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Questions and Answers
What is the first step to solve $7\frac{1}{2} \div \frac{3}{4}$?
What is the first step to solve $7\frac{1}{2} \div \frac{3}{4}$?
- Convert $\frac{3}{4}$ to a decimal.
- Add $7 \frac{1}{2}$ and $\frac{3}{4}$.
- Multiply $7$ by $\frac{3}{4}$.
- Convert $7\frac{1}{2}$ to an improper fraction. (correct)
What does $7\frac{1}{2}$ equal when converted to an improper fraction?
What does $7\frac{1}{2}$ equal when converted to an improper fraction?
- $\frac{7}{4}$
- $\frac{15}{2}$
- $\frac{7}{2}$
- $\frac{17}{2}$ (correct)
After converting $7\frac{1}{2}$ to an improper fraction, what is the next step in solving the expression?
After converting $7\frac{1}{2}$ to an improper fraction, what is the next step in solving the expression?
- Multiply by the reciprocal of $\frac{3}{4}$. (correct)
- Subtract $\frac{3}{4}$ from $7\frac{1}{2}$.
- Add $\frac{3}{4}$ to $7\frac{1}{2}$.
- Evaluate $\frac{3}{4}$ before proceeding.
What is the reciprocal of $\frac{3}{4}$?
What is the reciprocal of $\frac{3}{4}$?
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What is the final result of $7\frac{1}{2} \div \frac{3}{4}$?
What is the final result of $7\frac{1}{2} \div \frac{3}{4}$?
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Study Notes
Steps to Solve the Division of a Mixed Number and a Fraction
- Begin with the expression: ( 7\frac{1}{2} \div \frac{3}{4} )
- Convert the mixed number ( 7\frac{1}{2} ) into an improper fraction.
Converting Mixed Numbers to Improper Fractions
- To convert ( 7\frac{1}{2} ):
- Multiply the whole number (7) by the denominator (2): ( 7 \times 2 = 14 )
- Add the numerator (1): ( 14 + 1 = 15 )
- The improper fraction is ( \frac{15}{2} )
Next Steps After Conversion
- After converting to an improper fraction, the next step is to rewrite the division operation as multiplication.
- Use the reciprocal of the second fraction:
- ( 7\frac{1}{2} \div \frac{3}{4} ) becomes ( \frac{15}{2} \times \frac{4}{3} )
Finding the Reciprocal
- The reciprocal of ( \frac{3}{4} ) is ( \frac{4}{3} )
Final Calculation
- Multiply the fractions:
- ( \frac{15}{2} \times \frac{4}{3} = \frac{15 \times 4}{2 \times 3} = \frac{60}{6} = 10 )
- The final result of ( 7\frac{1}{2} \div \frac{3}{4} ) is ( 10 )
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