Question

Translate to an equation and solve. The label on a bottle of rubbing alcohol indicates that it is \(70 \%\) isopropyl alcohol. If the bottle contains 473 milliliters, how many milliliters of isopropyl alcohol does it contain?

Short answer

Answer: 331.1 milliliters

Step-by-step solution

Understand the problem

First, we need to figure out the percentage of isopropyl alcohol in the bottle. According to the problem, 70% of the bottle is isopropyl alcohol.

Write the equation

We can solve the problem by finding 70% of 473 milliliters. To do this, we can convert the percentage to a decimal and multiply it by the total amount of liquid in the bottle. The equation for this is: Amount of isopropyl alcohol = (Percentage as decimal) * (Total amount of liquid)

Convert the percentage to a decimal

To convert the percentage to a decimal, we divide it by 100. So, 70% can be converted to a decimal by dividing 70 by 100: 70% = 70 / 100 = 0.7

Multiply the decimal by the total amount of liquid

Now, multiply the decimal (0.7) by the total amount of liquid in the bottle (473 milliliters) to find out how many milliliters of isopropyl alcohol there are: Amount of isopropyl alcohol = 0.7 * 473

Calculate the result

After multiplying the decimal by the total amount of liquid, we get: Amount of isopropyl alcohol = 331.1 So, there are 331.1 milliliters of isopropyl alcohol in the bottle.

Key concepts

Basic Math Operations

When solving alcohol percentage problems, it's crucial to understand basic math operations. These operations include addition, subtraction, multiplication, and division. Each of these operations plays a vital role in finding solutions to everyday mathematical problems.

Here are some foundational aspects:

• Addition: Combining two or more numbers to find their total sum.
• Subtraction: Taking one number away from another to find the difference.
• Multiplication: Finding the total of one number taken a particular number of times.
• Division: Separating a number into specified equal parts.

In our example, we primarily use multiplication because we need to find a percentage of a given number. And remember, applying these basic operations correctly helps streamline the problem-solving process, making math less daunting and more accessible.

Converting Percentages to Decimals

Converting percentages to decimals is a necessary skill for solving percentage problems. To find out how much isopropyl alcohol is in the bottle, we must first convert the percentage into a decimal. This conversion helps in performing accurate calculations using basic math operations more effectively.

Here's how you can easily convert percentages to decimals:

• Step 1: Take the percentage value you have. In this case, it is 70%.
• Step 2: Divide the percentage by 100. So for 70%, you perform the calculation 70/100.
• Step 3: The result is your decimal value. For this example, 70% becomes 0.7.

This simple division process is crucial as it transforms the percentage into a form that can be easily multiplied by other numbers to find specific quantities, like the amount of isopropyl alcohol in our exercise.

Word Problems in Math

Word problems in math, such as the one given in the rubbing alcohol exercise, are an excellent way to apply mathematical concepts to real-world situations. They require careful reading and interpretation to understand what is being asked, often involving more than one math operation to arrive at the solution.

When tackling word problems:

• Read Carefully: Understand what the problem is asking for. Identify key details and figures relevant to solving the problem.
• Translate Words to Equations: Convert the narrative into mathematical expressions. This often involves converting percentages to decimals, then using operations like multiplication to find the answer.
• Plan Your Approach: Decide what operations are needed to solve the problem efficiently. This includes knowing when to multiply, divide, or convert one form to another.

Practicing word problems enhances problem-solving skills by encouraging logical reasoning and critical thinking. They help students learn how to make connections between different mathematical concepts and apply them effectively.