Operations between fractions and mixed numbers worksheet (with ... - Free Printable
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Step-by-step solution for: Operations between fractions and mixed numbers worksheet (with ...
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Show Answer Key & Explanations
Step-by-step solution for: Operations between fractions and mixed numbers worksheet (with ...
Here are the step-by-step solutions for the math problems on the worksheet.
1) $\frac{1}{2} + 3\frac{1}{4}$
* First, find a common denominator for the fractions $\frac{1}{2}$ and $\frac{1}{4}$. The common denominator is 4.
* Convert $\frac{1}{2}$ to fourths: $\frac{1 \times 2}{2 \times 2} = \frac{2}{4}$.
* Add the whole number and the fractions: $3 + (\frac{2}{4} + \frac{1}{4}) = 3\frac{3}{4}$.
2) $5\frac{2}{3} - \frac{1}{5}$
* Find a common denominator for 3 and 5, which is 15.
* Convert the fractions: $\frac{2}{3} = \frac{10}{15}$ and $\frac{1}{5} = \frac{3}{15}$.
* Subtract: $5\frac{10}{15} - \frac{3}{15} = 5\frac{7}{15}$.
3) $\frac{1}{4} \times 5\frac{1}{3}$
* Convert the mixed number to an improper fraction: $5\frac{1}{3} = \frac{(5 \times 3) + 1}{3} = \frac{16}{3}$.
* Multiply straight across: $\frac{1}{4} \times \frac{16}{3} = \frac{16}{12}$.
* Simplify the fraction by dividing top and bottom by 4: $\frac{4}{3}$.
* Convert back to a mixed number: $1\frac{1}{3}$.
4) $4\frac{2}{3} \div \frac{3}{5}$
* Convert the mixed number to an improper fraction: $4\frac{2}{3} = \frac{14}{3}$.
* To divide by a fraction, multiply by its reciprocal (flip it): $\frac{14}{3} \times \frac{5}{3}$.
* Multiply straight across: $\frac{14 \times 5}{3 \times 3} = \frac{70}{9}$.
* Convert to a mixed number ($70 \div 9 = 7$ with remainder 7): $7\frac{7}{9}$.
5) $\frac{4}{7} + 5\frac{2}{3}$
* Find a common denominator for 7 and 3, which is 21.
* Convert fractions: $\frac{4}{7} = \frac{12}{21}$ and $\frac{2}{3} = \frac{14}{21}$.
* Add them up: $5 + (\frac{12}{21} + \frac{14}{21}) = 5\frac{26}{21}$.
* Since $\frac{26}{21}$ is bigger than 1, convert it to $1\frac{5}{21}$.
* Add that 1 to the whole number 5: $6\frac{5}{21}$.
7) $\frac{3}{5} \times 2\frac{1}{2}$
* Convert the mixed number: $2\frac{1}{2} = \frac{5}{2}$.
* Multiply: $\frac{3}{5} \times \frac{5}{2}$. You can cancel out the 5s.
* Result: $\frac{3}{2}$.
* Convert to mixed number: $1\frac{1}{2}$.
9) $\frac{2}{9} \times 4\frac{1}{3}$
* Convert the mixed number: $4\frac{1}{3} = \frac{13}{3}$.
* Multiply: $\frac{2}{9} \times \frac{13}{3} = \frac{26}{27}$.
* This cannot be simplified further.
10) $10\frac{1}{2} \times \frac{3}{4}$
* Convert the mixed number: $10\frac{1}{2} = \frac{21}{2}$.
* Multiply: $\frac{21}{2} \times \frac{3}{4} = \frac{63}{8}$.
* Convert to mixed number ($63 \div 8 = 7$ remainder 7): $7\frac{7}{8}$.
11) $1\frac{1}{4} + 3\frac{5}{6}$ *(Note: Problem inferred from image layout)*
* Common denominator for 4 and 6 is 12.
* Convert: $1\frac{3}{12} + 3\frac{10}{12}$.
* Add: $4\frac{13}{12}$.
* Simplify $\frac{13}{12}$ to $1\frac{1}{12}$.
* Final answer: $5\frac{1}{12}$.
12) $15\frac{3}{8} - \frac{1}{6}$
* Common denominator for 8 and 6 is 24.
