Here are the step-by-step solutions for each problem on the worksheet.
1. $\frac{3}{4} - \frac{1}{4}$
Since the bottom numbers (denominators) are the same, just subtract the top numbers: $3 - 1 = 2$.
Result: $\frac{2}{4}$. This simplifies to $\frac{1}{2}$.
2. $\frac{60}{90} - \frac{30}{90}$
Subtract the tops: $60 - 30 = 30$.
Result: $\frac{30}{90}$. Divide top and bottom by 30 to simplify to $\frac{1}{3}$.
3. $\frac{10}{13} - \frac{2}{13}$
Subtract the tops: $10 - 2 = 8$.
Result: $\frac{8}{13}$.
4. $\frac{150}{85} - \frac{60}{85}$
Subtract the tops: $150 - 60 = 90$.
Result: $\frac{90}{85}$. Both end in 0 or 5, so divide by 5.
$90 \div 5 = 18$ and $85 \div 5 = 17$.
Final Answer: $\frac{18}{17}$ (or $1 \frac{1}{17}$).
5. $\frac{13}{2} - \frac{7}{2}$
Subtract the tops: $13 - 7 = 6$.
Result: $\frac{6}{2}$. Since 6 divided by 2 is 3, the answer is $3$.
6. $\frac{30}{42} - \frac{24}{42}$
Subtract the tops: $30 - 24 = 6$.
Result: $\frac{6}{42}$. Both can be divided by 6.
$6 \div 6 = 1$ and $42 \div 6 = 7$.
Final Answer: $\frac{1}{7}$.
7. $\frac{6}{8} - \frac{1}{2}$
The bottoms are different. Change $\frac{1}{2}$ to eighths by multiplying top and bottom by 4 ($\frac{4}{8}$).
Now solve: $\frac{6}{8} - \frac{4}{8} = \frac{2}{8}$.
Simplify $\frac{2}{8}$ to $\frac{1}{4}$.
8. $\frac{10}{12} - \frac{1}{3}$
Change $\frac{1}{3}$ to twelfths by multiplying top and bottom by 4 ($\frac{4}{12}$).
Now solve: $\frac{10}{12} - \frac{4}{12} = \frac{6}{12}$.
Simplify $\frac{6}{12}$ to $\frac{1}{2}$.
9. $\frac{4}{6} - \frac{5}{18}$
Change $\frac{4}{6}$ to eighteenths by multiplying top and bottom by 3 ($\frac{12}{18}$).
Now solve: $\frac{12}{18} - \frac{5}{18} = \frac{7}{18}$.
10. $\frac{11}{9} - \frac{2}{4}$
First, simplify $\frac{2}{4}$ to $\frac{1}{2}$. Now we have $\frac{11}{9} - \frac{1}{2}$.
Find a common denominator for 9 and 2, which is 18.
$\frac{11}{9}$ becomes $\frac{22}{18}$ (multiply by 2).
$\frac{1}{2}$ becomes $\frac{9}{18}$ (multiply by 9).
Subtract: $\frac{22}{18} - \frac{9}{18} = \frac{13}{18}$.
11. $\frac{6}{7} - \frac{3}{5}$
Common denominator for 7 and 5 is 35.
$\frac{6}{7}$ becomes $\frac{30}{35}$ ($6 \times 5$).
$\frac{3}{5}$ becomes $\frac{21}{35}$ ($3 \times 7$).
Subtract: $\frac{30}{35} - \frac{21}{35} = \frac{9}{35}$.
12. $\frac{2}{3} - \frac{4}{10}$
First, simplify $\frac{4}{10}$ to $\frac{2}{5}$. Now we have $\frac{2}{3} - \frac{2}{5}$.
Common denominator for 3 and 5 is 15.
$\frac{2}{3}$ becomes $\frac{10}{15}$ ($2 \times 5$).
$\frac{2}{5}$ becomes $\frac{6}{15}$ ($2 \times 3$).
Subtract: $\frac{10}{15} - \frac{6}{15} = \frac{4}{15}$.
Final Answer:
1. 1/2
2. 1/3
3. 8/13
4. 18/17
5. 3
6. 1/7
7. 1/4
8. 1/2
9. 7/18
10. 13/18
11. 9/35
12. 4/15
Parent Tip: Review the logic above to help your child master the concept of adding and subtracting unlike denominators.
