Converting Decimals to Mixed Numbers: 4.18 to 4 and 2/11

To convert 4.18 (which is 4 and 18 hundredths) to a mixed number, we will follow these steps:

1. Understand the Decimal: The number 4.18 can be separated into its whole number part and its decimal part. Here, '4' is the whole number, and '.18' is the decimal part.
2. Convert the Decimal to a Fraction: The decimal '.18' can be expressed as a fraction. Since there are two digits after the decimal point, we can express it as follows:
   • Write '.18' as 18/100.
3. Simplify the Fraction: The fraction 18/100 can be simplified by finding the greatest common divisor (GCD) of 18 and 100.
   • Both numbers can be divided by 2:
   • 18 ÷ 2 = 9
   • 100 ÷ 2 = 50

   So, 18/100 = 9/50.

4. Convert the Improper Fraction to a Mixed Number: The fraction 9/50 cannot be simplified further, so we will keep it as is. Now we can write our total:
   • The mixed number can now be represented as 4 9/50.
5. Find a Common Denominator for 2/11: Since we need to verify whether this is equivalent to 4 and 2/11, we need to find a common fraction. Find a denominator that fits both fractions!
   • The least common multiple (LCM) of 50 and 11 is 550.
   • 9/50 can be converted:
6. To convert 9/50 to a denominator of 550:
• 9/50 × 11/11 = 99/550.
7. Now convert 2/11 to a denominator of 550:
• 2/11 × 50/50 = 100/550.
8. Comparing the fractions:
• We can see that 99/550 does not equal 100/550!
• Thus, 4.18 does not equal to 4 and 2/11, but is 4 and 9/50.

In conclusion, 4.18 is equivalent to 4 and 9/50 and not 4 and 2/11.