To solve the division of fractions problem [tex]\( \frac{3}{14} \div 3 \)[/tex], follow these steps:
1. Rewrite the Division as Multiplication by the Reciprocal:
Dividing by a number is the same as multiplying by its reciprocal. The reciprocal of 3 is [tex]\( \frac{1}{3} \)[/tex]. So the division can be rewritten as:
[tex]\[
\frac{3}{14} \div 3 = \frac{3}{14} \times \frac{1}{3}
\][/tex]
2. Multiply the Numerators Together:
The numerators of the fractions are 3 and 1. Multiply these together:
[tex]\[
3 \times 1 = 3
\][/tex]
3. Multiply the Denominators Together:
The denominators of the fractions are 14 and 3. Multiply these together:
[tex]\[
14 \times 3 = 42
\][/tex]
4. Form the New Fraction:
After performing the multiplication of the numerators and the denominators, combine them into a new fraction:
[tex]\[
\frac{3 \times 1}{14 \times 3} = \frac{3}{42}
\][/tex]
5. Simplify the Fraction (if possible):
Finally, check if the fraction can be simplified. In this case:
[tex]\[
\frac{3}{42}
\][/tex]
Since both the numerator and the denominator can be divided by their greatest common divisor, which is 3:
[tex]\[
\frac{3 \div 3}{42 \div 3} = \frac{1}{14}
\][/tex]
Therefore, the final simplified fraction is [tex]\( \frac{1}{14} \)[/tex].
When expressed as a decimal, [tex]\( \frac{1}{14} \approx 0.07142857142857142 \)[/tex].
So, the result of [tex]\( \frac{3}{14} \div 3 \approx 0.07142857142857142 \)[/tex].
