Adding and Subtracting Fractions with Unlike Denominators Review ... - Free Printable
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Step-by-step solution for: Adding and Subtracting Fractions with Unlike Denominators Review ...
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Step-by-step solution for: Adding and Subtracting Fractions with Unlike Denominators Review ...
Here are the step-by-step solutions for each problem on the worksheet.
1. To add the fractions $\frac{5}{12}$ and $\frac{3}{4}$, what must first be done?
To add fractions, the bottom numbers (denominators) must be the same. Since 12 and 4 are different, you cannot add them directly. You need to find a number that both 12 and 4 can divide into evenly.
* Correct Option: c) find a common denominator
2. Find the sum: $\frac{1}{2} + \frac{1}{4}$
* The denominators are 2 and 4. The common denominator is 4.
* Change $\frac{1}{2}$ to fourths: $\frac{1 \times 2}{2 \times 2} = \frac{2}{4}$.
* Add: $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$.
3. Find the difference: $\frac{2}{3} - \frac{1}{9}$
* The denominators are 3 and 9. The common denominator is 9.
* Change $\frac{2}{3}$ to ninths: $\frac{2 \times 3}{3 \times 3} = \frac{6}{9}$.
* Subtract: $\frac{6}{9} - \frac{1}{9} = \frac{5}{9}$.
4. Find the sum: $2\frac{1}{8} + 6\frac{1}{2}$
* Add the whole numbers: $2 + 6 = 8$.
* Add the fractions: $\frac{1}{8} + \frac{1}{2}$. The common denominator is 8.
* Change $\frac{1}{2}$ to eighths: $\frac{4}{8}$.
* Add fractions: $\frac{1}{8} + \frac{4}{8} = \frac{5}{8}$.
* Combine: $8\frac{5}{8}$.
5. Find the difference: $5\frac{2}{4} - 2\frac{1}{3}$
* First, simplify $\frac{2}{4}$ to $\frac{1}{2}$. So, $5\frac{1}{2} - 2\frac{1}{3}$.
* Subtract whole numbers: $5 - 2 = 3$.
* Subtract fractions: $\frac{1}{2} - \frac{1}{3}$. The common denominator is 6.
* $\frac{1}{2} = \frac{3}{6}$ and $\frac{1}{3} = \frac{2}{6}$.
* $\frac{3}{6} - \frac{2}{6} = \frac{1}{6}$.
* Combine: $3\frac{1}{6}$.
6. Find the sum: $\frac{3}{4} + 1\frac{7}{12}$
* Keep the whole number 1 aside for now. Add $\frac{3}{4} + \frac{7}{12}$.
* Common denominator is 12. Change $\frac{3}{4}$ to twelfths: $\frac{3 \times 3}{4 \times 3} = \frac{9}{12}$.
* Add: $\frac{9}{12} + \frac{7}{12} = \frac{16}{12}$.
* Simplify $\frac{16}{12}$: It goes in 1 time with 4 left over ($1\frac{4}{12}$).
* Simplify $\frac{4}{12}$ to $\frac{1}{3}$. So, $1\frac{1}{3}$.
* Add this to the original whole number 1: $1 + 1\frac{1}{3} = 2\frac{1}{3}$.
7. Find the difference: $3\frac{4}{10} - \frac{2}{5}$
* Simplify $\frac{4}{10}$ to $\frac{2}{5}$. So, $3\frac{2}{5} - \frac{2}{5}$.
* Subtract the fractions: $\frac{2}{5} - \frac{2}{5} = 0$.
* The whole number remains 3.
* Answer: 3.
8. Find the sum of three sixths and nine twelfths.
* Write as numbers: $\frac{3}{6} + \frac{9}{12}$.
* Simplify $\frac{3}{6}$ to $\frac{1}{2}$ and $\frac{9}{12}$ to $\frac{3}{4}$.
* Problem: $\frac{1}{2} + \frac{3}{4}$.
