Order the fractions 2/3, 5/7, 5/8, and 6/21 from least to greatest.

Question

ScanSolve AI Tutor · Accepted Answer

To arrange fractions in ascending order, we need to compare their values. We can do this by finding a common denominator for all fractions or by converting them to decimals. Using a common denominator ensures precision.

Identify the given fractions.
The fractions are $\frac{2}{3}, \frac{5}{7}, \frac{5}{8}, \frac{6}{21}$ .
Find the least common multiple (LCM) of the denominators.
The denominators are 3, 7, 8, and 21.
Notice that $21 = 3 \times 7$ .
So, the LCM of (3, 7, 8, 21) is the LCM of (3, 7, 8).
LCM(3, 7, 8) = $3 \times 7 \times 8 = 21 \times 8 = 168$ .
The common denominator is 168.
Convert each fraction to an equivalent fraction with the common denominator of 168.
For $\frac{2}{3}$ : Multiply numerator and denominator by $\frac{168}{3} = 56$ .
$\frac{2}{3} = \frac{2 \times 56}{3 \times 56} = \frac{112}{168}$
For $\frac{5}{7}$ : Multiply numerator and denominator by $\frac{168}{7} = 24$ .
$\frac{5}{7} = \frac{5 \times 24}{7 \times 24} = \frac{120}{168}$
For $\frac{5}{8}$ : Multiply numerator and denominator by $\frac{168}{8} = 21$ .
$\frac{5}{8} = \frac{5 \times 21}{8 \times 21} = \frac{105}{168}$
For $\frac{6}{21}$ : Multiply numerator and denominator by $\frac{168}{21} = 8$ .
$\frac{6}{21} = \frac{6 \times 8}{21 \times 8} = \frac{48}{168}$
Compare the numerators of the equivalent fractions.
The equivalent fractions are $\frac{112}{168}, \frac{120}{168}, \frac{105}{168}, \frac{48}{168}$ .
Arranging the numerators in ascending order: 48, 105, 112, 120.
Write the original fractions in ascending order.
Corresponding to the ordered numerators, the fractions in ascending order are:
$\frac{48}{168} = \frac{6}{21}$
$\frac{105}{168} = \frac{5}{8}$
$\frac{112}{168} = \frac{2}{3}$
$\frac{120}{168} = \frac{5}{7}$

The fractions in ascending order are:
$\frac{6}{21}, \frac{5}{8}, \frac{2}{3}, \frac{5}{7}$

Order the fractions 2/3, 5/7, 5/8, and 6/21 from least to greatest.

Answer

Step-by-step solution

Identify the given fractions.

Find the least common multiple (LCM) of the denominators.

Convert each fraction to an equivalent fraction with the common denominator of 168.

Compare the numerators of the equivalent fractions.

Write the original fractions in ascending order.

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