Ordering Mixed Numbers

Show your work for each problem.

1.
Which list puts $2\frac{1}{2}$ , $1\frac{3}{4}$ , $3\frac{1}{5}$ in order from least to greatest?
1. a) $3\frac{1}{5} < 2\frac{1}{2} < 1\frac{3}{4}$
2. b) $2\frac{1}{2} < 1\frac{3}{4} < 3\frac{1}{5}$
3. c) $1\frac{3}{4} < 2\frac{1}{2} < 3\frac{1}{5}$
4. d) $1\frac{3}{4} < 3\frac{1}{5} < 2\frac{1}{2}$
Answer: $1\frac{3}{4} < 2\frac{1}{2} < 3\frac{1}{5}$
The whole parts are all different, so they decide the order: $1 < 2 < 3$ . So $1\frac{3}{4} < 2\frac{1}{2} < 3\frac{1}{5}$ .
2.
Which number is the largest: $4\frac{1}{6}$ , $3\frac{5}{6}$ , $4\frac{1}{3}$ ? Write the answer as a mixed number, like 2 1/5.
Answer: 4 1/3
$3\frac{5}{6}$ has only 3 wholes, so it is the smallest. $4\frac{1}{6}$ and $4\frac{1}{3}$ both have 4 wholes, and $\frac{1}{3} > \frac{1}{6}$ (thirds are bigger pieces). The largest is $4\frac{1}{3}$ .
3.
Which number is the smallest: $\frac{9}{4}$ , $2\frac{1}{2}$ , $1\frac{7}{8}$ , $\frac{11}{5}$ ?
Answer: 1 7/8
1. What is the whole part of $\frac{9}{4}$ ? 2
2. What is the whole part of $\frac{11}{5}$ ? 2
3. Which number has whole part 1? Write the answer as a mixed number, like 3 1/2. 1 7/8
4.
Before ordering a list, Mia changes $\frac{17}{5}$ into a mixed number. What does she get? Write the answer as a mixed number, like 1 2/3.
Answer: 3 2/5
$17 = 3 \times 5 + 2$ , so $\frac{17}{5} = 3\frac{2}{5}$ : 3 wholes and 2 fifths left over.
5.
Order from least to greatest: $2\frac{3}{8}$ , $1\frac{5}{8}$ , $2\frac{7}{8}$
Answer: 1 5/8 < 2 3/8 < 2 7/8
1. Which number has the smallest whole part? Write the answer as a mixed number, like 3 1/4. 1 5/8
2. The other two numbers have the same whole part. What is it? 2
3. Both fractions are eighths. Which numerator is smaller, 3 or 7? 3
4. Which number is the largest? Write the answer as a mixed number, like 3 1/4. 2 7/8
6.
Order from greatest to least: $1\frac{1}{2}$ , $3\frac{1}{4}$ , $2$ , $\frac{5}{2}$
Answer: 3 1/4 > 5/2 > 2 > 1 1/2
1. Write $\frac{5}{2}$ as a mixed number, like 4 1/3. 2 1/2
2. Which number has the largest whole part? Write the answer as a mixed number, like 4 1/3. 3 1/4
3. Which is greater, $2$ or $2\frac{1}{2}$ ? Write the answer as a mixed number, like 4 1/3. 2 1/2
4. Which number comes last (the smallest)? Write the answer as a mixed number, like 4 1/3. 1 1/2
7.
Which list puts $\frac{7}{2}$ , $3\frac{1}{3}$ , $3\frac{3}{4}$ , $3\frac{1}{8}$ in order from greatest to least?
1. a) $3\frac{3}{4} > 3\frac{1}{3} > \frac{7}{2} > 3\frac{1}{8}$
2. b) $3\frac{3}{4} > \frac{7}{2} > 3\frac{1}{3} > 3\frac{1}{8}$
3. c) $\frac{7}{2} > 3\frac{3}{4} > 3\frac{1}{3} > 3\frac{1}{8}$
4. d) $3\frac{1}{8} > 3\frac{1}{3} > \frac{7}{2} > 3\frac{3}{4}$
Answer: $3\frac{3}{4} > \frac{7}{2} > 3\frac{1}{3} > 3\frac{1}{8}$
$\frac{7}{2} = 3\frac{1}{2}$ . With denominator 24: $\frac{3}{4} = \frac{18}{24}$ , $\frac{1}{2} = \frac{12}{24}$ , $\frac{1}{3} = \frac{8}{24}$ , $\frac{1}{8} = \frac{3}{24}$ . So $3\frac{3}{4} > \frac{7}{2} > 3\frac{1}{3} > 3\frac{1}{8}$ .
