Which fraction below is equivalent to 10/12?
The correct answer and explanation is:
The equivalent fraction to 10/12 is 5/6.
Explanation:
To find an equivalent fraction, you can simplify the original fraction by dividing both the numerator (the top number) and the denominator (the bottom number) by their greatest common divisor (GCD). In the case of 10/12, the greatest common divisor of 10 and 12 is 2.
- Start by identifying the GCD of 10 and 12, which is 2.
- Divide both the numerator and denominator by 2:
- Numerator: 10 ÷ 2 = 5
- Denominator: 12 ÷ 2 = 6
Thus, 10/12 simplifies to 5/6.
This process works because dividing both parts of a fraction by the same number doesn’t change its value. You’re essentially scaling the fraction down to its simplest form, making it easier to work with while maintaining its equivalence to the original fraction.
To confirm that 5/6 is equivalent to 10/12, you can cross-multiply or check if both fractions represent the same proportion. When you cross-multiply, you will get:
10 × 6 = 60
12 × 5 = 60
Since both products are equal, the fractions are indeed equivalent.
This method of simplifying fractions applies to all rational numbers. The key takeaway is that simplifying fractions helps you find the simplest form while maintaining the same value.