Problem 59 - Algebra 1

Question

Find the number. $$ 45 \% \text { of } 84 $$

Step-by-Step Solution

Answer

45% of 84 is 37.8

Step 1: Understand the problem

We are asked to find 45% of the number 84. Percentage is a way of expressing a number as a fraction of 100. So we want to find out what number amounts to 45 out of every 100 with respect to the number 84.

Step 2: Apply the formula

We use the formula to find the percentage of a number, which is (percentage/100) * Number. Therefore, we have to evaluate (45/100) * 84.

Step 3: Calculate the result

Let's do the arithmetic: when we divide 45 by 100, we get 0.45. Then we multiply this number by 84. The precision of your calculation might depend on the requirements of your task. The multiplication gives us 37.8.

Key Concepts

Arithmetic Skills

When tackling percentage problems, honing your arithmetic skills is essential. In this exercise, you face the task of calculating 45% of 84, an arithmetic operation involving both division and multiplication.
To break it down:

• First, convert the percentage into a decimal form. Here, 45% becomes 0.45. This happens because percentages are simply numbers over 100.
• Then, multiply this decimal figure by the number in question, which in this case is 84. This requires basic multiplication skills.
• The calculation results in 37.8, giving you the number that represents 45% of 84.

By following these steps, you're practicing arithmetic skills in dividing and multiplying, which are foundational in math. Not only does this exercise improve numeracy, but it also builds confidence in handling percentages with ease.

Basic Math Concepts

Having a strong grasp of basic math concepts is crucial when dealing with percentages.
A percentage represents a part of a whole, specifically a part out of 100. Therefore, when you encounter the term 'percent,' understand that it stems from the Latin per centum, meaning 'by the hundred.'
In practical terms:

• Calculating a percentage involves understanding fractions and the concept of wholes.
• The fraction is formed by dividing the percentage value by 100, turning it into a decimal.
• The concept of multiplication comes in as you apply this decimal to find a part of another number.

In our example, finding 45% of 84 translates to the operation 0.45 times 84. Each step reinforces understanding of how percentages work within the broader context of basic mathematical operations.

Problem Solving in Mathematics

Problem-solving in mathematics requires a strategic approach to dissect and address questions like the one in this exercise.
The problem is straightforward once you apply a systematic strategy:

• First, understand the question and identify what exactly you're solving for. Here, it's a specific percentage of a given number.
• Second, apply the correct formula. For percentages, the formula \[ \left( \frac{percentage}{100} \right) \times \text{Number} \] is essential.
• Third, execute the arithmetic operations in sequence, as shown in the solution. Carefully follow through to ensure accuracy.

This approach is a powerful problem-solving tool, not just for math exams but also for real-world scenarios where percentages often reveal critical insights. By practicing these steps, you sharpen your ability to approach math challenges methodically and confidently.