Problem 38 - Prealgebra

Question

A certain brand of vitamin \(\mathrm{C}\) contains \(600 \mathrm{mg}\) per tablet. A bottle contains 150 vitamins. How many total grams of vitamin \(\mathrm{C}\) are in this bottle?

Step-by-Step Solution

Answer

The bottle contains 90 grams of vitamin C.

Step 1: Understand the Problem

You are given that each tablet contains 600 mg of vitamin C and a bottle contains 150 tablets. We need to calculate the total amount of vitamin C in the entire bottle.

Step 2: Calculate Total Milligrams

Multiply the number of tablets by the amount of vitamin C per tablet. This will give you the total amount of vitamin C in milligrams in the bottle. \[\text{Total milligrams} = 150 \times 600 = 90000 \text{ mg}\]

Step 3: Convert Milligrams to Grams

Since there are 1000 milligrams in one gram, convert the total milligrams to grams by dividing by 1000.\[\text{Total grams} = \frac{90000}{1000} = 90 \text{ grams}\]

Step 4: Conclusion

The bottle contains a total of 90 grams of vitamin C.

Key Concepts

Understanding Unit Conversion

Unit conversion is a process that helps translate a quantity from one measurement unit to another. For example, converting milligrams (mg) into grams (g) is essential when dealing with smaller amounts of substances, like vitamins.
To convert between units, you need to know the conversion factor. Here, the conversion factor is 1000 because there are 1000 milligrams in 1 gram.

• To convert milligrams to grams: divide the number of milligrams by 1000.
• To convert grams to milligrams: multiply the number of grams by 1000.

Understanding this simple conversion allows for easy comparison and computation in both scientific and everyday scenarios.

Multiplication in Problem Solving

Multiplication is a powerful mathematical operation used to find the total of equal groups. It simplifies repetitive addition by allowing you to compute large numbers quickly and efficiently.
In the scenario of calculating the total vitamin C in a bottle, multiplication was used to determine how much vitamin C is present in all tablets combined. Imagine each tablet as containing a separate amount of vitamin C, and multiplication becomes the tool to sum up all these amounts at once.

• Instead of adding 600 milligrams repeatedly for 150 times, multiply 600 by 150 directly.
• This operation results in 90,000 milligrams as a total.

Practicing multiplication with real-world examples promotes both understanding and speed in problem solving.

Effective Problem Solving Techniques

Problem solving involves understanding a question, determining what information is necessary, and calculating the answer. Initially, break down the problem into smaller steps to make it more manageable.
In the vitamin C problem, this involves:

• Identifying the given information, such as the amount of vitamin C per tablet and the number of tablets.
• Using multiplication to find the total amount in milligrams.
• Executing unit conversion to get the final answer in grams.

Following a logical sequence simplifies even complex problems and prevents errors, ensuring you arrive at the correct solution efficiently.

Measurement Units in Everyday Use

Measurement units like milligrams and grams provide standardized ways to describe quantities. Different units are suitable for different contexts, such as milligrams for smaller amounts and grams for larger ones. Milligrams are often used in dosing medications and supplements, where precision is crucial due to the small amounts involved. In contrast, grams are more frequently used in cooking or when dealing with slightly larger quantities.
Understanding these units allows individuals to make more informed decisions and calculations in everyday life, whether checking nutrient content or cooking recipes. By mastering the concept of measurement units, you can avoid common pitfalls and ensure accuracy in any activity that involves quantifying substances or ingredients.