91Ó°ÊÓ

To compare a decimal and a fraction, the first step is to convert the decimal to a fraction. This makes it easier to evaluate and compare.

For instance, let’s convert the decimal 0.8 to a fraction. Every decimal can be expressed as a fraction with a denominator of a power of 10. In this case, 0.8 is the same as \(\frac{8}{10}\).

Next, simplify the fraction if possible. Dividing both the numerator and the denominator by their greatest common divisor, which is 2, simplifies \(\frac{8}{10}\) to \(\frac{4}{5}\).

Now, 0.8 is converted to \(\frac{4}{5}\). This step is crucial so you can clearly compare two fractions.

After converting any decimal to a fraction, the next step is to compare the fractions using cross-multiplication. Here’s how it works:

Let’s compare \(\frac{1}{8}\) and \(\frac{4}{5}\). Instead of finding common denominators, you can use cross-multiplication to determine which fraction is larger.

Multiply the numerator of the first fraction by the denominator of the second fraction:
\( 1 \times 5 = 5 \)

Then, multiply the numerator of the second fraction by the denominator of the first fraction:
\( 4 \times 8 = 32 \)

By comparing the products, you can see that 5 is less than 32. Therefore: \(\frac{1}{8} < \frac{4}{5}\).

Cross-multiplication is a reliable method to avoid common denominator calculations and still effectively determine the relationship between fractions.

Comparing fractions requires understanding their relative sizes, which can be done effectively by cross-multiplication as demonstrated above.

When you compare fractions \(\frac{1}{8}\) and \0.8, the relationship can be stated as:
\(\frac{1}{8} < 0.8\)

Summarizing the steps:

• Convert any decimals to fractions.
• Simplify the fractions if possible.
• Use cross-multiplication to compare the fractions.

Now, you have shown that \(\frac{1}{8} < \frac{4}{5}\), which translates back to \(\frac{1}{8} < 0.8\). This method ensures you can accurately compare fractions and decimals every time!