Fraction worksheet

1. Result (simplified): 9/10

1. Multiply straight across: top times top, and bottom times bottom

   $\frac{3}{4}\times \frac{6}{5}$$=\frac{3\times 6}{4\times 5}$$=\frac{18}{20}$

2. Simplify: divide the top and bottom by 2, the biggest number that goes into both evenly

   $\frac{18÷2}{20÷2}$$=\frac{9}{10}$

2. Result (simplified): 5/3

1. You can only add or subtract pieces of the same size. So find the smallest number that both 3 and 6 go into evenly (the LCD)

   $\text{LCD(}3\text{,}6\text{)}$$=6$

2. Rewrite both fractions with 6 on the bottom: multiply the top and bottom of 3/3 by 2. This changes how they look, not what they're worth

   $\frac{3}{3}+\frac{4}{6}$$=\frac{3\times 2}{3\times 2}+\frac{4}{6}$$=\frac{6}{6}+\frac{4}{6}$

3. Add the top numbers. The bottom stays the same, because the pieces are still the same size

   $\frac{6+4}{6}$$=\frac{10}{6}$

4. Simplify: divide the top and bottom by 2, the biggest number that goes into both evenly (as a mixed number, 1 2/3)

   $\frac{10÷2}{6÷2}$$=\frac{5}{3}$

3. Result (simplified): 8/5

1. Dividing by a fraction is the same as multiplying by it flipped upside down: keep the first fraction, change ÷ to ×, and flip the second

   $\frac{4}{3}÷\frac{5}{6}$$=\frac{4}{3}\times \frac{6}{5}$

2. Multiply straight across: top times top, and bottom times bottom

   $\frac{4}{3}\times \frac{6}{5}$$=\frac{4\times 6}{3\times 5}$$=\frac{24}{15}$

3. Simplify: divide the top and bottom by 3, the biggest number that goes into both evenly (as a mixed number, 1 3/5)

   $\frac{24÷3}{15÷3}$$=\frac{8}{5}$

4. Result (simplified): 7/12

1. Dividing by a fraction is the same as multiplying by it flipped upside down: keep the first fraction, change ÷ to ×, and flip the second

   $\frac{3}{6}÷\frac{6}{7}$$=\frac{3}{6}\times \frac{7}{6}$

2. Multiply straight across: top times top, and bottom times bottom

   $\frac{3}{6}\times \frac{7}{6}$$=\frac{3\times 7}{6\times 6}$$=\frac{21}{36}$

3. Simplify: divide the top and bottom by 3, the biggest number that goes into both evenly

   $\frac{21÷3}{36÷3}$$=\frac{7}{12}$

5. Result (simplified): 15/16

1. Dividing by a fraction is the same as multiplying by it flipped upside down: keep the first fraction, change ÷ to ×, and flip the second

   $\frac{3}{4}÷\frac{4}{5}$$=\frac{3}{4}\times \frac{5}{4}$

2. Multiply straight across: top times top, and bottom times bottom

   $\frac{3}{4}\times \frac{5}{4}$$=\frac{3\times 5}{4\times 4}$$=\frac{15}{16}$

3. No number except 1 divides both the top and the bottom, so the fraction can't get any simpler

   $\frac{15}{16}$

6. Result (simplified): 4/3

1. Dividing by a fraction is the same as multiplying by it flipped upside down: keep the first fraction, change ÷ to ×, and flip the second

   $\frac{2}{3}÷\frac{3}{6}$$=\frac{2}{3}\times \frac{6}{3}$

2. Multiply straight across: top times top, and bottom times bottom

   $\frac{2}{3}\times \frac{6}{3}$$=\frac{2\times 6}{3\times 3}$$=\frac{12}{9}$

3. Simplify: divide the top and bottom by 3, the biggest number that goes into both evenly (as a mixed number, 1 1/3)

   $\frac{12÷3}{9÷3}$$=\frac{4}{3}$

7. Result (simplified): 1/3

1. Multiply straight across: top times top, and bottom times bottom

   $\frac{3}{6}\times \frac{4}{6}$$=\frac{3\times 4}{6\times 6}$$=\frac{12}{36}$

2. Simplify: divide the top and bottom by 12, the biggest number that goes into both evenly

   $\frac{12÷12}{36÷12}$$=\frac{1}{3}$

8. Result (simplified): 1

1. Dividing by a fraction is the same as multiplying by it flipped upside down: keep the first fraction, change ÷ to ×, and flip the second

   $\frac{3}{3}÷\frac{6}{6}$$=\frac{3}{3}\times \frac{6}{6}$

2. Multiply straight across: top times top, and bottom times bottom

   $\frac{3}{3}\times \frac{6}{6}$$=\frac{3\times 6}{3\times 6}$$=\frac{18}{18}$

3. Simplify: divide the top and bottom by 18, the biggest number that goes into both evenly

   $\frac{18÷18}{18÷18}$$=1$

9. Result (simplified): 2/7

1. You can only add or subtract pieces of the same size. So find the smallest number that both 3 and 7 go into evenly (the LCD)

   $\text{LCD(}3\text{,}7\text{)}$$=21$

2. Rewrite both fractions with 21 on the bottom: multiply the top and bottom of 3/3 by 7, and multiply the top and bottom of 5/7 by 3. This changes how they look, not what they're worth

   $\frac{3}{3}-\frac{5}{7}$$=\frac{3\times 7}{3\times 7}-\frac{5\times 3}{7\times 3}$$=\frac{21}{21}-\frac{15}{21}$

3. Subtract the top numbers. The bottom stays the same, because the pieces are still the same size

   $\frac{21-15}{21}$$=\frac{6}{21}$

4. Simplify: divide the top and bottom by 3, the biggest number that goes into both evenly

   $\frac{6÷3}{21÷3}$$=\frac{2}{7}$

10. Result (simplified): 1/28

1. You can only add or subtract pieces of the same size. So find the smallest number that both 4 and 7 go into evenly (the LCD)

   $\text{LCD(}4\text{,}7\text{)}$$=28$

2. Rewrite both fractions with 28 on the bottom: multiply the top and bottom of 3/4 by 7, and multiply the top and bottom of 5/7 by 4. This changes how they look, not what they're worth

   $\frac{3}{4}-\frac{5}{7}$$=\frac{3\times 7}{4\times 7}-\frac{5\times 4}{7\times 4}$$=\frac{21}{28}-\frac{20}{28}$

3. Subtract the top numbers. The bottom stays the same, because the pieces are still the same size

   $\frac{21-20}{28}$$=\frac{1}{28}$

4. No number except 1 divides both the top and the bottom, so the fraction can't get any simpler

   $\frac{1}{28}$