To simplify [tex]\( 5 \frac{1}{4} \div 57 \)[/tex], we will follow these steps:
1. Convert the mixed number to an improper fraction.\
A mixed number such as [tex]\( 5 \frac{1}{4} \)[/tex] can be written as an improper fraction. Here, [tex]\( 5 \frac{1}{4} \)[/tex] can be converted into a single fraction by combining the whole number and the fractional part:
[tex]\[
5 \frac{1}{4} = 5 + \frac{1}{4}
\][/tex]
When adding these, the whole number 5 needs to be expressed with a denominator of 4:
[tex]\[
5 = \frac{5 \times 4}{4} = \frac{20}{4}
\][/tex]
Adding the fractional part:
[tex]\[
\frac{20}{4} + \frac{1}{4} = \frac{21}{4}
\][/tex]
So, [tex]\( 5 \frac{1}{4} \)[/tex] as an improper fraction is [tex]\( \frac{21}{4} \)[/tex].
2. Divide the improper fraction by 57.\
Now, we need to evaluate [tex]\( \frac{21}{4} \div 57 \)[/tex]. Division by a whole number can be transformed into multiplication by its reciprocal. Thus,
[tex]\[
\frac{21}{4} \div 57 = \frac{21}{4} \times \frac{1}{57}
\][/tex]
Multiplying these fractions, we get:
[tex]\[
\frac{21 \times 1}{4 \times 57} = \frac{21}{228}
\][/tex]
Simplifying further, we recognize that 21 and 228 have a common factor of 3:
[tex]\[
\frac{21 \div 3}{228 \div 3} = \frac{7}{76}
\][/tex]
3. Express as a decimal (optional).\
To express [tex]\(\frac{7}{76}\)[/tex] as a decimal, you divide the numerator by the denominator:
[tex]\[
\frac{7}{76} \approx 0.09210526315789473
\][/tex]
Therefore, the simplified value of [tex]\( 5 \frac{1}{4} \div 57 \)[/tex] is:
[tex]\[
0.09210526315789473
\][/tex]