* Common denominator is 4. $\frac{1}{2} = \frac{2}{4}$.
* Add: $\frac{2}{4} + \frac{3}{4} = \frac{5}{4}$.
* Convert to mixed number: $1\frac{1}{4}$.
9. Find the difference of six eighths and three fourths.
* Write as numbers: $\frac{6}{8} - \frac{3}{4}$.
* Simplify $\frac{6}{8}$ by dividing top and bottom by 2: $\frac{3}{4}$.
* Problem: $\frac{3}{4} - \frac{3}{4}$.
* Answer: 0.
10. Find the sum of five and five eighths plus one and one fourth.
* Write as numbers: $5\frac{5}{8} + 1\frac{1}{4}$.
* Add whole numbers: $5 + 1 = 6$.
* Add fractions: $\frac{5}{8} + \frac{1}{4}$. Common denominator is 8.
* $\frac{1}{4} = \frac{2}{8}$.
* $\frac{5}{8} + \frac{2}{8} = \frac{7}{8}$.
* Combine: $6\frac{7}{8}$.
11. Find the difference of three and two eighths minus two and one forth.
* Write as numbers: $3\frac{2}{8} - 2\frac{1}{4}$.
* Simplify $\frac{2}{8}$ to $\frac{1}{4}$. So, $3\frac{1}{4} - 2\frac{1}{4}$.
* Subtract whole numbers: $3 - 2 = 1$.
* Subtract fractions: $\frac{1}{4} - \frac{1}{4} = 0$.
* Answer: 1.
12. Find the missing fraction: $4\frac{1}{4} + \_\_\_ = 7\frac{1}{2}$
* To find the missing part, subtract $4\frac{1}{4}$ from $7\frac{1}{2}$.
* $7\frac{1}{2} - 4\frac{1}{4}$.
* Common denominator is 4. $\frac{1}{2} = \frac{2}{4}$.
* $7\frac{2}{4} - 4\frac{1}{4}$.
* Whole numbers: $7 - 4 = 3$.
* Fractions: $\frac{2}{4} - \frac{1}{4} = \frac{1}{4}$.
* Answer: $3\frac{1}{4}$.
13. Find the missing fraction: $6\frac{3}{4} - \_\_\_ = 2\frac{1}{4}$
* To find what was taken away, subtract the result from the starting number.
* $6\frac{3}{4} - 2\frac{1}{4}$.
* Whole numbers: $6 - 2 = 4$.
* Fractions: $\frac{3}{4} - \frac{1}{4} = \frac{2}{4}$.
* Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
* Answer: $4\frac{1}{2}$.
14. Find the missing fraction: $\_\_\_ + 8\frac{1}{2} = 10\frac{3}{8}$
* Subtract $8\frac{1}{2}$ from $10\frac{3}{8}$.
* $10\frac{3}{8} - 8\frac{1}{2}$.
* Common denominator is 8. $\frac{1}{2} = \frac{4}{8}$.
* Problem: $10\frac{3}{8} - 8\frac{4}{8}$.
* You cannot subtract $\frac{4}{8}$ from $\frac{3}{8}$, so borrow 1 from the 10.
* $10$ becomes $9$, and add $\frac{8}{8}$ to $\frac{3}{8}$ to get $\frac{11}{8}$.
* New problem: $9\frac{11}{8} - 8\frac{4}{8}$.
* Whole numbers: $9 - 8 = 1$.
* Fractions: $\frac{11}{8} - \frac{4}{8} = \frac{7}{8}$.
* Answer: $1\frac{7}{8}$.
Final Answer:
1. c) find a common denominator
2. $\frac{3}{4}$
3. $\frac{5}{9}$
4. $8\frac{5}{8}$
5. $3\frac{1}{6}$
6. $2\frac{1}{3}$
7. $3$
8. $1\frac{1}{4}$
9. $0$
10. $6\frac{7}{8}$
11. $1$
12. $3\frac{1}{4}$
13. $4\frac{1}{2}$
14. $1\frac{7}{8}$
1. To add the fractions $\frac{5}{12}$ and $\frac{3}{4}$, what must first be done?
To add fractions, the bottom numbers (denominators) must be the same. Since 12 and 4 are different, you cannot add them directly. You need to find a number that both 12 and 4 can divide into evenly.
