Subtracting Fractions

Show your work for each problem.

1.
What is $\frac{5}{8} - \frac{2}{8}$ ?
1. a) $\frac{3}{8}$
2. b) $\frac{3}{0}$
3. c) $\frac{7}{8}$
4. d) $\frac{3}{16}$
Answer: $\frac{3}{8}$
With same denominators, subtract numerators: $5 - 2 = 3$ . Keep the denominator: $\frac{3}{8}$ . Never subtract denominators!
2.
Calculate $\frac{7}{9} - \frac{4}{9}$ and give your answer as a fraction.
Answer: 3/9
$\frac{7}{9} - \frac{4}{9} = \frac{7-4}{9} = \frac{3}{9}$ . Note: This can be simplified to $\frac{1}{3}$ , but $\frac{3}{9}$ is also correct.
3.
What is $\frac{11}{12} - \frac{5}{12}$ ?
1. a) $\frac{1}{2}$
2. b) $\frac{6}{0}$
3. c) $\frac{6}{12}$
4. d) $\frac{16}{12}$
Answer: $\frac{1}{2}$
$\frac{11}{12} - \frac{5}{12} = \frac{6}{12} = \frac{1}{2}$ (simplified by dividing both by 6).
4.
Subtract: $\frac{9}{10} - \frac{3}{10}$
Answer: 3/5
1. Are the denominators the same? yes
2. Subtract the numerators: 9 - 3 = ? 6
3. Write the result with denominator 10 6/10
4. Simplify by dividing both by GCF (2) 3/5
5.
What is the LCD (Least Common Denominator) of $\frac{1}{4}$ and $\frac{1}{6}$ ?
1. a)6
2. b)12
3. c)10
4. d)24
Answer: 12
Multiples of 4: 4, 8, 12... Multiples of 6: 6, 12... The LCD is 12 (smallest number divisible by both 4 and 6).
6.
Calculate $\frac{3}{4} - \frac{1}{2}$ . Give your answer in simplest form.
Answer: 1/4
LCD of 4 and 2 is 4. $\frac{1}{2} = \frac{2}{4}$ . So $\frac{3}{4} - \frac{2}{4} = \frac{1}{4}$ .
7.
Calculate $\frac{5}{6} - \frac{1}{4}$
Answer: 7/12
1. What is the LCD of 6 and 4? 12
2. Convert $\frac{5}{6}$ to twelfths: $\frac{5 \times 2}{6 \times 2}$ = ? 10/12
3. Convert $\frac{1}{4}$ to twelfths: $\frac{1 \times 3}{4 \times 3}$ = ? 3/12
4. Subtract: $\frac{10}{12} - \frac{3}{12}$ = ? 7/12
8.
What is $\frac{2}{3} - \frac{1}{4}$ ?
1. a) $\frac{5}{12}$
2. b) $\frac{8}{12}$
3. c) $\frac{1}{7}$
4. d) $\frac{1}{-1}$
Answer: $\frac{5}{12}$
LCD = 12. $\frac{2}{3} = \frac{8}{12}$ , $\frac{1}{4} = \frac{3}{12}$ . So $\frac{8}{12} - \frac{3}{12} = \frac{5}{12}$ .
9.
Calculate $\frac{7}{10} - \frac{2}{5}$ . Give your answer in simplest form.
Answer: 3/10
LCD = 10. $\frac{2}{5} = \frac{4}{10}$ . So $\frac{7}{10} - \frac{4}{10} = \frac{3}{10}$ (already simplified).
10.
A recipe calls for $\frac{3}{4}$ cup of sugar. You want to use $\frac{1}{3}$ cup less. How much sugar will you use?
Answer: 5/12
1. What operation do you need? subtraction
2. What is the LCD of 4 and 3? 12
3. Convert $\frac{3}{4}$ to twelfths 9/12
4. Convert $\frac{1}{3}$ to twelfths 4/12
5. Calculate $\frac{9}{12} - \frac{4}{12}$ 5/12
11.
Calculate $\frac{4}{5} - \frac{1}{3}$
Answer: 7/15
1. What is the LCD of 5 and 3? 15
2. Convert $\frac{4}{5}$ to fifteenths 12/15
3. Convert $\frac{1}{3}$ to fifteenths 5/15
4. Subtract: $\frac{12}{15} - \frac{5}{15}$ 7/15
12.
Calculate $\frac{5}{6} - \frac{2}{9}$ . Give your answer in simplest form.
Answer: 11/18
LCD = 18. $\frac{5}{6} = \frac{15}{18}$ , $\frac{2}{9} = \frac{4}{18}$ . So $\frac{15}{18} - \frac{4}{18} = \frac{11}{18}$ (already simplified).
13.
What is $\frac{7}{8} - \frac{2}{3}$ ?
1. a) $\frac{21}{24}$
2. b) $\frac{5}{5}$
3. c) $\frac{5}{24}$
4. d) $\frac{1}{24}$
Answer: $\frac{5}{24}$
LCD = 24. $\frac{7}{8} = \frac{21}{24}$ , $\frac{2}{3} = \frac{16}{24}$ . So $\frac{21}{24} - \frac{16}{24} = \frac{5}{24}$ .
14.
You had $\frac{5}{6}$ of a pizza. You ate $\frac{3}{8}$ of the original pizza. How much pizza is left?
Answer: 11/24
1. What is the LCD of 6 and 8? 24
2. Convert $\frac{5}{6}$ to 24ths 20/24
3. Convert $\frac{3}{8}$ to 24ths 9/24
4. Subtract: $\frac{20}{24} - \frac{9}{24}$ 11/24
15.
Calculate $\frac{11}{12} - \frac{3}{8}$ . Give your answer in simplest form.
Answer: 13/24
LCD = 24. $\frac{11}{12} = \frac{22}{24}$ , $\frac{3}{8} = \frac{9}{24}$ . So $\frac{22}{24} - \frac{9}{24} = \frac{13}{24}$ (already simplified).
16.
Simplify: $\frac{7}{9} - \frac{5}{12}$
Answer: 13/36
1. What is the LCD of 9 and 12? 36
2. Convert $\frac{7}{9}$ to 36ths 28/36
3. Convert $\frac{5}{12}$ to 36ths 15/36
4. Subtract: $\frac{28}{36} - \frac{15}{36}$ 13/36