Problem 112 - Prealgebra

Question

The average California cow can produce 2,305 gallons of milk annually. How much milk can a cow produce each day? Round your answer to the nearest hundredth of a gallon. www.moomilk.com/faq.htm

Step-by-Step Solution

Answer

A cow can produce 6.32 gallons of milk each day.

Step 1: Identify Annual Milk Production

We know that the average California cow can produce 2,305 gallons of milk annually. This value represents the total milk production over 365 days.

Step 2: Determine Daily Milk Production Formula

To find out how much milk a cow produces each day, we'll divide the annual production by the number of days in a year. The formula is: \[ \text{Daily Milk Production} = \frac{\text{Annual Milk Production}}{\text{Days in a Year}} \]

Step 3: Calculate Daily Milk Production

Using the formula from Step 2, we substitute in the known values: \[ \text{Daily Milk Production} = \frac{2,305}{365} \approx 6.31644 \, \text{gallons} \].

Step 4: Round the Daily Production

Since we need to round the gallons to the nearest hundredth, 6.31644 rounds to 6.32 gallons.

Key Concepts

Fractions and Division

Fractions and division go hand in hand when working with numbers that need to be divided into smaller parts. In this exercise, we use division to determine how much milk a cow produces each day from its annual production. When you divide any number, like 2,305 gallons of milk, by another number, such as 365 days in a year, you are finding how much is in each part. This is essentially a division problem.

Here’s how this concept breaks down:

• Numerator: The number on top in a fraction represents the thing you're dividing up. In our problem, it's the annual milk production: 2,305 gallons.
• Denominator: The number on the bottom tells you how many parts you are dividing the numerator into. For us, this is the 365 days in a year.

When you calculate \(\frac{2,305}{365}\), you're essentially figuring out how much milk is produced per day. This fraction helps us understand the average daily production.

Rounding Numbers

Rounding numbers is a crucial part of making numerical data easier to understand and work with. Often, exact numbers produced by division might have a lot of decimal places, making it cumbersome to interpret. That's why we round our results, especially when discussing real-world figures like daily milk production.

Here's how we round to the nearest hundredth:

• Identify the third decimal place. In our case, 6.31644 has 6 in the third place.
• If that number is 5 or greater, increase the second decimal place by one. Otherwise, keep it the same. So, 6.316 becomes 6.32 because 6 in the third place tells us to round up.

Rounding makes our result more manageable: Although the cow produces approximately 6.31644 gallons a day, we simply say it produces 6.32 gallons every day.

Problem-Solving Steps

Problem-solving in math involves understanding the problem, selecting the right operations, performing calculations, and then presenting results clearly. Our exercise exemplifies this idea from start to finish.

First, identify the key information. Here, it's the cow's annual milk production. Next, determine what you want to find - the milk produced in a day. Then develop a strategy using the right mathematical operation. In this case, division helps us split the yearly output into daily amounts.

After dividing, the calculation shows a precise number with many decimals, but practical usage requires us to round it. Finally, always recheck each step to ensure accuracy.

• Understand: Interpret what data you have (annual production).
• Plan: Decide on using division for daily production.
• Solve: Carry out the division and rounding.
• Verify: Confirm the solution makes sense in context.

These steps guide us from raw data to a concise answer that answers the problem fully.