Introduction to Mixed Numbers

Show your work for each problem.

1.
Which of these is a mixed number?
1. a) $2\frac{1}{3}$
2. b) $5$
3. c) $\frac{7}{4}$
4. d) $\frac{3}{4}$
Answer: $2\frac{1}{3}$
$2\frac{1}{3}$ has a whole number part (2) and a proper fraction part ( $\frac{1}{3}$ ). $\frac{3}{4}$ and $\frac{7}{4}$ are single fractions, and $5$ is a whole number.
2.
What is the whole number part of $4\frac{2}{5}$ ?
1. a) $\frac{2}{5}$
2. b) $4$
3. c) $5$
4. d) $2$
Answer: $4$
In $4\frac{2}{5}$ the whole number part is $4$ : there are 4 complete wholes. The fraction part is $\frac{2}{5}$ .
3.
Write 3 wholes and $\frac{2}{5}$ as a mixed number. Type it like 2 1/3.
Answer: 3 2/5
3 wholes plus $\frac{2}{5}$ is $3\frac{2}{5}$ , typed as 3 2/5.
4.
What is the fraction part of $6\frac{3}{8}$ ? Type it as a fraction, like 1/2.
Answer: 3/8
$6\frac{3}{8} = 6 + \frac{3}{8}$ , so the fraction part is $\frac{3}{8}$ .
5.
There are 2 whole pizzas and a third pizza with 5 of its 6 equal slices left. Write the amount of pizza as a mixed number.
Answer: 2 5/6
1. How many whole pizzas are there? 2
2. Into how many equal slices is one pizza cut? (denominator) 6
3. How many slices of the third pizza are left? (numerator) 5
4. Write the mixed number, like 2 1/3 2 5/6
6.
Name the parts of the mixed number $5\frac{1}{3}$ .
Answer: 5 1/3
1. What is the whole number part? 5
2. What is the numerator of the fraction part? 1
3. What is the denominator of the fraction part? 3
7.
You want to draw $1\frac{3}{4}$ with fraction bars. Answer the questions.
Answer: 1 3/4
1. How many bars do you shade completely? 1
2. Into how many equal parts do you split the next bar? 4
3. How many of those parts do you shade? 3
8.
A point on the number line is exactly halfway between 1 and 2. Which mixed number is it?
1. a) $1\frac{1}{2}$
2. b) $2\frac{1}{2}$
3. c) $1\frac{1}{4}$
4. d) $\frac{1}{2}$
Answer: $1\frac{1}{2}$
Halfway between 1 and 2 is 1 whole plus half of the next whole: $1\frac{1}{2}$ .
9.
Which of these is NOT written correctly as a mixed number?
1. a) $5\frac{2}{3}$
2. b) $1\frac{6}{5}$
3. c) $2\frac{3}{8}$
4. d) $3\frac{1}{2}$
Answer: $1\frac{6}{5}$
In $1\frac{6}{5}$ the fraction part $\frac{6}{5}$ is bigger than 1, so it is not proper. Written correctly it is $2\frac{1}{5}$ .
10.
How many minutes are in $1\frac{1}{2}$ hours?
Answer: 90
$1\frac{1}{2}$ hours = 60 minutes + 30 minutes = 90 minutes.
11.
On a number line, the space from 2 to 3 is split into 4 equal parts. You stop at the 3rd mark after 2. Which mixed number is it? Write it as a mixed number, like 2 1/3.
Answer: 2 3/4
You passed 2 wholes and then 3 of the 4 quarters: $2\frac{3}{4}$ .
12.
Place $3\frac{2}{5}$ on a number line from 0 to 5.
Answer: 3 2/5
1. Which whole number is just to the left of it? 3
2. Which whole number is just to the right of it? 4
3. Into how many equal parts do you split that space? 5
4. How many parts do you move to the right of 3? 2
13.
A train ride takes $2\frac{1}{4}$ hours. How many minutes is that?
Answer: 135
1. How many minutes are in 2 hours? 120
2. How many minutes are in a quarter of an hour? 15
3. How many minutes in total? 135
14.
A cake recipe needs $3\frac{1}{2}$ cups of flour. You only have a half cup measure. How many half cups do you need?
Answer: 7
1. How many half cups are in 1 whole cup? 2
2. How many half cups are in the 3 whole cups? 6
3. Add the extra half cup. How many half cups in total? 7
15.
Which expression has the same value as $2\frac{3}{4}$ ?
1. a) $4 + \frac{2}{3}$
2. b) $\frac{23}{4}$
3. c) $2 \times \frac{3}{4}$
4. d) $2 + \frac{3}{4}$
Answer: $2 + \frac{3}{4}$
A mixed number is a sum: $2\frac{3}{4} = 2 + \frac{3}{4}$ . $2 \times \frac{3}{4}$ is only $1\frac{1}{2}$ , and $\frac{23}{4}$ is almost 6.
16.
A board is $2\frac{1}{4}$ meters long. How many centimeters long is it?
Answer: 225
2 meters = 200 cm and $\frac{1}{4}$ meter = 25 cm, so the board is 225 cm long.
17.
$1\frac{7}{4}$ is not a correct mixed number. Fix it.
Answer: 2 3/4
1. How many whole ones fit in 7 quarters? 1
2. How many quarters are left over after taking out that whole? 3
3. What is the new whole number part? 2
4. Write the correct mixed number, like 2 1/3 2 3/4
18.
A hike takes $3\frac{1}{3}$ hours. How many minutes is that?
Answer: 200
1. How many minutes are in 3 hours? 180
2. How many minutes are in a third of an hour? 20
3. How many minutes in total? 200