Of course! Let's order each set of numbers from greatest to least by first expressing them as decimals.
### Part a
Given fractions: [tex]\( 3 \frac{1}{2}, \frac{13}{4}, 3 \frac{1}{8} \)[/tex]
1. Convert to improper fractions and then to decimals:
- [tex]\( 3 \frac{1}{2} = 3 + \frac{1}{2} = 3.5 \)[/tex]
- [tex]\( \frac{13}{4} = 3.25 \)[/tex]
- [tex]\( 3 \frac{1}{8} = 3 + \frac{1}{8} = 3.125 \)[/tex]
2. Order the decimals from greatest to least:
- [tex]\( 3.5, 3.25, 3.125 \)[/tex]
So, the ordered fractions are: [tex]\( 3 \frac{1}{2}, \frac{13}{4}, 3 \frac{1}{8} \)[/tex].
### Part b
Given fractions: [tex]\( \frac{5}{6}, \frac{2}{3}, 1 \frac{1}{12}, \frac{9}{12} \)[/tex]
1. Convert to decimals:
- [tex]\( \frac{5}{6} \approx 0.8333 \)[/tex]
- [tex]\( \frac{2}{3} \approx 0.6667 \)[/tex]
- [tex]\( 1 \frac{1}{12} = 1 + \frac{1}{12} \approx 1.0833 \)[/tex]
- [tex]\( \frac{9}{12} = \frac{3}{4} = 0.75 \)[/tex]
2. Order the decimals from greatest to least:
- [tex]\( 1.0833, 0.8333, 0.75, 0.6667 \)[/tex]
So, the ordered fractions are: [tex]\( 1 \frac{1}{12}, \frac{5}{6}, \frac{9}{12}, \frac{2}{3} \)[/tex].
### Part c
Given fractions: [tex]\( 1 \frac{2}{5}, \frac{4}{3} \)[/tex]
1. Convert to decimals:
- [tex]\( 1 \frac{2}{5} = 1 + \frac{2}{5} = 1.4 \)[/tex]
- [tex]\( \frac{4}{3} \approx 1.3333 \)[/tex]
2. Order the decimals from greatest to least:
- [tex]\( 1.4, 1.3333 \)[/tex]
So, the ordered fractions are: [tex]\( 1 \frac{2}{5}, \frac{4}{3} \)[/tex].
In summary, the ordered sets of numbers from greatest to least for each part are:
- a) [tex]\( 3 \frac{1}{2}, \frac{13}{4}, 3 \frac{1}{8} \)[/tex]
- b) [tex]\( 1 \frac{1}{12}, \frac{5}{6}, \frac{9}{12}, \frac{2}{3} \)[/tex]
- c) [tex]\( 1 \frac{2}{5}, \frac{4}{3} \)[/tex]
