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Dividing Mixed Numbers and Fractions

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Questions and Answers

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?

$\frac{7}{4}$

$\frac{15}{2}$

$\frac{7}{2}$

$\frac{17}{2}$ (correct)

After converting $7\frac{1}{2}$ to an improper fraction, what is the next step in solving the expression?

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 $\frac{3}{4}$?

<p>$\frac{4}{3}$</p> Signup and view all the answers

What is the final result of $7\frac{1}{2} \div \frac{3}{4}$?

<p>5</p> Signup and view all the answers

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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Description

This quiz focuses on solving the division of mixed numbers and fractions. It guides you through converting a mixed number into an improper fraction and finding the reciprocal of a fraction. Test your understanding of the steps involved in this calculation.