Problem 46 - Algebra 1: Concepts and Skills

Question

Evaluate. $$ 30 \% \text { of } 42 $$

Step-by-Step Solution

Answer

30% of 42 is 12.6

Step 1: Convert percentage to decimal

Convert the percent into a decimal. In this case, 30% is equivalent to 0.3.

Step 2: Multiply the decimal by the number

Now, multiply the converted decimal by the number to find the percent of the number. Therefore, 0.3 multiplied by 42 is 12.6.

Step 3: The Answer

Hence, 30% of 42 is 12.6.

Key Concepts

Converting Percentages to Decimals

Understanding how to transform percentages into decimals is foundational for many math problems. The process is surprisingly simple. A percentage represents a part per hundred. To convert a percentage to a decimal, divide it by 100. For example, 30% becomes \( \frac{30}{100} \), which simplifies to 0.3. This step is crucial and must be done correctly to ensure the rest of the problem is solved accurately.

It's also important to remember that when removing the percentage sign, you're essentially moving the decimal point two places to the left. So, 55% would be 0.55 in decimal form, and 7.5% would be 0.075. This method applies to all percentages, making it a universally helpful tool in mathematics.

Multiplying Decimals

Once you have converted your percentage to a decimal, the next step often involves multiplication. Multiplying decimals is essentially the same as multiplying whole numbers, with the additional step of placing the decimal point in the answer. To multiply decimals, line up the numbers based on their place value (ignoring the decimal places), multiply as you would with whole numbers, and then count the total number of decimal places in the factors. The product must have the same number of decimal places.

For instance, multiplying 0.3 (one decimal place) by 42 (no decimal places) results in a number with one decimal place. It's like saying 3 times 42, then putting the decimal point back to account for the single decimal place in the original multiplicand, resulting in 12.6.

Percent of a Number

Determining the percent of a number is an essential quantitative skill. Once you've converted the percentage to a decimal and understood how to multiply decimals, finding the percent of a number is the next logical step. It involves multiplying the base number by the decimal equivalent of the percentage. This tells you what portion of the base number the given percentage represents.

Consider '30% of 42'. After converting 30% to 0.3, you multiply it by 42. Visually, it helps to see this as 0.3 times 42, which gives you 12.6. Therefore, 30% of 42 equals 12.6, telling us that 30% of 42 is like taking 12.6 out of 42. It's useful for figuring out discounts, tax, and increasing or decreasing quantities by a certain percentage. Remember that the key is multiplying the whole number by the decimal form of the percentage.