What are three equivalent fractions for 1/6
The correct answer and explanation is:
Three Equivalent Fractions for 1/6:
- 2/12
- 3/18
- 4/24
Explanation (300 words):
An equivalent fraction is a fraction that represents the same part of a whole as another fraction, even though it may look different. These are created by multiplying or dividing both the numerator (top number) and the denominator (bottom number) of a fraction by the same non-zero number.
To find equivalent fractions for 1/6, we simply multiply the numerator and denominator by the same number:
- Multiply both by 2:
1×26×2=212\frac{1 \times 2}{6 \times 2} = \frac{2}{12}
So, 2/12 is equivalent to 1/6. - Multiply both by 3:
1×36×3=318\frac{1 \times 3}{6 \times 3} = \frac{3}{18}
So, 3/18 is also equivalent to 1/6. - Multiply both by 4:
1×46×4=424\frac{1 \times 4}{6 \times 4} = \frac{4}{24}
So, 4/24 is another equivalent fraction of 1/6.
This works because you’re scaling the fraction up or down evenly. You’re not changing its value—just how it’s expressed. Think of it like resizing a photo: the proportions remain the same even if the image gets larger.
This concept is important in math because it allows us to compare, add, or subtract fractions more easily. For example, when adding fractions with different denominators, we often convert them to equivalent fractions with a common denominator first.
Understanding equivalent fractions also helps when simplifying fractions. For example, if you are given 4/24 and asked to simplify it, you divide both the numerator and denominator by 4 (their greatest common divisor) and get 1/6.
In summary, equivalent fractions are different ways of writing the same value. By multiplying or dividing both parts of a fraction by the same number, we create a new fraction that looks different but is equal in value.