San Diego Zoo: Killer Whale Vs Dolphin Fish Consumption

Dec 11, 2025 by Admin 56 views

Hey guys, ever wondered about the dining habits of the magnificent marine creatures at the San Diego Zoo? Today, we're diving deep into a fascinating math problem that sheds some light on just how much fish these aquatic giants munch on. We're talking about the dolphins and the powerful killer whales, and figuring out their daily fish intake is more interesting than it sounds, especially when we get into the world of mixed numbers and multiplication. So, grab your thinking caps, because we're about to break down this problem step-by-step, making sure everyone can follow along, no matter your math comfort level. We'll explore the specifics of the dolphins' diet and then use that information to calculate the killer whales' much larger appetite. It's a great way to practice our fractions and mixed numbers in a real-world context, showing that math is all around us, even when we're thinking about zoo animals. We'll start by understanding the initial amount of fish the dolphins consume, which is given as a mixed number, $3 rac{1}{8}$ buckets. This number tells us that the dolphins eat more than three whole buckets but less than four. Then, we'll tackle the core of the problem: the killer whales eat $2 rac{3}{5}$ times as much fish as the dolphins. This phrase 'times as much' is our key indicator that we need to perform multiplication. We'll convert these mixed numbers into improper fractions, which makes multiplication much easier. Remember, converting a mixed number like $a rac{b}{c}$ to an improper fraction involves the formula $( rac{ac+b}{c})$ . So, for the dolphins' fish intake, $3 rac{1}{8}$ becomes $( rac{3 imes 8 + 1}{8}) = rac{25}{8}$ . For the multiplier representing the killer whales' portion, $2 rac{3}{5}$ becomes $( rac{2 imes 5 + 3}{5}) = rac{13}{5}$ . Once we have these improper fractions, we can multiply them together to find the total number of fish buckets consumed by the killer whales each day. This process not only helps us solve the problem but also reinforces important mathematical skills. We'll make sure to explain each conversion and multiplication step clearly, so stick around to see how these ocean giants fuel their impressive lives!

Understanding the Dolphins' Daily Fish Intake

Alright, let's get down to business with our first piece of information: the dolphins at the San Diego Zoo eat $3 rac{1}{8}$ buckets of fish each day. This is our starting point, the baseline we'll use to figure out the killer whales' much larger meal. Now, $3 rac{1}{8}$ is what we call a mixed number. It's a whole number (3) combined with a fraction ( $rac{1}{8}$ ). It means the dolphins eat three full buckets of fish, plus an additional one-eighth of another bucket. While this might seem like a specific detail, it's crucial for our calculation. Before we can do any fancy multiplication, especially with another mixed number, it's usually way easier if we convert these mixed numbers into improper fractions. Don't let the term 'improper' fool you; it just means the numerator (the top number) is larger than or equal to the denominator (the bottom number). It's simply a different way to represent the same quantity, and it makes multiplication and division a breeze. To convert $3 rac{1}{8}$ into an improper fraction, we use a simple formula: multiply the whole number by the denominator, and then add the numerator. The result becomes the new numerator, and the denominator stays the same. So, for $3 rac{1}{8}$ :

Multiply the whole number (3) by the denominator (8): $3 imes 8 = 24$ .
Add the numerator (1) to that result: $24 + 1 = 25$ .
Keep the original denominator (8).

So, $3 rac{1}{8}$ buckets of fish is the same as $rac{25}{8}$ buckets. Now we have a much more manageable form to work with! This $rac{25}{8}$ represents the daily fish consumption for the dolphins. It's a significant amount, but as we'll see, it's just a fraction of what the killer whales consume. Understanding this initial value is key. It's like setting the stage for the main event. We've taken a mixed number, which can sometimes feel a bit clunky for calculations, and transformed it into an improper fraction, which is a powerhouse for mathematical operations. This step is fundamental, and getting it right ensures the rest of our calculation will be accurate. So, next time you see a mixed number, remember this conversion trick – it's a game-changer for solving problems like this one. Keep this $rac{25}{8}$ in mind, because it's the foundation for calculating the killer whales' massive appetite!

