The pacific ocean covers 1/3 of Earth surface the Atlantic Ocean cover 1/5 of Earth surface, what fraction of Earth surface is covered by both oceans?
The Correct Answer and Explanation is:
To solve the problem, we are asked to find the fraction of Earth’s surface that is covered by both the Pacific Ocean and the Atlantic Ocean combined. Let’s first break down the fractions and add them together:
- The Pacific Ocean covers (\frac{1}{3}) of Earth’s surface.
- The Atlantic Ocean covers (\frac{1}{5}) of Earth’s surface.
To add these fractions, we need a common denominator. The denominators here are 3 and 5, and their least common denominator (LCD) is 15. To convert each fraction to have a denominator of 15, we proceed as follows:
[
\frac{1}{3} = \frac{5}{15} \quad (\text{multiply both numerator and denominator by 5})
]
[
\frac{1}{5} = \frac{3}{15} \quad (\text{multiply both numerator and denominator by 3})
]
Now that both fractions have the same denominator, we can add them:
[
\frac{5}{15} + \frac{3}{15} = \frac{8}{15}
]
Thus, the Pacific Ocean and the Atlantic Ocean together cover (\frac{8}{15}) of Earth’s surface.
Explanation:
In this problem, we added two fractions that represent portions of Earth’s surface covered by different oceans. The Pacific Ocean covers (\frac{1}{3}), and the Atlantic Ocean covers (\frac{1}{5}). Since these fractions have different denominators, we first found the least common denominator (LCD), which is 15. By converting each fraction to have the denominator of 15, we could easily add them.
The process of finding the least common denominator ensures that the fractions are in comparable terms. Once the fractions were converted, we added the numerators while keeping the denominator the same, giving us (\frac{8}{15}). Therefore, the two oceans together cover (\frac{8}{15}) of Earth’s surface. This method works for adding any fractions, provided the correct LCD is used.
This type of problem is commonly encountered in real-life situations where portions or fractions of a whole are involved, such as area calculations or when dealing with parts of a whole object.