Improper Fractions

Show your work for each problem.

1.
Which fraction is improper?
1. a) $\frac{3}{8}$
2. b) $\frac{1}{2}$
3. c) $\frac{9}{7}$
4. d) $\frac{5}{9}$
Answer: $\frac{9}{7}$
$\frac{9}{7}$ is improper because its numerator 9 is greater than its denominator 7. The other three fractions have a smaller numerator than denominator, so they are proper.
2.
A cake is cut into 4 equal pieces. From two identical cakes you take 7 pieces. Write this amount as a fraction of one cake.
Answer: 7/4
Each piece is $\frac{1}{4}$ of a cake, so 7 pieces are $\frac{7}{4}$ of a cake. That is more than one whole cake.
3.
A chocolate bar has 6 equal pieces. Tom eats 8 pieces from two identical bars. What fraction of one bar did he eat?
Answer: 8/6
1. How many equal pieces make one whole bar? 6
2. How many pieces did Tom eat? 8
3. Write the fraction of one bar that Tom ate. 8/6
4.
Which fraction is equal to 1?
1. a) $\frac{1}{6}$
2. b) $\frac{5}{6}$
3. c) $\frac{6}{6}$
4. d) $\frac{6}{5}$
Answer: $\frac{6}{6}$
In $\frac{6}{6}$ the numerator equals the denominator: all six sixths together make one whole, so $\frac{6}{6} = 1$ .
5.
What whole number is $\frac{6}{3}$ equal to?
Answer: 2
$6 \div 3 = 2$ , so $\frac{6}{3} = 2$ . Six thirds make two wholes.
6.
Write the whole number 2 as a fraction with denominator 4: $2 = \frac{\square}{4}$ . What number goes in the box?
Answer: 8
1. How many quarters make 1 whole? 4
2. How many quarters make 2 wholes? 8
3. So $2 = \frac{\square}{4}$ . What number goes in the box? 8
7.
Where is $\frac{5}{4}$ on the number line?
1. a)Exactly at 1
2. b)Between 1 and 2
3. c)Between 2 and 3
4. d)Between 0 and 1
Answer: Between 1 and 2
$\frac{4}{4} = 1$ , and $\frac{5}{4}$ is one more quarter, so it lies just to the right of 1, between 1 and 2.
8.
$\frac{7}{3}$ lies between two whole numbers. Find the smaller one.
Answer: 2
1. How many thirds make 1 whole? 3
2. How many thirds make 2 wholes? 6
3. How many thirds make 3 wholes? 9
4. 7 is between 6 and 9. So $\frac{7}{3}$ lies between which smaller whole number and 3? 2
9.
Which improper fraction is equal to a whole number?
1. a) $\frac{12}{3}$
2. b) $\frac{9}{6}$
3. c) $\frac{10}{4}$
4. d) $\frac{7}{2}$
Answer: $\frac{12}{3}$
$12 \div 3 = 4$ , so $\frac{12}{3} = 4$ . The others are not whole numbers: $\frac{7}{2}$ lies between 3 and 4, $\frac{10}{4}$ between 2 and 3, and $\frac{9}{6}$ between 1 and 2.
10.
Write the whole number 3 as a fraction with denominator 4: $3 = \frac{\square}{4}$ . What number goes in the box?
Answer: 12
Each whole has 4 quarters, so 3 wholes have $3 \times 4 = 12$ quarters: $3 = \frac{12}{4}$ .
11.
Find the value of $\frac{15}{5}$ . Is it a whole number?
Answer: 3
1. How many fifths make one whole? 5
2. How many groups of 5 fit into 15? 3
3. So what is $\frac{15}{5}$ ? 3
12.
What is the smallest whole number you can put in the box so that $\frac{\square}{7}$ is an improper fraction?
Answer: 7
An improper fraction needs a numerator of at least 7. The smallest choice is 7, which gives $\frac{7}{7} = 1$ .
13.
At a party, every pizza is cut into 8 equal slices. The guests eat 19 slices. What fraction of a pizza did they eat?
Answer: 19/8
1. How many slices make one whole pizza? 8
2. How many slices were eaten? 19
3. Write the fraction of a pizza that was eaten. 19/8
4. How many whole pizzas were eaten completely? 2
14.
How far past 1 is $\frac{9}{5}$ on the number line? Give the answer as a fraction.
Answer: 4/5
1. Write 1 as a fraction with denominator 5. What is the numerator? 5
2. How many more fifths does $\frac{9}{5}$ have than $\frac{5}{5}$ ? 4
3. So how far past 1 is $\frac{9}{5}$ ? 4/5
15.
Which fraction is the greatest?
1. a) $\frac{8}{8}$
2. b) $\frac{11}{12}$
3. c) $\frac{3}{2}$
4. d) $\frac{12}{11}$
Answer: $\frac{3}{2}$
$\frac{11}{12}$ is less than 1 and $\frac{8}{8} = 1$ . $\frac{12}{11}$ is only one eleventh past 1, while $\frac{3}{2}$ is one half past 1, so $\frac{3}{2}$ is the greatest.
16.
How many fractions with denominator 4 (like $\frac{5}{4}$ ) lie between 1 and 2, not counting 1 and 2 themselves?
Answer: 3
$1 = \frac{4}{4}$ and $2 = \frac{8}{4}$ . In between are $\frac{5}{4}$ , $\frac{6}{4}$ and $\frac{7}{4}$ : 3 fractions.
17.
Which is greater: $\frac{13}{6}$ or $\frac{9}{4}$ ? Enter the greater fraction.
Answer: 9/4
1. How many sixths make 2 wholes? 12
2. How far past 2 is $\frac{13}{6}$ ? Write it as a fraction. 1/6
3. How many quarters make 2 wholes? 8
4. How far past 2 is $\frac{9}{4}$ ? Write it as a fraction. 1/4
5. Which fraction is greater? 9/4
18.
Find the smallest improper fraction with denominator 5 that is greater than 2.
Answer: 11/5
1. Write 1 as a fraction with denominator 5. What is the numerator? 5
2. Write 2 as a fraction with denominator 5. What is the numerator? 10
3. The numerator must be greater than 10. What is the smallest whole number greater than 10? 11
4. Write the fraction. 11/5