What fractions are not equivalent to 7/8
The correct answer and explanation is:
Fractions that are not equivalent to 78\frac{7}{8} would include any fraction where the numerator and denominator do not maintain the same proportional relationship as 7 and 8.
For instance, consider the fraction 68\frac{6}{8}. While it has the same denominator, the numerator is smaller, meaning it represents a value less than 78\frac{7}{8}. This fraction is not equivalent to 78\frac{7}{8}.
Another example is 79\frac{7}{9}. Although the numerator is the same, the denominator has changed. The denominator now being 9 instead of 8 alters the proportionality between the numerator and the denominator. Since the value of 79\frac{7}{9} is slightly greater than 78\frac{7}{8}, it is not equivalent.
Furthermore, a fraction like 1416\frac{14}{16} is not equivalent either, even though both 14 and 16 share a factor with 7 and 8. If we simplify 1416\frac{14}{16} by dividing both the numerator and denominator by 2, we get 78\frac{7}{8}. However, this fraction starts as a different form, making it distinct from 78\frac{7}{8} before simplification.
To determine whether two fractions are equivalent, one can cross-multiply. For example, to check if 78\frac{7}{8} is equal to 68\frac{6}{8}, cross-multiplying would give 7×87 \times 8 and 8×68 \times 6, yielding 56 and 48, respectively. Since these values do not match, we can conclude that 78\frac{7}{8} and 68\frac{6}{8} are not equivalent.
In summary, fractions that do not have the same proportionality between the numerator and denominator as 78\frac{7}{8} are not equivalent. These fractions might be larger or smaller, and simplifying them would not yield 78\frac{7}{8}.