* Convert: $\frac{3}{8} = \frac{9}{24}$ and $\frac{1}{6} = \frac{4}{24}$.
* Subtract: $15\frac{9}{24} - \frac{4}{24} = 15\frac{5}{24}$.
13) $14\frac{1}{2} - \frac{3}{4}$
* Common denominator is 4.
* Convert $\frac{1}{2}$ to $\frac{2}{4}$. So we have $14\frac{2}{4} - \frac{3}{4}$.
* You can't take 3 away from 2, so borrow 1 from the 14.
* $14\frac{2}{4}$ becomes $13\frac{6}{4}$ (since $1 = \frac{4}{4}$).
* Now subtract: $13\frac{6}{4} - \frac{3}{4} = 13\frac{3}{4}$.
14) $\frac{2}{9} \times 1\frac{5}{9}$
* Convert mixed number: $1\frac{5}{9} = \frac{14}{9}$.
* Multiply: $\frac{2}{9} \times \frac{14}{9} = \frac{28}{81}$.
15) $\frac{4}{5} \div 3\frac{1}{5}$
* Convert mixed number: $3\frac{1}{5} = \frac{16}{5}$.
* Flip and multiply: $\frac{4}{5} \times \frac{5}{16}$.
* Cancel the 5s and simplify $\frac{4}{16}$ to $\frac{1}{4}$.
16) $\frac{3}{4} + 9\frac{1}{5}$
* Common denominator for 4 and 5 is 20.
* Convert: $\frac{3}{4} = \frac{15}{20}$ and $\frac{1}{5} = \frac{4}{20}$.
* Add: $9 + (\frac{15}{20} + \frac{4}{20}) = 9\frac{19}{20}$.
Final Answer:
1) $3\frac{3}{4}$
2) $5\frac{7}{15}$
3) $1\frac{1}{3}$
4) $7\frac{7}{9}$
5) $6\frac{5}{21}$
7) $1\frac{1}{2}$
9) $\frac{26}{27}$
10) $7\frac{7}{8}$
11) $5\frac{1}{12}$
12) $15\frac{5}{24}$
13) $13\frac{3}{4}$
14) $\frac{28}{81}$
15) $\frac{1}{4}$
16) $9\frac{19}{20}$
1) $\frac{1}{2} + 3\frac{1}{4}$
* First, find a common denominator for the fractions $\frac{1}{2}$ and $\frac{1}{4}$. The common denominator is 4.
* Convert $\frac{1}{2}$ to fourths: $\frac{1 \times 2}{2 \times 2} = \frac{2}{4}$.
* Add the whole number and the fractions: $3 + (\frac{2}{4} + \frac{1}{4}) = 3\frac{3}{4}$.
2) $5\frac{2}{3} - \frac{1}{5}$
* Find a common denominator for 3 and 5, which is 15.
* Convert the fractions: $\frac{2}{3} = \frac{10}{15}$ and $\frac{1}{5} = \frac{3}{15}$.
* Subtract: $5\frac{10}{15} - \frac{3}{15} = 5\frac{7}{15}$.
3) $\frac{1}{4} \times 5\frac{1}{3}$
* Convert the mixed number to an improper fraction: $5\frac{1}{3} = \frac{(5 \times 3) + 1}{3} = \frac{16}{3}$.
* Multiply straight across: $\frac{1}{4} \times \frac{16}{3} = \frac{16}{12}$.
* Simplify the fraction by dividing top and bottom by 4: $\frac{4}{3}$.
* Convert back to a mixed number: $1\frac{1}{3}$.
4) $4\frac{2}{3} \div \frac{3}{5}$
* Convert the mixed number to an improper fraction: $4\frac{2}{3} = \frac{14}{3}$.
* To divide by a fraction, multiply by its reciprocal (flip it): $\frac{14}{3} \times \frac{5}{3}$.
* Multiply straight across: $\frac{14 \times 5}{3 \times 3} = \frac{70}{9}$.
* Convert to a mixed number ($70 \div 9 = 7$ with remainder 7): $7\frac{7}{9}$.
5) $\frac{4}{7} + 5\frac{2}{3}$
* Find a common denominator for 7 and 3, which is 21.
