To reduce the mixed number [tex]\( 3 \frac{4}{12} \)[/tex] to its lowest terms, we will follow these steps:
1. Convert the mixed number to an improper fraction:
The given mixed number is [tex]\( 3 \frac{4}{12} \)[/tex].
To convert it to an improper fraction, we multiply the whole number part (3) by the denominator (12) and then add the numerator (4):
[tex]\[
3 \times 12 + 4 = 36 + 4 = 40
\][/tex]
Therefore, the improper fraction is:
[tex]\[
\frac{40}{12}
\][/tex]
2. Simplify the improper fraction:
To simplify the fraction [tex]\(\frac{40}{12}\)[/tex], we need to find the greatest common divisor (GCD) of 40 and 12. The GCD of 40 and 12 is 4.
We divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{40 \div 4}{12 \div 4} = \frac{10}{3}
\][/tex]
Thus, the simplified form of the improper fraction [tex]\(\frac{40}{12}\)[/tex] is [tex]\(\frac{10}{3}\)[/tex].
3. Convert the improper fraction back to a mixed number, if necessary:
Sometimes, it's helpful to understand the improper fraction as a mixed number. For [tex]\(\frac{10}{3}\)[/tex], the whole number part is obtained by dividing the numerator by the denominator:
[tex]\[
10 \div 3 = 3 \text{ remainder } 1
\][/tex]
Therefore, [tex]\(\frac{10}{3}\)[/tex] can be written as the mixed number [tex]\( 3 \frac{1}{3}\)[/tex].
4. Verify the decimal representation:
The decimal representation of the fraction [tex]\(\frac{10}{3}\)[/tex] is obtained by dividing 10 by 3:
[tex]\[
10 \div 3 \approx 3.3333333333333335
\][/tex]
5. Conclusion:
So, the mixed number [tex]\( 3 \frac{4}{12} \)[/tex] reduces to the improper fraction [tex]\(\frac{10}{3}\)[/tex], which is in its lowest terms. In decimal form, it is approximately [tex]\( 3.3333333333333335 \)[/tex].
