Problem 77 - Algebra 1: Concepts and Skills

Question

Add. Write the answer as a decimal. (Skills Review pp. 759, 767) $$\frac{7}{8}+0.25$$

Step-by-Step Solution

Answer

The sum of \(\frac{7}{8}\) and 0.25, written as a decimal, is 1.125.

Step 1: Convert Fraction to Decimal

Begin by converting the fraction \(\frac{7}{8}\) into a decimal. This can be done by dividing the numerator by the denominator. So, \(\frac{7}{8} = 0.875\).

Step 2: Add Decimals

Now that both numbers are in decimal format, add 0.875 (which is converted from \(\frac{7}{8}\)) to 0.25. The result of this addition is 1.125.

Key Concepts

Converting Fractions to Decimals

Understanding how to convert fractions to decimals is an essential arithmetic skill. A fraction represents a part of a whole and is made up of two numbers: the numerator, positioned above the fraction line, and the denominator, below it. To convert a fraction into a decimal, you divide the numerator by the denominator.

For example, to convert \( \frac{7}{8} \) into a decimal, we divide 7 (the numerator) by 8 (the denominator), using either a calculator or long division. The resulting decimal is 0.875. It's often helpful to know common fraction-to-decimal conversions, like \( \frac{1}{2} \) being 0.5 or \( \frac{1}{4} \) being 0.25, to speed up this process.

When dividing, if the digits after the decimal place continue to repeat, you can round the decimal to a certain number of places. For instance, \( \frac{1}{3} \) equals approximately 0.333. Knowing how to convert fractions to decimals accurately is crucial when tackling problems in mathematics as well as in real-life situations.

Decimal Addition

Once you've converted all numbers to decimals, performing addition is straightforward. Decimal addition follows the same principles as adding whole numbers; however, it's critical to align the decimal points. This ensures that the places (tenths, hundredths, thousandths, etc.) match up.

Let's add 0.875 and 0.25. Write down both numbers with the decimal points aligned:

• 0.875
• + 0.250

Next, add each column, starting from the rightmost digit and moving left. Any time a column adds to 10 or more, carry over to the next column on the left. Adding the numbers above gives us 1.125. Decimal addition is a basic operation used in many different areas, such as finance, engineering, and everyday life, making it a vital skill to master.

Arithmetic Skills Review

Arithmetic involves the basic operations of addition, subtraction, multiplication, and division. Reviewing these skills periodically is important to keep them sharp, as they form the foundation for most mathematical tasks.

An excellent way to practice is by working through problems that combine these operations, such as adding fractions and decimals. When you encounter mixed numbers (a combination of whole numbers and fractions), remember to convert all components to decimals before performing any operations.

Moreover, you can improve your mental arithmetic by estimating results before performing exact calculations. For instance, knowing that \( \frac{7}{8} \) is a little less than 1 and that 0.25 is a quarter can help you estimate the final sum as slightly more than 1, which can then be fine-tuned into the exact answer, 1.125, through precise calculation. Constant practice and applying these skills in practical scenarios will enhance your proficiency and confidence in arithmetic.