convert this proper fraction in it’s simplest form 14 20
The correct answer and explanation is:
The given proper fraction is: 1420\frac{14}{20}
✅ Simplest Form:
To simplify the fraction, divide both the numerator and the denominator by their greatest common divisor (GCD).
- Factors of 14: 1, 2, 7, 14
- Factors of 20: 1, 2, 4, 5, 10, 20
- Common factors: 1, 2
- Greatest common factor: 2
Now divide both the numerator and the denominator by 2: 14÷220÷2=710\frac{14 \div 2}{20 \div 2} = \frac{7}{10}
✅ Final Answer:
1420=710\frac{14}{20} = \frac{7}{10}
📝 300-Word Explanation:
Simplifying fractions is a key skill in mathematics that helps make numbers easier to work with and understand. When you simplify a fraction, you reduce it to its lowest or simplest form, meaning the numerator (top number) and the denominator (bottom number) share no common factors except 1.
The given fraction is 14/20, which is a proper fraction because the numerator is smaller than the denominator. To simplify this, we find the greatest common divisor (GCD)—the largest number that evenly divides both 14 and 20.
Listing the factors of both numbers helps:
- Factors of 14 are: 1, 2, 7, 14
- Factors of 20 are: 1, 2, 4, 5, 10, 20
The common factors of 14 and 20 are 1 and 2. Among these, 2 is the greatest. So, we divide both 14 and 20 by 2: 14÷220÷2=710\frac{14 \div 2}{20 \div 2} = \frac{7}{10}
This gives us 7/10, the simplest form of 14/20. This fraction is equivalent to the original but uses smaller numbers, making it easier to understand or work with in math problems, especially in comparing, adding, or subtracting fractions.
Understanding how to simplify fractions also strengthens number sense and helps in more advanced topics like algebra and ratios. It’s a foundational skill used in everyday life—like when dividing a pizza, calculating discounts, or adjusting recipes. Always reduce fractions unless asked to keep the original form.