Identify the numeric order of these mixed numbers from largest to smallest: 2(3/6)

Question

, 4(1/3),1(3/4),1(4/5)
.

Answer 1

To compare the mixed numbers \(2\frac{3}{6}\), \(4\frac{1}{3}\), \(1\frac{3}{4}\), and \(1\frac{4}{5}\), we can convert them to improper fractions.

1. \(2\frac{3}{6} = 2 + \frac{3}{6} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2}\)

2. \(4\frac{1}{3} = 4 + \frac{1}{3} = \frac{12}{3} + \frac{1}{3} = \frac{13}{3}\)

3. \(1\frac{3}{4} = 1 + \frac{3}{4} = \frac{4}{4} + \frac{3}{4} = \frac{7}{4}\)

4. \(1\frac{4}{5} = 1 + \frac{4}{5} = \frac{5}{5} + \frac{4}{5} = \frac{9}{5}\)

Now, we'll find a common denominator to compare these improper fractions:

• The denominators are 2, 3, 4, and 5. The least common multiple (LCM) of these numbers is 60.

Now, let's convert each improper fraction to have a common denominator of 60:

1. For \(\frac{5}{2}\): \[ \frac{5}{2} = \frac{5 \times 30}{2 \times 30} = \frac{150}{60} \]

2. For \(\frac{13}{3}\): \[ \frac{13}{3} = \frac{13 \times 20}{3 \times 20} = \frac{260}{60} \]

3. For \(\frac{7}{4}\): \[ \frac{7}{4} = \frac{7 \times 15}{4 \times 15} = \frac{105}{60} \]

4. For \(\frac{9}{5}\): \[ \frac{9}{5} = \frac{9 \times 12}{5 \times 12} = \frac{108}{60} \]

Now we can compare:

• \(\frac{260}{60}\) (which is \(4\frac{1}{3}\)),
• \(\frac{150}{60}\) (which is \(2\frac{3}{6}\)),
• \(\frac{108}{60}\) (which is \(1\frac{4}{5}\)),
• \(\frac{105}{60}\) (which is \(1\frac{3}{4}\)).

Ordering these from largest to smallest, we have:

1. \(4\frac{1}{3}\) (largest)
2. \(2\frac{3}{6}\)
3. \(1\frac{4}{5}\)
4. \(1\frac{3}{4}\) (smallest)

In conclusion, the order from largest to smallest is: \[ 4\frac{1}{3}, , 2\frac{3}{6}, , 1\frac{4}{5}, , 1\frac{3}{4} \]