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Chapter 2: Problem 4

Complete the subtraction: $$8-3 \frac{4}{5}=7 \frac{4}{5}-3 \frac{4}{5}=4-\frac{1}{5}$$

Short Answer

Expert verified
The solution to the subtraction problem is \(\frac{4}{5}\).

Step by step solution

01

Subtract the Whole Numbers

Start by subtracting the whole numbers. Let's subtract 7 from 8. This gives us 1.
02

Subtract the Fractions

Now, move on to the fractions. Subtract \(\frac{4}{5}\) from \(\frac{4}{5}\). This yields 0.
03

Combine Whole Number and Fraction

Combine the result of the whole number subtraction (1) with the result of the fraction subtraction (0). So, \(1 + 0 = 1\).
04

Subtract remaining fractions

Now subtract remaining \(\frac{1}{5}\) from the result. So, \(1 - \frac{1}{5} = \frac{4}{5}\).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Whole Numbers
Whole numbers are the basics of counting and they include zero and all the positive integers like 1, 2, 3, and so on. They are numbers without fractions or decimals. In everyday life, we use whole numbers for counting objects, like counting 8 apples.

When you subtract whole numbers, like in the exercise (8 - 7), you simply take away one from the other. Here, subtracting 7 from 8 gives us 1.
  • Start with the larger whole number.
  • Take away the smaller number from it.
  • The result is also a whole number.
Working with Fractions
Fractions represent parts of a whole and are made up of two numbers: the numerator and the denominator. For example, in the fraction \(\frac{4}{5}\), 4 is the numerator (part) and 5 is the denominator (whole).

Fraction subtraction is simple when the denominators are the same. You just subtract the numerators. In our exercise, subtracting \(\frac{4}{5}\) from \(\frac{4}{5}\) equals zero because both parts are equal.
  • Ensure both fractions have the same denominator.
  • Subtract the numerators.
  • Keep the denominator the same.
Exploring Mixed Numbers
Mixed numbers combine whole numbers and fractions and are often seen in everyday measurements, like 3\(\frac{1}{2}\) cups of flour. They are written as a whole number followed by a fraction.

When subtracting mixed numbers, like 7\(\frac{4}{5}\) - 3\(\frac{4}{5}\), handle the whole numbers and fractions separately as shown in the exercise.
  • Separate out the whole numbers and subtract them.
  • Do the same with the fractions.
  • Combine the results at the end.
Basics of Prealgebra
Prealgebra is all about understanding the basics of arithmetic operations like addition and subtraction, involving whole numbers, fractions, and mixed numbers. It's the foundation you need before moving onto more complex math topics.

In prealgebra, problems like the exercise given teach you how to approach and solve math problems step by step.
  • Break down problems into smaller steps.
  • Solve each part individually.
  • Combine results for the final solution.

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Most popular questions from this chapter

Convert the decimal to a fraction. $$0.325$$

Use newspapers or the Internet to find and list situations in which decimals are used. Determine whether the decimals you find are exact values or approximations. INote: Large numbers (such as 3.2 billion) used to describe values such as the balance of trade or the national debt are approximations. Smaller numbers (such as 1.5866 ) used to describe business transactions such as an exchange rate or a stock price are exact values.]

Divide and round to the nearest hundredth. Then check by estimating the quotient. $$129.38 \div 4.47$$

Place the correct symbol, \(<\) or \(>,\) between the two numbers. $$\frac{8}{15} \quad 0.543$$

Convert the decimal to a fraction. $$0.25$$
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