8.
Four planks are $2\frac{3}{4}$ m, $\frac{11}{5}$ m, $2\frac{5}{8}$ m and $\frac{13}{6}$ m long. Which length is the second shortest? Write the answer as a mixed number, like 3 1/2.
Answer: 2 1/5
All four have 2 wholes. $\frac{1}{6}$ and $\frac{1}{5}$ are less than $\frac{1}{2}$ , and $\frac{1}{6} < \frac{1}{5}$ . Also $\frac{5}{8} < \frac{6}{8} = \frac{3}{4}$ . Order: $\frac{13}{6} < \frac{11}{5} < 2\frac{5}{8} < 2\frac{3}{4}$ . The second shortest is $\frac{11}{5} = 2\frac{1}{5}$ m.
9.
Order from least to greatest: $\frac{11}{4}$ , $2\frac{5}{6}$ , $2\frac{2}{3}$ , $\frac{7}{3}$
Answer: 7/3 < 2 2/3 < 11/4 < 2 5/6
1. Write $\frac{11}{4}$ as a mixed number, like 1 1/2. 2 3/4
2. Write $\frac{7}{3}$ as a mixed number, like 1 1/2. 2 1/3
3. All four numbers have whole part 2. What is the least common denominator of 4, 6 and 3? 12
4. $\frac{3}{4} = \frac{\square}{12}$ . What goes in the box? 9
5. Which number is the largest? Write the answer as a mixed number, like 1 1/2. 2 5/6
10.
Four friends run a half marathon. Their times are: Ana $2\frac{3}{5}$ h, Ben $\frac{5}{2}$ h, Cara $2\frac{7}{10}$ h, Dan $\frac{11}{4}$ h. Who was the fastest?
1. a)Cara
2. b)Dan
3. c)Ben
4. d)Ana
Answer: Ben
As decimals: Ana $2.6$ , Ben $\frac{5}{2} = 2.5$ , Cara $2.7$ , Dan $\frac{11}{4} = 2.75$ . The smallest time is $2.5$ h, so Ben was the fastest.
11.
To order the times $\frac{23}{8}$ h, $2\frac{7}{10}$ h and $2\frac{3}{4}$ h, Leo changes each one into a decimal. What is $\frac{23}{8}$ as a decimal?
Answer: 2.875
$\frac{23}{8} = 2\frac{7}{8} = 2.875$ . With $2\frac{7}{10} = 2.7$ and $2\frac{3}{4} = 2.75$ the order is $2\frac{7}{10} < 2\frac{3}{4} < \frac{23}{8}$ .
12.
Use decimals to order from greatest to least: $\frac{9}{4}$ , $2\frac{1}{5}$ , $2\frac{3}{10}$ , $\frac{19}{8}$
Answer: 19/8 > 2 3/10 > 9/4 > 2 1/5
1. Write $\frac{9}{4}$ as a decimal. 2.25
2. Write $2\frac{1}{5}$ as a decimal. 2.2
3. Write $2\frac{3}{10}$ as a decimal. 2.3
4. Write $\frac{19}{8}$ as a decimal. 2.375
5. Which of the four decimals comes last in descending order (the smallest)? 2.2
13.
Which number lies between $2\frac{1}{2}$ and $3$ on the number line?
1. a) $3\frac{1}{8}$
2. b) $\frac{5}{2}$
3. c) $\frac{9}{4}$
4. d) $\frac{17}{6}$
Answer: $\frac{17}{6}$
$\frac{9}{4} = 2\frac{1}{4}$ is less than $2\frac{1}{2}$ , $\frac{5}{2} = 2\frac{1}{2}$ is equal to it, and $3\frac{1}{8}$ is more than 3. Only $\frac{17}{6} = 2\frac{5}{6}$ lies between, because $\frac{1}{2} < \frac{5}{6} < 1$ .
14.
