Question

level 157
which shows these fractions in order from least to greatest?
\\( \frac{10}{4}, 1\frac{3}{4}, 3\frac{3}{4}, \frac{9}{4} \\)
select an answer
a \\( 1\frac{3}{4}, 3\frac{3}{4}, \frac{9}{4}, \frac{10}{4} \\)
b \\( 1\frac{3}{4}, \frac{9}{4}, \frac{10}{4}, 3\frac{3}{4} \\)
c \\( \frac{9}{4}, 1\frac{3}{4}, \frac{10}{4}, 3\frac{3}{4} \\)
d \\( 3\frac{3}{4}, \frac{10}{4}, \frac{9}{4}, 1\frac{3}{4} \\)

Explanation:

Step1: Convert mixed numbers to improper fractions

First, convert the mixed numbers \(1\frac{3}{4}\) and \(3\frac{3}{4}\) to improper fractions.
For \(1\frac{3}{4}\): \(1\frac{3}{4}=\frac{1\times4 + 3}{4}=\frac{7}{4}\)
For \(3\frac{3}{4}\): \(3\frac{3}{4}=\frac{3\times4+3}{4}=\frac{15}{4}\)
The given fractions are \(\frac{10}{4}\), \(\frac{7}{4}\), \(\frac{15}{4}\), \(\frac{9}{4}\)

Step2: Compare the numerators

Since all fractions have the same denominator (4), we can compare their numerators. The numerators are 10, 7, 15, 9.
Ordering the numerators from least to greatest: \(7 < 9 < 10 < 15\)

Step3: Map back to original fractions

Now, map these numerators back to the original fractions:

• \(\frac{7}{4}\) is \(1\frac{3}{4}\)
• \(\frac{9}{4}\) is \(\frac{9}{4}\)
• \(\frac{10}{4}\) is \(\frac{10}{4}\)
• \(\frac{15}{4}\) is \(3\frac{3}{4}\)

So the order from least to greatest is \(1\frac{3}{4},\frac{9}{4},\frac{10}{4},3\frac{3}{4}\)

Answer:

B. \(1\frac{3}{4},\frac{9}{4},\frac{10}{4},3\frac{3}{4}\)