Problem 12 - Prealgebra

Question

Find the percent of each number mentally. $$60 \% \text { of } 55$$

Step-by-Step Solution

Answer

60% of 55 is 33.

Step 1: Understand the Problem

We need to find 60% of 55. This means we want to know what 60% of the number 55 is, using mental math.

Step 2: Express Percent as a Fraction or Decimal

To make it easier, we express 60% as a decimal. Remember that 60% is equivalent to 0.6. This is because percent means 'per hundred', so 60% is 60 out of 100, which is 60 divided by 100 or 0.6.

Step 3: Multiply the Decimal by the Number

Now, we multiply the decimal form of the percent (0.6) by the number 55. Calculate mentally or estimate: \[ 0.6 \times 55 \approx 33 \]

Key Concepts

Mental Math

When we tackle math problems, especially percentages, mental math can become a powerful tool. It involves calculating in your head without relying on tools or paper. This skill is handy for quick everyday calculations.
It's good to start with simple concepts:

• Rounding numbers to make calculations easier.
• Breaking numbers into smaller parts (like breaking 60 into 50 + 10) to simplify multiplication.
• Using simple fractions that are easy to handle mentally.

Using mental math for percentages, like finding 60% of a number, simplifies the process as you understand and practice more. Gradually, estimating answers and performing mental math will become second nature.

Fractions and Decimals

Understanding fractions and decimals is key to tackling percentage problems. A percentage is essentially a fraction of 100. For example, 60% can be seen as the fraction \( \frac{60}{100} \) or as the decimal 0.6.
When you convert percentages to fractions or decimals:

• To convert to a fraction, write the percentage over 100 and simplify if necessary.
• To convert to a decimal, divide the percentage by 100.

This conversion facilitates easier multiplication. Instead of dealing with percentages directly, you often convert them to decimals. Multiplying decimals is usually simpler, and it lays the groundwork for solving percentage problems mentally.

Multiplication Concepts

Multiplication is at the heart of finding percentages. Once a percentage is converted into a decimal, the problem reduces to a basic multiplication task.
Here, you multiply the decimal equivalent of the percentage by the number in question. For example, to find 60% of 55, consider the problem as multiplying 0.6 by 55.

• Start by breaking down numbers for easy multiplication.
• Multiply 0.6 by components of 55 you can handle mentally, or use rounding for estimation.
• Practice different multiplication strategies to improve your speed and accuracy.

As you hone this skill, you'll become comfortable using these concepts for larger numbers and more complex calculations without paper or calculators.