Which fraction is equivalent to 6/9? A. 18/36 B. 3/4 C. 1/3 D. 12/18
The correct answer and explanation is:
The correct answer is D. 12/18.
Explanation:
To determine which fraction is equivalent to 6/9, it helps to understand what equivalent fractions are. Equivalent fractions are different fractions that represent the same value or proportion of the whole. They occur when both the numerator (top number) and denominator (bottom number) of a fraction are multiplied or divided by the same nonzero number.
Start with the fraction 6/9. You can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD). The GCD of 6 and 9 is 3.
- Divide numerator: 6 ÷ 3 = 2
- Divide denominator: 9 ÷ 3 = 3
This means 6/9 simplifies to 2/3.
Now, check the given options to see which fraction equals 2/3 when simplified or can be converted to 6/9 by multiplying numerator and denominator:
- A. 18/36
Simplify by dividing numerator and denominator by 18:
18 ÷ 18 = 1
36 ÷ 18 = 2
This simplifies to 1/2, which is not equal to 2/3. - B. 3/4
This is already in simplest form and clearly not equal to 2/3. - C. 1/3
This is not equal to 2/3. - D. 12/18
Simplify by dividing numerator and denominator by 6:
12 ÷ 6 = 2
18 ÷ 6 = 3
This simplifies to 2/3, which is equivalent to 6/9.
Another way to confirm this is by cross-multiplying between 6/9 and 12/18:
- Multiply 6 × 18 = 108
- Multiply 9 × 12 = 108
Since both cross-products are equal, the fractions 6/9 and 12/18 are equivalent.
Therefore, 12/18 is the fraction equivalent to 6/9.