Calculating the Killer Whales' Fish Consumption

Now that we've got the dolphins' fish intake nicely converted into an improper fraction, $rac{25}{8}$ buckets, it's time to tackle the main event: the killer whales eat $2 rac{3}{5}$ times as much fish as the dolphins. This is where the real calculation happens, guys! The phrase "times as much" is our big clue that we need to multiply. We need to multiply the dolphins' fish consumption by the factor representing the killer whales' appetite. Just like we did with the dolphins' fish amount, we need to convert the killer whales' multiplier, $2 rac{3}{5}$ , into an improper fraction. Let's use that same handy formula: multiply the whole number by the denominator and add the numerator.

For $2 rac{3}{5}$ : Multiply the whole number (2) by the denominator (5): $2 imes 5 = 10$ .
Add the numerator (3) to that result: $10 + 3 = 13$ .
Keep the original denominator (5).

So, $2 rac{3}{5}$ is equivalent to the improper fraction $rac{13}{5}$ . Now we have all the pieces ready for multiplication. We need to multiply the dolphins' fish amount ( $rac{25}{8}$ ) by the killer whales' multiplier ( $rac{13}{5}$ ). The multiplication of fractions is pretty straightforward. You multiply the numerators together to get the new numerator, and you multiply the denominators together to get the new denominator.

So, we have:

rac{25}{8} imes rac{13}{5} = rac{25 imes 13}{8 imes 5}

Let's do the multiplication:

Numerator: $25 imes 13$ . We can break this down: $25 imes 10 = 250$ , and $25 imes 3 = 75$ . Add them together: $250 + 75 = 325$ .
Denominator: $8 imes 5 = 40$ .

This gives us the fraction $rac{325}{40}$ . This is the answer in improper fraction form. But wait, we're dealing with buckets of fish, and usually, it's easier to understand a mixed number for quantities like this. Plus, improper fractions can often be simplified. So, our next step is to convert this improper fraction back into a mixed number and simplify it if possible.

Simplifying and Converting the Final Answer

So, we've landed on $rac{325}{40}$ as the number of buckets of fish the killer whales eat daily. Pretty hefty, right? Now, before we declare victory, we always want to simplify our fractions and present them in the most understandable way. For quantities like buckets of fish, a mixed number is usually clearer than a big improper fraction. Plus, $rac{325}{40}$ can definitely be simplified.

First, let's simplify the fraction $rac{325}{40}$ . We need to find the greatest common divisor (GCD) for both 325 and 40. Looking at these numbers, we can see they both end in 0 or 5, which means they are both divisible by 5. Let's divide both the numerator and the denominator by 5:

$325 ext{ divided by } 5 = 65$
$40 ext{ divided by } 5 = 8$

So, our simplified improper fraction is $rac{65}{8}$ . This is already much better! It means the killer whales eat 65 eighths of a bucket of fish each day. But again, let's make this even more intuitive by converting it into a mixed number. To convert an improper fraction like $rac{65}{8}$ into a mixed number, we perform division. We divide the numerator (65) by the denominator (8).

How many times does 8 go into 65? Let's think of our multiplication tables for 8: $8 imes 8 = 64$ . So, 8 goes into 65 a total of 8 times.
What's the remainder? $65 - 64 = 1$ .

The whole number part of our mixed number is the quotient (8). The remainder (1) becomes the numerator of the fraction part, and the denominator stays the same (8).

Therefore, $rac{65}{8}$ converts to $8 rac{1}{8}$ .

And there you have it! The killer whales at the San Diego Zoo eat $8 rac{1}{8}$ buckets of fish each day. Isn't that incredible? They eat more than eight full buckets, plus an extra eighth of a bucket, every single day. This is significantly more than the dolphins' $3 rac{1}{8}$ buckets. It really puts into perspective the massive caloric needs of these apex predators. This problem, starting with simple mixed numbers, took us through converting to improper fractions, multiplying fractions, simplifying, and finally converting back to a mixed number. It's a complete workout for your fraction skills, all inspired by the amazing animals at the zoo. So next time you're at the zoo, you can marvel not only at the size and power of the killer whales but also at the sheer volume of food required to keep them healthy and happy. Math truly helps us understand the world around us in fascinating ways!