There are 144 competitors joining the swimming competition. 5/12 of the competitors live on Hong Kong Island, 1/3 of the competitors live in Kowloon and the rest of the competitors live in the New Territories.
What fraction of the competitors live on Hong Kong Island and in Kowloon?
How many competitors live on Hong Kong Island and in Kowloon?
How many competitors live in the New Territories?
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We have a swimming competition with 144 competitors. Five-twelfths of them live on Hong Kong Island, one-third live in Kowloon, and the rest live in the New Territories. Let's visualize this distribution and solve the questions step by step.
Let's solve the first question: What fraction of competitors live on Hong Kong Island and in Kowloon? We need to add five-twelfths plus one-third. First, we find a common denominator, which is twelve. We convert one-third to four-twelfths. Then we add five-twelfths plus four-twelfths equals nine-twelfths. Finally, we simplify nine-twelfths to three-fourths.
Now let's calculate how many competitors live on Hong Kong Island and in Kowloon. We multiply 144 by three-fourths. We can calculate this as 144 divided by 4, times 3. 144 divided by 4 equals 36, and 36 times 3 equals 108. So 108 competitors live on Hong Kong Island and in Kowloon.
Finally, let's find how many competitors live in the New Territories. We can subtract the number living on Hong Kong Island and in Kowloon from the total: 144 minus 108 equals 36. Alternatively, we can calculate the fraction living in New Territories as 1 minus three-fourths, which equals one-fourth. Then 144 times one-fourth equals 36 competitors.
Let's summarize our final answers. The fraction of competitors living on Hong Kong Island and in Kowloon is three-fourths. The number of competitors living on Hong Kong Island and in Kowloon is 108. The number of competitors living in the New Territories is 36. We can verify our answer: 108 plus 36 equals 144, which matches the total number of competitors.