Problem 70 - Algebra 1: Concepts and Skills

Question

Complete the statement using \(<,>,\) or \(=\). \(\frac{8}{5} ? 1.6\)

Step-by-Step Solution

Answer

\(\frac{8}{5} = 1.6\)

Step 1: Convert Fraction to Decimal

To convert the given fraction \(\frac{8}{5}\) to a decimal, perform the division operation which gives 1.6.

Step 2: Compare the decimal representation of the fraction and the given decimal

Now compare the decimal number obtained in Step 1 (i.e., 1.6) with the given decimal number (i.e., 1.6). Since both the numbers are the same, hence their relationship is equal to each other.

Key Concepts

Converting Fractions to Decimals

Converting fractions to decimals is a fundamental skill in mathematics. It helps in comparing numbers and understanding their relationships better. To convert a fraction into a decimal, you simply divide the numerator (top number) by the denominator (bottom number). For instance, if you have the fraction \( \frac{8}{5} \), you would perform the division \( 8 \div 5 \).

• The numerator is divided by the denominator.
• The result is a decimal representation of the fraction.

Once you have a fraction in decimal form, it becomes easier to compare it with other decimals. In our example, dividing 8 by 5 gives us 1.6. Therefore, the fraction \( \frac{8}{5} \) is equivalent to the decimal 1.6. This conversion lays the groundwork for easy comparison between different numerical forms.

Division Operation

The division operation is a crucial arithmetic process used not only for converting fractions to decimals but also for many other calculations. When you perform a division, you are essentially splitting a quantity into equal parts. In the context of fractions, this involves dividing the numerator by the denominator.
Let's take the exercise of dividing 8 by 5 as an example. Here’s what you do:

• Set up the division by writing 8 under the division bar and 5 outside.
• Determine how many times 5 can go into 8. In this case, it goes 1 time.
• Subtract the product of 5 and 1 from 8, giving a remainder.
• Continue this process to find a decimal, adding zeros if necessary.

As you follow these steps, the result will be 1.6, demonstrating the conversion from a fraction to a decimal through division. Mastering this operation will greatly enhance your mathematical skills.

Decimal Comparison

Decimal comparison is an important concept when you need to determine the relationship between two decimal numbers. This involves looking at the digits in each place value, starting from the left.
For comparing two decimals like 1.6 and 1.6, follow these steps:

• Start by comparing the tenths place. If the digits are the same, move to the next place value.
• Here, both numbers have 1 in the ones place and 6 in the tenths place.
• Since these digits are identical, the numbers are equal.

When comparing more complex decimals, continue this process as needed, examining hundredths, thousandths, and beyond if necessary. Understanding decimal comparison allows you to see which number is greater, lesser, or if they are equal. By mastering these steps, you'll confidently tackle similar problems with ease.