Which fraction is equivalent to -3/2?
The Correct Answer and Explanation is:
To find an equivalent fraction for (-\frac{3}{2}), we need to multiply both the numerator and the denominator by the same non-zero number. This is because multiplying or dividing both the numerator and denominator by the same number results in a fraction that is equivalent to the original.
Let’s go through a few examples:
- Multiplying both the numerator and denominator by 2:
[
-\frac{3}{2} \times \frac{2}{2} = \frac{-3 \times 2}{2 \times 2} = \frac{-6}{4}
]
Therefore, (-\frac{6}{4}) is an equivalent fraction to (-\frac{3}{2}). - Multiplying both the numerator and denominator by 3:
[
-\frac{3}{2} \times \frac{3}{3} = \frac{-3 \times 3}{2 \times 3} = \frac{-9}{6}
]
So, (-\frac{9}{6}) is another equivalent fraction. - Multiplying both the numerator and denominator by 4:
[
-\frac{3}{2} \times \frac{4}{4} = \frac{-3 \times 4}{2 \times 4} = \frac{-12}{8}
]
Here, (-\frac{12}{8}) is also equivalent to (-\frac{3}{2}).
Why are these fractions equivalent?
The principle behind equivalent fractions is that they represent the same value or ratio, even though they appear different. When you multiply both the numerator (top number) and the denominator (bottom number) by the same factor, you’re essentially scaling the fraction without changing its overall value. For instance, (-\frac{3}{2}) means “negative 3 divided by 2,” and multiplying both the numerator and denominator by any number (like 2, 3, or 4) does not change the ratio of the numbers. You’re just expressing the same fraction in a different form.
Therefore, the fractions (-\frac{6}{4}), (-\frac{9}{6}), and (-\frac{12}{8}) are all equivalent to (-\frac{3}{2}), as they represent the same value.