Subtracting Fractions from Whole Numbers Worksheets - Free Printable

To solve these problems, we need to subtract fractions from whole numbers. Here is the step-by-step thinking process for solving these types of problems:

1. Convert the whole number to a fraction: To subtract a fraction from a whole number, we first need to turn the whole number into a fraction that has the same denominator (bottom number) as the fraction we are subtracting.
* For example, if we have $11 - \frac{5}{6}$, we change $11$ into a fraction. Since the denominator is $6$, we think of $11$ as $\frac{11 \times 6}{6}$.
* $11 \times 6 = 66$, so $11 = \frac{66}{6}$.

2. Subtract the numerators: Once the denominators are the same, we just subtract the top numbers (numerators).
* $\frac{66}{6} - \frac{5}{6} = \frac{66 - 5}{6} = \frac{61}{6}$.

3. Simplify to a mixed number: Since the numerator is larger than the denominator, we can convert it back to a mixed number.
* $61 \div 6 = 10$ with a remainder of $1$.
* So, $\frac{61}{6} = 10 \frac{1}{6}$.

Let's apply this method to all the problems on the sheet.

Problem 1: $11 - \frac{5}{6}$
* Convert $11$: $11 = \frac{66}{6}$
* Subtract: $\frac{66}{6} - \frac{5}{6} = \frac{61}{6}$
* Mixed number: $10 \frac{1}{6}$

Problem 2: $21 - \frac{11}{12}$
* Convert $21$: $21 = \frac{21 \times 12}{12} = \frac{252}{12}$
* Subtract: $\frac{252}{12} - \frac{11}{12} = \frac{241}{12}$
* Mixed number: $241 \div 12 = 20$ remainder $1$. Answer: $20 \frac{1}{12}$

Problem 3: $2 - \frac{10}{11}$
* Convert $2$: $2 = \frac{22}{11}$
* Subtract: $\frac{22}{11} - \frac{10}{11} = \frac{12}{11}$
* Mixed number: $12 \div 11 = 1$ remainder $1$. Answer: $1 \frac{1}{11}$

Problem 4: $7 - \frac{4}{9}$
* Convert $7$: $7 = \frac{63}{9}$
* Subtract: $\frac{63}{9} - \frac{4}{9} = \frac{59}{9}$
* Mixed number: $59 \div 9 = 6$ remainder $5$. Answer: $6 \frac{5}{9}$

Problem 5: $8 - \frac{3}{7}$
* Convert $8$: $8 = \frac{56}{7}$
* Subtract: $\frac{56}{7} - \frac{3}{7} = \frac{53}{7}$
* Mixed number: $53 \div 7 = 7$ remainder $4$. Answer: $7 \frac{4}{7}$

Problem 6: $4 - \frac{5}{9}$
* Convert $4$: $4 = \frac{36}{9}$
* Subtract: $\frac{36}{9} - \frac{5}{9} = \frac{31}{9}$
* Mixed number: $31 \div 9 = 3$ remainder $4$. Answer: $3 \frac{4}{9}$

Problem 7: $7 - \frac{1}{3}$
* Convert $7$: $7 = \frac{21}{3}$
* Subtract: $\frac{21}{3} - \frac{1}{3} = \frac{20}{3}$
* Mixed number: $20 \div 3 = 6$ remainder $2$. Answer: $6 \frac{2}{3}$

Problem 8: $9 - \frac{6}{7}$
* Convert $9$: $9 = \frac{63}{7}$
* Subtract: $\frac{63}{7} - \frac{6}{7} = \frac{57}{7}$
* Mixed number: $57 \div 7 = 8$ remainder $1$. Answer: $8 \frac{1}{7}$

Problem 9: $3 - \frac{13}{14}$
* Convert $3$: $3 = \frac{42}{14}$
* Subtract: $\frac{42}{14} - \frac{13}{14} = \frac{29}{14}$
* Mixed number: $29 \div 14 = 2$ remainder $1$. Answer: $2 \frac{1}{14}$

Problem 10: $5 - \frac{1}{12}$
* Convert $5$: $5 = \frac{60}{12}$
* Subtract: $\frac{60}{12} - \frac{1}{12} = \frac{59}{12}$
* Mixed number: $59 \div 12 = 4$ remainder $11$. Answer: $4 \frac{11}{12}$

Problem 11: $9 - \frac{4}{6}$
* First, simplify $\frac{4}{6}$ to $\frac{2}{3}$.
* Convert $9$: $9 = \frac{27}{3}$
* Subtract: $\frac{27}{3} - \frac{2}{3} = \frac{25}{3}$
* Mixed number: $25 \div 3 = 8$ remainder $1$. Answer: $8 \frac{1}{3}$

Problem 12: $2 - \frac{8}{11}$
* Convert $2$: $2 = \frac{22}{11}$
* Subtract: $\frac{22}{11} - \frac{8}{11} = \frac{14}{11}$
* Mixed number: $14 \div 11 = 1$ remainder $3$. Answer: $1 \frac{3}{11}$

Problem 13: $4 - \frac{2}{7}$
* Convert $4$: $4 = \frac{28}{7}$
* Subtract: $\frac{28}{7} - \frac{2}{7} = \frac{26}{7}$
* Mixed number: $26 \div 7 = 3$ remainder $5$. Answer: $3 \frac{5}{7}$

Problem 14: $6 - \frac{1}{2}$
* Convert $6$: $6 = \frac{12}{2}$
* Subtract: $\frac{12}{2} - \frac{1}{2} = \frac{11}{2}$
* Mixed number: $11 \div 2 = 5$ remainder $1$. Answer: $5 \frac{1}{2}$

Final Answer:
1) $10 \frac{1}{6}$
2) $20 \frac{1}{12}$
3) $1 \frac{1}{11}$
4) $6 \frac{5}{9}$
5) $7 \frac{4}{7}$
6) $3 \frac{4}{9}$
7) $6 \frac{2}{3}$
8) $8 \frac{1}{7}$
9) $2 \frac{1}{14}$
10) $4 \frac{11}{12}$
11) $8 \frac{1}{3}$
12) $1 \frac{3}{11}$
13) $3 \frac{5}{7}$
14) $5 \frac{1}{2}$