Problem 63 - Algebra 1: Concepts and Skills

Question

Write the fraction or mixed number as a decimal. (Skills Review pp. 763,767) $$ 6 \frac{7}{8} $$

Step-by-Step Solution

Answer

The mixed number \(6 \frac{7}{8}\) can be written as the decimal 6.875.

Step 1: Find the Decimal Equivalent of the Fraction

We begin by converting the fraction 7/8 into a decimal. This can be done by dividing 7 by 8, which equals 0.875.

Step 2: Combine the Whole Number and the Decimal

Next, we simply add the whole number part of the mixed number (which is 6) to the decimal we found in step 1. Thus, 6 + 0.875 = 6.875.

Key Concepts

Mixed Numbers as Decimals

Understanding how to convert mixed numbers into decimals is a vital skill in mathematics. A mixed number consists of a whole number and a fraction, such as \( 6\frac{7}{8} \). To convert this to a decimal, we tackle each part separately. Start with the fraction: converting \( \frac{7}{8} \) to a decimal involves basic division. Divide the numerator (7) by the denominator (8) to get 0.875.

Next, incorporate the whole number by simply placing it in front of the decimal point, combining them into a single decimal. The result of adding the whole number 6 to the decimal 0.875 gives us 6.875. This method works for any mixed number and is a fundamental aspect of many mathematical operations.

Decimal Equivalent of Fraction

The decimal equivalent of a fraction is found by performing the division of the fraction’s numerator by its denominator. For example, the fraction \( \frac{7}{8} \) can be converted to a decimal by dividing 7 by 8, which equals 0.875.

To make this process easier, remember that decimals and fractions are two ways of representing the same concept: portions of a whole. It's like cutting a cake into equal parts. If you cut it into 8 pieces and take 7, you'd have \( \frac{7}{8} \) of the cake, which can also be expressed as 0.875 of the whole cake when using decimal notation. Converting fractions to their decimal form is a basic skill that enables students to work with numbers in various contexts, such as measurements, probabilities, and financial calculations.

Basic Arithmetic Skills

Converting fractions to decimals is just one of the many basic arithmetic skills that are foundational to mathematics. These skills include operations such as addition, subtraction, multiplication, and division. With mixed numbers, these operations often require the additional steps of converting between mixed numbers and improper fractions or decimals. For instance, in the example of \( 6\frac{7}{8} \), you used division to find the decimal equivalent of the fraction, and then addition to combine it with the whole number.

Strengthening these basic arithmetic skills provides students with the tools necessary to tackle more complex problems. Practice with converting numbers between different forms, and routinely use these operations to build confidence and proficiency in mathematics.