* Correct Option: c) find a common denominator
2. Find the sum: $\frac{1}{2} + \frac{1}{4}$
* The denominators are 2 and 4. The common denominator is 4.
* Change $\frac{1}{2}$ to fourths: $\frac{1 \times 2}{2 \times 2} = \frac{2}{4}$.
* Add: $\frac{2}{4} + \frac{1}{4} = \frac{3}{4}$.
3. Find the difference: $\frac{2}{3} - \frac{1}{9}$
* The denominators are 3 and 9. The common denominator is 9.
* Change $\frac{2}{3}$ to ninths: $\frac{2 \times 3}{3 \times 3} = \frac{6}{9}$.
* Subtract: $\frac{6}{9} - \frac{1}{9} = \frac{5}{9}$.
4. Find the sum: $2\frac{1}{8} + 6\frac{1}{2}$
* Add the whole numbers: $2 + 6 = 8$.
* Add the fractions: $\frac{1}{8} + \frac{1}{2}$. The common denominator is 8.
* Change $\frac{1}{2}$ to eighths: $\frac{4}{8}$.
* Add fractions: $\frac{1}{8} + \frac{4}{8} = \frac{5}{8}$.
* Combine: $8\frac{5}{8}$.
5. Find the difference: $5\frac{2}{4} - 2\frac{1}{3}$
* First, simplify $\frac{2}{4}$ to $\frac{1}{2}$. So, $5\frac{1}{2} - 2\frac{1}{3}$.
* Subtract whole numbers: $5 - 2 = 3$.
* Subtract fractions: $\frac{1}{2} - \frac{1}{3}$. The common denominator is 6.
* $\frac{1}{2} = \frac{3}{6}$ and $\frac{1}{3} = \frac{2}{6}$.
* $\frac{3}{6} - \frac{2}{6} = \frac{1}{6}$.
* Combine: $3\frac{1}{6}$.
6. Find the sum: $\frac{3}{4} + 1\frac{7}{12}$
* Keep the whole number 1 aside for now. Add $\frac{3}{4} + \frac{7}{12}$.
* Common denominator is 12. Change $\frac{3}{4}$ to twelfths: $\frac{3 \times 3}{4 \times 3} = \frac{9}{12}$.
* Add: $\frac{9}{12} + \frac{7}{12} = \frac{16}{12}$.
* Simplify $\frac{16}{12}$: It goes in 1 time with 4 left over ($1\frac{4}{12}$).
* Simplify $\frac{4}{12}$ to $\frac{1}{3}$. So, $1\frac{1}{3}$.
* Add this to the original whole number 1: $1 + 1\frac{1}{3} = 2\frac{1}{3}$.
7. Find the difference: $3\frac{4}{10} - \frac{2}{5}$
* Simplify $\frac{4}{10}$ to $\frac{2}{5}$. So, $3\frac{2}{5} - \frac{2}{5}$.
* Subtract the fractions: $\frac{2}{5} - \frac{2}{5} = 0$.
* The whole number remains 3.
* Answer: 3.
8. Find the sum of three sixths and nine twelfths.
* Write as numbers: $\frac{3}{6} + \frac{9}{12}$.
* Simplify $\frac{3}{6}$ to $\frac{1}{2}$ and $\frac{9}{12}$ to $\frac{3}{4}$.
* Problem: $\frac{1}{2} + \frac{3}{4}$.
* Common denominator is 4. $\frac{1}{2} = \frac{2}{4}$.
* Add: $\frac{2}{4} + \frac{3}{4} = \frac{5}{4}$.
* Convert to mixed number: $1\frac{1}{4}$.
