Simplifying the Ratio of 28 Days to 8 Weeks: A Step-by-Step Guide
Understanding and simplifying ratios is a foundational skill in mathematics, particularly when dealing with measurements. In this article, we will explore how to simplify the ratio of 28 days to 8 weeks in lowest terms. This process involves converting the units to a common denominator so that the ratio can be expressed as a fraction and simplified to its simplest form.
Conversion of Weeks to Days
To begin with, it is crucial to understand the relationship between weeks and days. By definition, we know that 1 week consists of 7 days. Therefore, to convert weeks into days, we multiply the number of weeks by 7:
1 week 7 days
8 weeks 8 times; 7 56 days
This conversion allows us to express both parts of the ratio, 28 days and 8 weeks, in the same units of measurement, i.e., days.
Expressing the Ratio as a Fraction
Now that we have both quantities in days, we can express the ratio as a fraction:
28 days to 56 days ( frac{28}{56} )
Simplifying the Fraction to Lowest Terms
Next, we simplify the fraction ( frac{28}{56} ) to its lowest terms. To do this, we need to find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 28 and 56 is 28. Dividing both the numerator and the denominator by 28, we get:
( frac{28 div 28}{56 div 28} frac{1}{2} )
Thus, the simplified ratio in lowest terms is 1:2 or 1/2.
Conclusion
In summary, to simplify the ratio of 28 days to 8 weeks, we first converted 8 weeks into days, which is 56 days. Then, we expressed the ratio as a fraction, ( frac{28}{56} ), and simplified it to its lowest terms, which is 1:2 or 1/2. Understanding this process not only helps in solving similar problems but also reinforces the concept of ratios and fractions.