What is 4 1/2 divided by 3/4

What is 4 1/2 divided by 3/4??

The Correct Answer and Explanation is :

To solve the problem of dividing ( 4 \frac{1}{2} ) by ( \frac{3}{4} ), we first need to convert the mixed number ( 4 \frac{1}{2} ) into an improper fraction.

Step 1: Convert the Mixed Number

A mixed number consists of a whole number and a fraction. To convert ( 4 \frac{1}{2} ):

1. Multiply the whole number by the denominator of the fractional part:
   ( 4 \times 2 = 8 ).
2. Add the result to the numerator of the fractional part:
   ( 8 + 1 = 9 ).
3. Place this sum over the original denominator:
   ( 4 \frac{1}{2} = \frac{9}{2} ).

Step 2: Set Up the Division Problem

Now, we can rewrite the division problem:

[
\frac{9}{2} \div \frac{3}{4}
]

Step 3: Convert Division to Multiplication

To divide by a fraction, we multiply by its reciprocal. The reciprocal of ( \frac{3}{4} ) is ( \frac{4}{3} ). Thus, the problem becomes:

[
\frac{9}{2} \times \frac{4}{3}
]

Step 4: Multiply the Fractions

Now we can multiply the fractions:

1. Multiply the numerators:
   ( 9 \times 4 = 36 ).
2. Multiply the denominators:
   ( 2 \times 3 = 6 ).

So, we have:

[
\frac{36}{6}
]

Step 5: Simplify the Result

Now, we simplify ( \frac{36}{6} ):

[
\frac{36}{6} = 6
]

Final Answer

Thus, ( 4 \frac{1}{2} \div \frac{3}{4} = 6 ).

Conclusion

Dividing mixed numbers and fractions involves converting the mixed number to an improper fraction, changing the division to multiplication by using the reciprocal, and simplifying the resulting fraction. Understanding these steps is crucial for effectively solving similar problems in mathematics.