* Convert fractions: $\frac{4}{7} = \frac{12}{21}$ and $\frac{2}{3} = \frac{14}{21}$.
* Add them up: $5 + (\frac{12}{21} + \frac{14}{21}) = 5\frac{26}{21}$.
* Since $\frac{26}{21}$ is bigger than 1, convert it to $1\frac{5}{21}$.
* Add that 1 to the whole number 5: $6\frac{5}{21}$.
7) $\frac{3}{5} \times 2\frac{1}{2}$
* Convert the mixed number: $2\frac{1}{2} = \frac{5}{2}$.
* Multiply: $\frac{3}{5} \times \frac{5}{2}$. You can cancel out the 5s.
* Result: $\frac{3}{2}$.
* Convert to mixed number: $1\frac{1}{2}$.
9) $\frac{2}{9} \times 4\frac{1}{3}$
* Convert the mixed number: $4\frac{1}{3} = \frac{13}{3}$.
* Multiply: $\frac{2}{9} \times \frac{13}{3} = \frac{26}{27}$.
* This cannot be simplified further.
10) $10\frac{1}{2} \times \frac{3}{4}$
* Convert the mixed number: $10\frac{1}{2} = \frac{21}{2}$.
* Multiply: $\frac{21}{2} \times \frac{3}{4} = \frac{63}{8}$.
* Convert to mixed number ($63 \div 8 = 7$ remainder 7): $7\frac{7}{8}$.
11) $1\frac{1}{4} + 3\frac{5}{6}$ *(Note: Problem inferred from image layout)*
* Common denominator for 4 and 6 is 12.
* Convert: $1\frac{3}{12} + 3\frac{10}{12}$.
* Add: $4\frac{13}{12}$.
* Simplify $\frac{13}{12}$ to $1\frac{1}{12}$.
* Final answer: $5\frac{1}{12}$.
12) $15\frac{3}{8} - \frac{1}{6}$
* Common denominator for 8 and 6 is 24.
* Convert: $\frac{3}{8} = \frac{9}{24}$ and $\frac{1}{6} = \frac{4}{24}$.
* Subtract: $15\frac{9}{24} - \frac{4}{24} = 15\frac{5}{24}$.
13) $14\frac{1}{2} - \frac{3}{4}$
* Common denominator is 4.
* Convert $\frac{1}{2}$ to $\frac{2}{4}$. So we have $14\frac{2}{4} - \frac{3}{4}$.
* You can't take 3 away from 2, so borrow 1 from the 14.
* $14\frac{2}{4}$ becomes $13\frac{6}{4}$ (since $1 = \frac{4}{4}$).
* Now subtract: $13\frac{6}{4} - \frac{3}{4} = 13\frac{3}{4}$.
14) $\frac{2}{9} \times 1\frac{5}{9}$
* Convert mixed number: $1\frac{5}{9} = \frac{14}{9}$.
* Multiply: $\frac{2}{9} \times \frac{14}{9} = \frac{28}{81}$.
15) $\frac{4}{5} \div 3\frac{1}{5}$
* Convert mixed number: $3\frac{1}{5} = \frac{16}{5}$.
* Flip and multiply: $\frac{4}{5} \times \frac{5}{16}$.
* Cancel the 5s and simplify $\frac{4}{16}$ to $\frac{1}{4}$.
16) $\frac{3}{4} + 9\frac{1}{5}$
* Common denominator for 4 and 5 is 20.
* Convert: $\frac{3}{4} = \frac{15}{20}$ and $\frac{1}{5} = \frac{4}{20}$.
* Add: $9 + (\frac{15}{20} + \frac{4}{20}) = 9\frac{19}{20}$.
Final Answer:
1) $3\frac{3}{4}$
2) $5\frac{7}{15}$
3) $1\frac{1}{3}$
4) $7\frac{7}{9}$
5) $6\frac{5}{21}$
7) $1\frac{1}{2}$
9) $\frac{26}{27}$
10) $7\frac{7}{8}$
11) $5\frac{1}{12}$
12) $15\frac{5}{24}$
13) $13\frac{3}{4}$
14) $\frac{28}{81}$
15) $\frac{1}{4}$
16) $9\frac{19}{20}$
Parent Tip: Review the logic above to help your child master the concept of operations with mixed numbers worksheet.
