Problem 56 - Elementary Algebra

Question

Answer the question by setting up and solving an appropriate equation. What is \(160 \%\) of 70 ?

Step-by-Step Solution

Answer

160% of 70 is 112.

Step 1: Convert Percentage to Decimal

To find what 160% of 70 is, first convert the percentage to a decimal. This is done by dividing 160 by 100. Hence, \( 160\% = 1.6 \).

Step 2: Set Up the Equation

Next, set up the equation to calculate 160% of 70. The equation is: \( 1.6 \times 70 \).

Step 3: Perform the Multiplication

Multiply the decimal obtained in Step 1 by 70: \( 1.6 \times 70 = 112 \).

Step 4: Write the Solution

Conclude that 160% of 70 is 112.

Key Concepts

Converting Percentages to Decimals

Converting percentages to decimals is a fundamental arithmetic skill that simplifies many calculations. To convert a percentage into a decimal, you divide the percentage value by 100.
It's like moving the decimal point two places to the left. For example, to convert 160% to a decimal, you divide by 100, resulting in 1.6.

• Always remember that the '%' symbol means "per 100." So, 160% means 160 per 100, or simply 160 divided by 100.
• To avoid confusion, think about how 10% becomes 0.1 when converted to a decimal.

These conversions are helpful when solving various mathematical problems because calculations with decimals are more straightforward than working directly with percentages.

Setting Up Equations

Creating equations from words or problems is a crucial skill in algebra and arithmetic. When you want to find a certain percentage of a number, setting up the correct equation is essential.
The structure is straightforward:

• Convert the percentage to a decimal first, as we covered in the previous section.
• Then multiply this decimal by the number in question.
• For instance, to find 160% of 70, you first convert 160% to 1.6, and then your equation becomes: \( 1.6 \times 70 \).

In forming such an equation, you're simplifying the process by creating a clear guide on what needs to be calculated.

Multiplication of Decimals

Multiplying decimals follows the same basic principles as regular multiplication. However, understanding the placement of the decimal point in the solution is important. This step requires precision.

• After setting up the equation, such as \( 1.6 \times 70 \), perform the multiplication as you would with whole numbers.
• Ignore the decimal point for the moment and multiply 16 by 70, obtaining 1120.
• Then, place the decimal point back in the result. Since 1.6 has one decimal place, your final answer should have one decimal place as well.
• Therefore, 1120 becomes 112.0, or simply 112, when completing the multiplication.

By focusing on correct placement and handling of decimals, you'll avoid common mistakes and arrive at accurate results.