To solve the division of fractions problem [tex]\(\frac{7}{2} \div \frac{9}{4}\)[/tex], we can follow these steps:
### Step 1: Understand the Operation
Division of fractions can be turned into multiplication by the reciprocal of the second fraction. This means that:
[tex]\[
\frac{7}{2} \div \frac{9}{4} \text{ is equivalent to } \frac{7}{2} \times \frac{4}{9}
\][/tex]
### Step 2: Multiply the Fractions
Now, we need to multiply the two fractions together.
To multiply fractions, multiply the numerators together and the denominators together:
[tex]\[
\frac{7}{2} \times \frac{4}{9}
\][/tex]
### Step 3: Calculate the Numerator
Multiply the numerators of these fractions:
[tex]\[
7 \times 4 = 28
\][/tex]
### Step 4: Calculate the Denominator
Multiply the denominators of these fractions:
[tex]\[
2 \times 9 = 18
\][/tex]
### Step 5: Formulate the New Fraction
So, we have:
[tex]\[
\frac{28}{18}
\][/tex]
### Step 6: Simplify the Fraction
To simplify the fraction, find the greatest common divisor (GCD) of the numerator and the denominator and divide both by that number.
The GCD of 28 and 18 is 2.
Divide both the numerator and the denominator by 2:
[tex]\[
\frac{28 \div 2}{18 \div 2} = \frac{14}{9}
\][/tex]
### Step 7: Convert to Mixed Number (if needed)
Since [tex]\(\frac{14}{9}\)[/tex] is an improper fraction, we may convert it to a mixed number for better understanding, though it's not required here.
Doing this we get:
[tex]\[
\frac{14}{9} = 1 \frac{5}{9}
\][/tex]
### Final Exact Result in Decimal Form
Additionally, if we convert [tex]\(\frac{14}{9}\)[/tex] into a decimal, it is approximately:
[tex]\[
1.5555555555555554~
\][/tex]
So, the result of [tex]\(\frac{7}{2} \div \frac{9}{4}\)[/tex] is:
[tex]\[
1.5555555555555554
\][/tex]