9. Find the difference of six eighths and three fourths.
* Write as numbers: $\frac{6}{8} - \frac{3}{4}$.
* Simplify $\frac{6}{8}$ by dividing top and bottom by 2: $\frac{3}{4}$.
* Problem: $\frac{3}{4} - \frac{3}{4}$.
* Answer: 0.
10. Find the sum of five and five eighths plus one and one fourth.
* Write as numbers: $5\frac{5}{8} + 1\frac{1}{4}$.
* Add whole numbers: $5 + 1 = 6$.
* Add fractions: $\frac{5}{8} + \frac{1}{4}$. Common denominator is 8.
* $\frac{1}{4} = \frac{2}{8}$.
* $\frac{5}{8} + \frac{2}{8} = \frac{7}{8}$.
* Combine: $6\frac{7}{8}$.
11. Find the difference of three and two eighths minus two and one forth.
* Write as numbers: $3\frac{2}{8} - 2\frac{1}{4}$.
* Simplify $\frac{2}{8}$ to $\frac{1}{4}$. So, $3\frac{1}{4} - 2\frac{1}{4}$.
* Subtract whole numbers: $3 - 2 = 1$.
* Subtract fractions: $\frac{1}{4} - \frac{1}{4} = 0$.
* Answer: 1.
12. Find the missing fraction: $4\frac{1}{4} + \_\_\_ = 7\frac{1}{2}$
* To find the missing part, subtract $4\frac{1}{4}$ from $7\frac{1}{2}$.
* $7\frac{1}{2} - 4\frac{1}{4}$.
* Common denominator is 4. $\frac{1}{2} = \frac{2}{4}$.
* $7\frac{2}{4} - 4\frac{1}{4}$.
* Whole numbers: $7 - 4 = 3$.
* Fractions: $\frac{2}{4} - \frac{1}{4} = \frac{1}{4}$.
* Answer: $3\frac{1}{4}$.
13. Find the missing fraction: $6\frac{3}{4} - \_\_\_ = 2\frac{1}{4}$
* To find what was taken away, subtract the result from the starting number.
* $6\frac{3}{4} - 2\frac{1}{4}$.
* Whole numbers: $6 - 2 = 4$.
* Fractions: $\frac{3}{4} - \frac{1}{4} = \frac{2}{4}$.
* Simplify $\frac{2}{4}$ to $\frac{1}{2}$.
* Answer: $4\frac{1}{2}$.
14. Find the missing fraction: $\_\_\_ + 8\frac{1}{2} = 10\frac{3}{8}$
* Subtract $8\frac{1}{2}$ from $10\frac{3}{8}$.
* $10\frac{3}{8} - 8\frac{1}{2}$.
* Common denominator is 8. $\frac{1}{2} = \frac{4}{8}$.
* Problem: $10\frac{3}{8} - 8\frac{4}{8}$.
* You cannot subtract $\frac{4}{8}$ from $\frac{3}{8}$, so borrow 1 from the 10.
* $10$ becomes $9$, and add $\frac{8}{8}$ to $\frac{3}{8}$ to get $\frac{11}{8}$.
* New problem: $9\frac{11}{8} - 8\frac{4}{8}$.
* Whole numbers: $9 - 8 = 1$.
* Fractions: $\frac{11}{8} - \frac{4}{8} = \frac{7}{8}$.
* Answer: $1\frac{7}{8}$.
Final Answer:
1. c) find a common denominator
2. $\frac{3}{4}$
3. $\frac{5}{9}$
4. $8\frac{5}{8}$
5. $3\frac{1}{6}$
6. $2\frac{1}{3}$
7. $3$
8. $1\frac{1}{4}$
9. $0$
10. $6\frac{7}{8}$
11. $1$
12. $3\frac{1}{4}$
13. $4\frac{1}{2}$
14. $1\frac{7}{8}$
Parent Tip: Review the logic above to help your child master the concept of fractions with different denominators worksheet.
