Problem 79 - Algebra 1: Concepts and Skills

Question

Add. Write the answer as a decimal. (Skills Review pp. 759, 767) $$\frac{12}{12}+0.12$$

Step-by-Step Solution

Answer

The sum of \(\frac{12}{12}\) and 0.12, written as decimal is 1.12

Step 1: Convert fraction to decimal

The fraction \(\frac{12}{12}\) can be converted to a decimal by performing the division. In this case, we divide 12 by 12 which equals 1.

Step 2: Add Decimals

After the fraction is converted to 1, it is added to the decimal 0.12. The sum is: \(1 + 0.12 = 1.12\).

Key Concepts

Decimal Conversion

Decimal conversion entails transforming a number from a fraction or another form into a decimal. This process often involves division. When a fraction is given, you convert it into a decimal by dividing the numerator by the denominator. In the exercise, the fraction \(\frac{12}{12}\) converts to a decimal by dividing 12 by 12, resulting in 1. This division signifies how many times the denominator (12) fits into the numerator (12). Because 12 fits exactly once, the decimal equivalent is 1. Understanding this conversion is crucial as it simplifies computations and makes addition with other decimals straightforward. Decimals are widely used in everyday life, such as in pricing and measurements, which is why mastering this conversion is essential.

Fraction to Decimal

Converting fractions to decimals is a foundational math skill. It allows for easier calculations, especially when dealing with mixed types of numbers. To convert a fraction to a decimal, divide the top number (numerator) by the bottom number (denominator). This method works for any fraction, even if it doesn't divide evenly.In practice:

• If the fraction is \(\frac{12}{12}\), dividing 12 by 12 equals 1, as in the provided solution.
• If a fraction like \(\frac{2}{5}\) needed conversion, you would divide 2 by 5, resulting in 0.4.

Key point: When converting, if the division doesn’t end, the decimal is repeating or terminating, which represents either an exact or approximate value of the fraction.

Arithmetic Operations

Arithmetic operations form the backbone of mathematical calculations. They include basic functions like addition, subtraction, multiplication, and division. In this exercise, the focus is on addition, more specifically, adding decimals. The steps to add decimals are straightforward:

• Align the decimal points of the numbers you're adding.
• Perform the addition as you would with whole numbers.
• Make sure the decimal point in the sum is aligned with the decimal points in the numbers you added.

Following the conversion in the exercise, we added 1 (from fraction \(\frac{12}{12}\)) to 0.12. By aligning the decimal points, calculating becomes a simple matter of adding 1.00 to 0.12, which equals 1.12. Being comfortable with these operations enables quick and accurate results in both simple and complex problems.