QuestionArrange these fractions in decreasing order: $\frac{5}{6}, \frac{1}{3}, \frac{7}{3}, \frac{5}{2}, \frac{5}{4}$ .

Studdy Solution

STEP 1

Assumptions1. We are given five fractions $\frac{5}{6}, \frac{1}{3}, \frac{7}{3}, \frac{5}{}, \frac{5}{4}$ . . We need to arrange these fractions in decreasing order.

STEP 2

To compare fractions, it's easiest if they all have the same denominator. We can find a common denominator by multiplying the denominators of all the fractions.
$Common\, denominator =6 \times \times \times2 \times4$

STEP 3

Calculate the common denominator.
$Common\, denominator =6 \times3 \times3 \times2 \times =216$

STEP 4

Now, convert each fraction to an equivalent fraction with the common denominator. The equivalent fraction is found by multiplying the numerator and the denominator of the fraction by the same number such that the denominator becomes the common denominator.
$\frac{}{6} = \frac{ \times36}{6 \times36}$ $\frac{1}{3} = \frac{1 \times72}{3 \times72}$ $\frac{7}{3} = \frac{7 \times72}{3 \times72}$ $\frac{}{2} = \frac{ \times108}{2 \times108}$ $\frac{}{4} = \frac{ \times54}{4 \times54}$

STEP 5

Calculate the equivalent fractions.
$\frac{5}{} = \frac{180}{216}$ $\frac{1}{3} = \frac{72}{216}$ $\frac{7}{3} = \frac{504}{216}$ $\frac{5}{2} = \frac{540}{216}$ $\frac{5}{4} = \frac{270}{216}$

STEP 6

Now, arrange the equivalent fractions in decreasing order.
$\frac{540}{216}>\frac{504}{216}>\frac{270}{216}>\frac{180}{216}>\frac{72}{216}$

STEP 7

Finally, convert the equivalent fractions back to the original fractions to get the fractions in decreasing order.
$\frac{5}{2}>\frac{7}{3}>\frac{5}{4}>\frac{5}{6}>\frac{1}{3}$ So, the correct option is C. $\frac{5}{2}>\frac{7}{3}>\frac{5}{4}>\frac{5}{6}>\frac{1}{3}$ .

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