A smoothie bar uses these amounts of five juices (in cups): $1\frac{2}{3}$ , $\frac{7}{4}$ , $1\frac{5}{8}$ , $\frac{3}{2}$ and $\frac{11}{6}$ . Order them from least to greatest.
Answer: 3/2 < 1 5/8 < 1 2/3 < 7/4 < 11/6
1. Write $\frac{7}{4}$ as a mixed number, like 2 1/2. 1 3/4
2. Write $\frac{11}{6}$ as a mixed number, like 2 1/2. 1 5/6
3. What is the least common denominator of 3, 4, 8, 2 and 6? 24
4. $\frac{2}{3} = \frac{\square}{24}$ . What goes in the box? 16
5. $\frac{5}{8} = \frac{\square}{24}$ . What goes in the box? 15
6. Which amount is in the middle of the order (third place)? Write the answer as a mixed number, like 2 1/2. 1 2/3
15.
Which number is the second largest: $3\frac{2}{7}$ , $\frac{13}{4}$ , $3\frac{3}{10}$ , $\frac{10}{3}$ ? Write the answer as a mixed number, like 2 1/2.
Answer: 3 3/10
Fraction parts as decimals: $\frac{2}{7} \approx 0.286$ , $\frac{1}{4} = 0.25$ , $\frac{3}{10} = 0.3$ , $\frac{1}{3} \approx 0.333$ . From greatest to least: $\frac{10}{3} > 3\frac{3}{10} > 3\frac{2}{7} > \frac{13}{4}$ . The second largest is $3\frac{3}{10}$ .
16.
Which list puts $4\frac{1}{3}$ , $\frac{22}{5}$ , $4\frac{3}{8}$ , $\frac{17}{4}$ in order from greatest to least?
1. a) $\frac{22}{5} > 4\frac{1}{3} > 4\frac{3}{8} > \frac{17}{4}$
2. b) $\frac{22}{5} > 4\frac{3}{8} > 4\frac{1}{3} > \frac{17}{4}$
3. c) $\frac{17}{4} > 4\frac{1}{3} > 4\frac{3}{8} > \frac{22}{5}$
4. d) $4\frac{3}{8} > \frac{22}{5} > 4\frac{1}{3} > \frac{17}{4}$
Answer: $\frac{22}{5} > 4\frac{3}{8} > 4\frac{1}{3} > \frac{17}{4}$
As decimals: $4\frac{1}{3} \approx 4.333$ , $\frac{22}{5} = 4.4$ , $4\frac{3}{8} = 4.375$ , $\frac{17}{4} = 4.25$ . So $\frac{22}{5} > 4\frac{3}{8} > 4\frac{1}{3} > \frac{17}{4}$ .
17.
Order from least to greatest: $3$ , $\frac{14}{5}$ , $3\frac{1}{9}$ , $\frac{25}{8}$ , $2\frac{9}{10}$
Answer: 14/5 < 2 9/10 < 3 < 3 1/9 < 25/8
1. Write $\frac{14}{5}$ as a mixed number, like 1 1/2. 2 4/5
2. Write $\frac{25}{8}$ as a mixed number, like 1 1/2. 3 1/8
3. $\frac{4}{5} = \frac{\square}{10}$ . What goes in the box? 8
4. Which fraction is smaller, $\frac{1}{9}$ or $\frac{1}{8}$ ? Type it as a fraction. 1/9
5. Which number is the largest? Write the answer as a mixed number, like 1 1/2. 3 1/8
18.
Four shelves are $3\frac{5}{12}$ m, $\frac{7}{2}$ m, $3\frac{4}{7}$ m and $\frac{10}{3}$ m long. Order them from longest to shortest.
Answer: 3 4/7 > 7/2 > 3 5/12 > 10/3
1. Write $\frac{7}{2}$ as a mixed number, like 2 1/4. 3 1/2
2. Write $\frac{10}{3}$ as a mixed number, like 2 1/4. 3 1/3
3. Which fraction part is greater than $\frac{1}{2}$ : $\frac{5}{12}$ , $\frac{4}{7}$ or $\frac{1}{3}$ ? Type it as a fraction. 4/7
4. $\frac{1}{3} = \frac{\square}{12}$ . What goes in the box? 4
5. Which length is the shortest? Write the answer as a mixed number, like 2 1/4. 3 1/3