Answer:
The inequality which correctly compares Three-fourths, One-seventh, and Five-sixths is : One-seventh < Three-fourths < Five-sixths.
The first option is correct.
Step-by-step explanation:
To determine which inequality correctly compares Three-fourths, One-seventh, and Five-sixths, we will arrange them in ascending order.
To do this, first, we will determine the LCM of the fractions denominators..
Three-fourths, One-seventh, and Five-sixths
[tex]\frac{3}{4}, \frac{1}{7}, and \frac{5}{6}[/tex]
The denominators are 4, 7 and 6.
LCM of 4,7 and 6 is 84
Then, we will write the fractions in a form whereby they all have the same denominators.
[tex]\frac{3}{4}, \frac{1}{7}, and \frac{5}{6}[/tex] can be written as
[tex]\frac{63}{84}, \frac{12}{84}, and \frac{70}{84}[/tex]
The resulting order of the numerators gives the order of the fractions.
Now, we will arrange [tex]\frac{63}{84}, \frac{12}{84}, and \frac{70}{84}[/tex] in ascending order. This becomes
[tex]\frac{12}{84}, \frac{63}{84},and \frac{70}{84}[/tex].
∴ The ascending order of the fractions is [tex]\frac{1}{7}, \frac{3}{4},and \frac{5}{6}[/tex].
That is, One-seventh, Three-fourths, and Five-sixths.
Hence, we can write that
One-seventh < Three-fourths < Five-sixths.
This is the inequality which correctly compares Three-fourths, One-seventh, and Five-sixths
