Problem 31 - Prealgebra

Question

Fish oil A bottle of fish oil contains 60 soft gels, each containing \(800 \mathrm{mg}\) of the omega- 3 fatty acid. How many total grams of the omega- 3 fatty acid are in this bottle?

Step-by-Step Solution

Answer

The bottle contains 48 grams of omega-3 fatty acid.

Step 1: Understand the unit conversion

To find the total grams of omega-3 fatty acid, we need to convert milligrams to grams. Recall that 1 gram equals 1000 milligrams.

Step 2: Determine total milligrams in one bottle

Each soft gel contains 800 mg of omega-3 fatty acid, and there are 60 soft gels in the bottle. Calculate the total milligrams by multiplying the number of soft gels by the milligrams per soft gel: \[ 800 \text{ mg/gel} \times 60 \text{ gels} = 48000 \text{ mg} \]

Step 3: Convert milligrams to grams

Convert the total milligrams of omega-3 fatty acid to grams using the conversion 1 gram = 1000 milligrams: \[ \frac{48000 \text{ mg}}{1000 \text{ mg/g}} = 48 \text{ g} \]

Key Concepts

Milligrams to Grams Conversion

When dealing with measurements, unit conversion is a crucial skill. Imagine you're looking at weights and see numbers in milligrams, but the answer you seek is in grams. This means you'll need to perform a unit conversion. Here's a simple rule you should always remember:

• 1 gram (g) is equal to 1000 milligrams (mg).

To convert milligrams to grams, you just need to divide the number of milligrams by 1000. For example, if you have 800 mg, you would calculate:\[ \frac{800 \text{ mg}}{1000} = 0.8 \text{ g} \]This conversion is particularly useful when you're dealing with nutritional labels or chemistry problems, where smaller quantities might be measured in milligrams but larger ones in grams. Keep practicing, and these conversions will become second nature.

Omega-3 Fatty Acid Calculation

When calculating the total amount of omega-3 fatty acids in a bottle of fish oil, there are a few steps to consider. Simply put, you will need to know:

• The amount of omega-3 in each soft gel.
• The total number of soft gels in the bottle.

For example, if each soft gel contains 800 mg of omega-3 and there are 60 soft gels in the bottle, you multiply them together to find the total:\[ 800 \text{ mg/gel} \times 60 \text{ gels} = 48000 \text{ mg} \]By understanding how much omega-3 is in each soft gel and the quantity of soft gels, properly estimating your intake becomes straightforward.

Multiplication for Total Amount

Multiplication is a fundamental mathematical operation, and grasping this concept can help you solve a multitude of problems. In this context, we are multiplying to find the total amount of omega-3 fatty acids in a bottle. Here's a simple way to think about it:

• Each gel cap has a certain amount of omega-3.
• There are multiple gel caps in the bottle.
• You multiply these two numbers to get the total amount.

For example, with 800 mg of omega-3 per soft gel and 60 soft gels, the multiplication looks like:\[ 800 \text{ mg/gel} \times 60 \text{ gels} = 48000 \text{ mg} \]This calculation gives you the total omega-3 content for the entire bottle. Remember, multiplication can help you determine totals in various contexts, whether dealing with money, items, or in this case, nutrients.

Prealgebra Problem Solving

Solving problems involving basic arithmetic operations is a core part of prealgebra. Prealgebra often involves understanding and organizing given information, then applying operations like addition, subtraction, multiplication, or division as needed. Here's a simple strategy:

• First, clearly understand what is asked.
• Identify the known values and what calculations are required.
• Execute operations step-by-step to find the solution.

In our fish oil example, you started by recognizing the need to calculate total mg of omega-3, followed by a conversion from mg to g. These steps required you to apply multiplication and division effectively. Developing these skills through practice equips you to tackle more complex problems with confidence.