Converting Improper Fractions to Mixed Numbers

Show your work for each problem.

1.
Which mixed number is equal to $\frac{7}{2}$ ?
1. a) $1\frac{5}{2}$
2. b) $3\frac{2}{7}$
3. c) $2\frac{1}{2}$
4. d) $3\frac{1}{2}$
Answer: $3\frac{1}{2}$
$7 \div 2 = 3$ remainder $1$ , so $\frac{7}{2} = 3\frac{1}{2}$ . Check: $3 \times 2 + 1 = 7$ .
2.
Convert $\frac{9}{4}$ to a mixed number. Write it as a mixed number, like 1 2/3.
Answer: 2 1/4
$9 \div 4 = 2$ remainder $1$ , so $\frac{9}{4} = 2\frac{1}{4}$ (2 wholes and 1 quarter).
3.
Convert $\frac{11}{3}$ to a mixed number.
Answer: 3 2/3
1. What is 11 ÷ 3, whole number only? 3
2. What is the remainder? 2
3. Write the mixed number (like 1 1/2): 3 2/3
4.
When you convert $\frac{17}{5}$ to $3\frac{2}{5}$ , what does the remainder 2 become?
1. a)The new numerator
2. b)The whole number part
3. c)The new denominator
4. d)Nothing, it is left out
Answer: The new numerator
$17 \div 5 = 3$ remainder $2$ . The 3 is the whole number part, the remainder 2 is the new numerator, and the denominator 5 stays the same.
5.
How many wholes are $\frac{15}{5}$ ? Answer with a whole number.
Answer: 3
$15 \div 5 = 3$ remainder $0$ . There is no fraction part left, so $\frac{15}{5} = 3$ .
6.
Convert $\frac{13}{6}$ to a mixed number.
Answer: 2 1/6
1. How many times does 6 fit into 13? 2
2. What is the remainder? 1
3. Write the mixed number (like 1 1/2): 2 1/6
7.
Which is $\frac{22}{6}$ written as a mixed number in simplest form?
1. a) $3\frac{2}{3}$
2. b) $4\frac{2}{6}$
3. c) $3\frac{4}{6}$
4. d) $3\frac{1}{3}$
Answer: $3\frac{2}{3}$
$22 \div 6 = 3$ remainder $4$ , so $3\frac{4}{6}$ . Simplify: $\frac{4}{6} = \frac{2}{3}$ , so $\frac{22}{6} = 3\frac{2}{3}$ . $3\frac{4}{6}$ has the right value but is not in simplest form.
8.
Convert $\frac{23}{5}$ to a mixed number. Write it as a mixed number, like 1 2/3.
Answer: 4 3/5
$5 \times 4 = 20$ and $23 - 20 = 3$ , so $\frac{23}{5} = 4\frac{3}{5}$ . Check: $4 \times 5 + 3 = 23$ .
9.
Convert $\frac{26}{8}$ to a mixed number in simplest form.
Answer: 3 1/4
1. What is 26 ÷ 8, whole number only? 3
2. What is the remainder? 2
3. Simplify the fraction part 2/8 by dividing the top and the bottom by 2. What is the new denominator? 4
4. Write the final mixed number (like 1 1/2): 3 1/4
10.
Convert $\frac{31}{7}$ to a mixed number, then check your answer.
Answer: 4 3/7
1. How many times does 7 fit into 31? 4
2. What is the remainder? 3
3. Write the mixed number (like 1 1/2): 4 3/7
4. Check: what is 4 × 7 + 3? 31
11.
Mia converted $\frac{19}{4}$ and got $3\frac{7}{4}$ . What is the correct answer?
1. a) $4\frac{3}{4}$ , because the fraction part must be less than one whole
2. b)Her answer is already correct
3. c) $3\frac{3}{4}$ , because only the numerator changes
4. d) $7\frac{3}{4}$ , because the remainder becomes the whole number
Answer: $4\frac{3}{4}$ , because the fraction part must be less than one whole
$\frac{7}{4}$ is still more than one whole, so another whole fits. $19 \div 4 = 4$ remainder $3$ , so $\frac{19}{4} = 4\frac{3}{4}$ .
12.
Convert $\frac{40}{6}$ to a mixed number in simplest form. Write it as a mixed number, like 1 2/5.
Answer: 6 2/3
$40 \div 6 = 6$ remainder $4$ , so $6\frac{4}{6}$ . Simplify $\frac{4}{6} = \frac{2}{3}$ : the answer is $6\frac{2}{3}$ .
13.
Convert $\frac{36}{9}$ . Is the result a mixed number or a whole number? Give its value.
Answer: 4
1. What is 36 ÷ 9, whole number only? 4
2. What is the remainder? 0
3. Check: what is 4 × 9 + 0? 36
14.
A baker fills a $\frac{1}{4}$ cup measure with sugar 27 times. How many cups of sugar is that, as a mixed number?
Answer: 6 3/4
1. Write the amount as an improper fraction: 27/4
2. How many full cups are in 27 quarters? 6
3. How many quarters are left over? 3
4. Write the mixed number (like 2 1/2): 6 3/4
15.
Convert $\frac{100}{8}$ to a mixed number in simplest form. Write it as a mixed number, like 3 1/5.
Answer: 12 1/2
$100 \div 8 = 12$ remainder $4$ , so $12\frac{4}{8}$ . Simplify $\frac{4}{8} = \frac{1}{2}$ : the answer is $12\frac{1}{2}$ .
16.
Which improper fraction is NOT equal to a whole number?
1. a) $\frac{64}{8}$
2. b) $\frac{45}{6}$
3. c) $\frac{42}{7}$
4. d) $\frac{54}{9}$
Answer: $\frac{45}{6}$
$42 \div 7 = 6$ , $54 \div 9 = 6$ and $64 \div 8 = 8$ have remainder 0. But $45 \div 6 = 7$ remainder $3$ , so $\frac{45}{6} = 7\frac{3}{6} = 7\frac{1}{2}$ .
17.
Convert $\frac{50}{12}$ to a mixed number in simplest form.
Answer: 4 1/6
1. What is 50 ÷ 12, whole number only? 4
2. What is the remainder? 2
3. Simplify the fraction part 2/12 by dividing the top and the bottom by 2. What is the new denominator? 6
4. Write the final mixed number (like 1 1/2): 4 1/6
18.
A class has 47 pencils. A box holds 8 pencils, so the pencils fill $\frac{47}{8}$ boxes. Write this as a mixed number and check it.
Answer: 5 7/8
1. How many boxes can be filled completely? 5
2. How many pencils are left over? 7
3. Write the mixed number (like 2 1/2): 5 7/8
4. Check: what is 5 × 8 + 7? 47