Write 5 1/6 as an improper fraction.
The correct answer and explanation is:
Correct Answer:
5 1/6 as an improper fraction is 31/6.
Explanation:
A mixed number is a whole number combined with a fraction. To convert a mixed number like 5 1/6 into an improper fraction, follow a standard method. First, identify the whole number part (5) and the fraction part (1/6). The goal is to express the entire quantity as a single fraction where the numerator is greater than the denominator.
To begin, multiply the whole number by the denominator of the fractional part. In this case, multiply 5 (whole number) by 6 (denominator of the fraction).
5 × 6 = 30
This result represents how many sixths are in the whole number part. Next, add the numerator of the fractional part to that result.
30 + 1 = 31
This total becomes the new numerator, while the denominator stays the same. So, the improper fraction is:
31/6
Improper fractions are useful in many math applications because they make certain operations like multiplication, division, and algebraic manipulation simpler. Rather than having to manage two parts (a whole number and a fraction), you deal with a single quantity. For example, 5 1/6 is harder to multiply by another fraction than 31/6.
To check your work, you can convert 31/6 back to a mixed number. Divide 31 by 6. The quotient is 5, and the remainder is 1. This gives 5 1/6, which confirms the conversion is correct.
Understanding how to shift between mixed numbers and improper fractions is a key skill in arithmetic and forms the foundation for higher-level math topics such as algebra, ratios, and proportional reasoning.