• Check the digit right after your desired decimal place. If it is 5 or higher, round up the last number you are keeping.
• If it is 4 or lower, keep the number as it is.

For instance, if your result is 4.512 and you round to two decimal places, it would become 4.51. Rounding is helpful in making numbers easier to read and use, especially in quick estimates or daily computations.

Numerator and Denominator

The terms numerator and denominator are fundamental in the understanding of fractions and division. In any fraction, the top number is the numerator, and the bottom number is the denominator. They help express the idea of parts of a whole.

• The numerator represents how many parts we are considering.
• The denominator indicates the total number of equal parts in the whole.

In the division operation \( \frac{5.175}{1.15} \), 5.175 is the numerator, and 1.15 is the denominator. These terms help set the framework for calculating the value of the fraction. Understanding these concepts is crucial because they play a key role not only in division and fractions but in various other mathematical operations and real-world applications.