Find a fraction that is equivalent to 1.5/9 with a whole number in both the numerator and denominator
The correct answer and explanation is:
✅ Correct Answer:
An equivalent fraction to 1.5/9 with whole numbers in both the numerator and denominator is:
3/18
📚 Explanation (300 words):
The original fraction is 1.5/9. However, fractions are typically expressed using whole numbers (integers) in both the numerator and the denominator. Since 1.5 is a decimal, we need to eliminate the decimal to make it a proper fraction.
🔢 Step 1: Convert the decimal to a whole number
To remove the decimal in 1.5, we can multiply both the numerator and denominator by 2: 1.5×29×2=318\frac{1.5 \times 2}{9 \times 2} = \frac{3}{18}
This works because multiplying both the numerator and denominator of a fraction by the same number does not change its value—it just gives us an equivalent fraction.
💡 Why is this valid?
Let’s look at the value of the original fraction: 1.59=0.1666…\frac{1.5}{9} = 0.1666\ldots
Now check the value of the new fraction: 318=0.1666…\frac{3}{18} = 0.1666\ldots
Both fractions have the same decimal representation, confirming that 1.5/9 and 3/18 are equivalent.
🔄 Simplifying Back:
If you simplify 3/18, you get: 3÷318÷3=16\frac{3 \div 3}{18 \div 3} = \frac{1}{6}
Interestingly, this shows that: 1.59=16\frac{1.5}{9} = \frac{1}{6}
✅ Conclusion:
The fraction 3/18 is equivalent to 1.5/9, and both have a value of 1/6 when simplified. This method of eliminating decimals in fractions is a useful skill in algebra and basic arithmetic, ensuring we work with clean, whole-number values.