How to Compare Fractions and Decimals

A step-by-step guide to Comparing Fractions and Decimals

Comparing fractions and decimals is an essential skill in mathematics. Here’s a step-by-step guide to help you master this skill.

Step 1: Understand the basics

• A fraction represents a part of a whole and is written as \(\frac{a}{b}\), where ‘a’ is the numerator and ‘b’ is the denominator.
• A decimal represents a part of a whole and is written using digits and a decimal point (e.g., 0.5, 0.25).

Step 2: Convert fractions to decimals or vice versa

To compare fractions and decimals, it’s easiest to convert one into the other so you’re comparing two values in the same format.

To convert a fraction to a decimal:

• Divide the numerator by the denominator: \(a ÷ b\).
• Write the result as a decimal.

Example: \((\frac{3}{4} = 3 ÷ 4 = 0.75\)

To convert a decimal to a fraction:

• Write the decimal as a fraction with a denominator of 10, 100, 1000, etc., depending on the number of decimal places.
• Simplify the fraction, if necessary.

Example: \(0.75 = \frac{75}{100 }= \frac{3}{4}\) (simplified)

Step 3: Compare the values

• If both values are in decimal form, compare them by looking at each digit from left to right.
• If both values are in fraction form, find a common denominator and compare the numerators.
• If one value is still a decimal and the other a fraction, choose the format you find easiest to compare and convert the remaining value to that format.

Example: Compare \(\frac{3}{4}\) and 0.6

• Convert \(\frac{3}{4}\) to a decimal: \(\frac{3}{4} = 0.75\)
• Compare 0.75 and 0.6: \(0.75 > 0.6\), so \(\frac{3}{4} > 0.6\)

Step 4: Practice

The more you practice comparing fractions and decimals, the better you’ll become at it. Try solving problems with different fractions and decimals to build your skills and confidence.