9514 1404 393
Answer:
- 1 7/12 is simplest form as a mixed number
- 19/12 is simplest form as an improper fraction
Step-by-step explanation:
A fraction is in simplest form when any common factors in the numerator and denominator have been factored out (cancelled). The fraction 7/12 has no common factors in the numerator and denominator. (7 is a prime number, and 12 = 2²·3 is not a multiple of 7.) Hence, the fraction 7/12 is in simplest form.
When the fraction is part of a mixed number, that mixed number is in simplest form when the fraction is. Here, 1 7/12 is in simplest form.
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The integer portion of a mixed number can be expressed over the fraction's denominator by multiplying it by 1 in the form (denominator)/(denominator).
[tex]1\dfrac{7}{12}=1\times\dfrac{12}{12}+\dfrac{7}{12}=\dfrac{1\times12+7}{12}=\dfrac{19}{12}[/tex]
Since the fraction 7/12 is in simplest form, this improper fraction is in simplest form. 19/12 is the simplest form of 1 7/12 when expressed as an improper fraction.
