Problem 32 - Prealgebra

Question

A bottle of fish oil contains 50 soft gels, each containing 300 mg of the omega- 6 fatty acid. How many total grams of the omega- 6 fatty acid are in this bottle?

Step-by-Step Solution

Answer

The bottle contains 15 grams of omega-6 fatty acid.

Step 1: Understand the Problem

The problem asks for the total grams of omega-6 fatty acid in a bottle containing 50 soft gels, with each soft gel having 300 mg of omega-6 fatty acid.

Step 2: Find the Total Milligrams

Multiply the number of soft gels (50) by the amount of omega-6 in each gel (300 mg): \[ 50 \times 300 = 15000 \text{ mg} \] There are 15000 mg of omega-6 fatty acid in the bottle.

Step 3: Convert Milligrams to Grams

Convert the total milligrams to grams by dividing by 1000, since 1 gram equals 1000 milligrams:\[ \frac{15000}{1000} = 15 \text{ grams} \]Thus, there are 15 grams of omega-6 fatty acid in the bottle.

Key Concepts

Conversion of Units

Converting units is an essential skill in math, helping you turn a measurement from one unit to another.
In this exercise, we've moved from milligrams (mg) to grams (g). Understanding how these conversions work will empower you to approach similar tasks with confidence.
Here's a quick guide on the conversion between mg and g:

• 1 gram (g) is equivalent to 1000 milligrams (mg)
• To convert from mg to g, divide the number of milligrams by 1000
• To convert from g to mg, multiply the number of grams by 1000

In our specific problem, we had 15000 mg of omega-6 fatty acid. When converting to grams, you simply divide 15000 by 1000, resulting in 15 grams. It’s all about knowing the relationship between these units and applying basic division.

Multiplication Problems

Multiplication is at the core of many math challenges, enabling you to calculate totals from repeated groups or items. In this problem, we used multiplication to find out the total amount of omega-6 fatty acid in the bottle of soft gels.
Here's how it works:

• Determine how many items or units you have (in this case, 50 soft gels)
• Identify how much each item contains (here, each soft gel contains 300 mg of omega-6 fatty acid)
• Multiply the two quantities: \[ 50 \times 300 = 15000 \]

By using multiplication, you can easily calculate the total amount by combining the smaller, identical contributions of each unit. This is a vital skill that is useful in various contexts, whether calculating ingredients, costs, or quantities.

Understanding Word Problems

Word problems often trip students up, not because they're difficult, but because they require translating a story or scenario into a mathematical equation. Understanding what is being asked is crucial to solving these steps effectively.
For example, in our problem, the key is to dissect the information:

• We have 50 soft gels, and each contains a specific amount of omega-6 fatty acid (300 mg)
• The goal is to find out the total grams of omega-6 in the bottle

First, you pull out the clear figures from the problem: the number of items and the amount per item. Then, using multiplication, you find the total in milligrams.
Finally, comprehension and conversion allow you to translate milligrams into grams. If you carefully analyze what each part of the problem represents, you can transform these word problems into structured mathematical solutions.