Which inequality correctly compares Three-fourths, One-seventh, and Five-sixths? One-seventh < Three-fourths < Five-sixths One-seventh < Five-sixths < Three-fourths Three-fourths < Five-sixths < One-seventh Three-fourths < One-seventh < Five-sixths

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

Answer:

d

Step-by-step explanation:

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