Problem 33 - Prealgebra

Question

A certain B-complex vitamin supplement contains \(50 \mathrm{mg}\) of riboflavin, or vitamin \(\mathrm{B}_{2}\). A bottle contains 80 vitamins. How many total grams of riboflavin are in this bottle?

Step-by-Step Solution

Answer

The bottle contains 4 grams of riboflavin in total.

Step 1: Convert Riboflavin per Vitamin from Milligrams to Grams

First, we need to convert the amount of riboflavin in each vitamin from milligrams to grams, because the final answer requires the total grams. Since there are 1000 milligrams in 1 gram, we can write:\[ 50 \text{ mg} = \frac{50}{1000} \text{ grams} = 0.05 \text{ grams} \]

Step 2: Calculate Total Riboflavin in the Bottle

Now, we need to calculate the total amount of riboflavin in the bottle. Each vitamin contains 0.05 grams of riboflavin, and there are 80 vitamins in total. Multiply these together to find the total riboflavin:\[ 0.05 \text{ grams/vitamin} \times 80 \text{ vitamins} = 4 \text{ grams} \]

Key Concepts

Unit Conversion

In many math or science problems, you might come across measurements given in different units. Learning how to convert between these units is key. For our exercise, the riboflavin amount per vitamin was initially given in milligrams. However, our goal is to find the total in grams. Knowing the conversion rule is crucial:

• 1 gram = 1000 milligrams

To convert milligrams into grams, you divide by 1000. Remember, division is essential here. For example, if you have 50 milligrams of riboflavin in one vitamin, you convert it by doing: \[ \frac{50 \text{ mg}}{1000} = 0.05 \text{ grams} \] This conversion is necessary, especially when the problem asks for the result in different units from those initially provided. Practice various conversions in different contexts to make sure you are confident with unit changes.

Multiplication

Multiplication is a basic arithmetic operation, yet incredibly powerful for solving larger problems efficiently. It allows us to sum up repeated additions quickly. In problems like this, where you are asked to find a total for many identical items, multiplication is your best friend.

• Each vitamin contains the same amount of riboflavin.
• We simply multiply the amount in one vitamin by the total number of vitamins.

For this problem, each vitamin contains 0.05 grams of riboflavin. To find the total amount in the whole bottle, you perform: \[ 0.05 \text{ grams/vitamin} \times 80 \text{ vitamins} = 4 \text{ grams} \] This tells you the combined riboflavin content. Always double-check your multiplication by verifying that the units make sense. In this case, we're left with grams, which correctly represents the total quantity we were looking to find.

Problem Solving

Tackling math problems often requires a strategic approach to identify what’s being asked and then systematically solving it.

• Understand the question: We were asked to find the total grams of riboflavin.
• Identify necessary steps: Perform unit conversion and multiplication.

Start by converting measurements into the desired unit; this forms your foundation for further calculations. Next, use multiplication to find the needed totals. Once you have all conversions and operations done, ensure your answer makes logical sense. By breaking the problem into simpler tasks, you remove complexity and gain clarity. Always have each intermediate answer verified before moving to the next step, and with practice, problem-solving becomes an intuitive and rewarding process.