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Chapter 4: Problem 442

In the following exercises, add. $$4 \frac{5}{8}+9 \frac{3}{8}$$

Short Answer

Expert verified
14

Step by step solution

01

Add the Whole Numbers

Add the whole number parts of the mixed numbers separately: \(4 + 9 = 13\).
02

Add the Fractions

Add the fractional parts of the mixed numbers: \(\frac{5}{8} + \frac{3}{8}\). Since the denominators are the same, simply add the numerators: \(\frac{5 + 3}{8} = \frac{8}{8} = 1\).
03

Combine the Results

Combine the sum of the whole numbers and the sum of the fractions: \(13 + 1 = 14\).

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Key Concepts

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

whole numbers
Whole numbers are the numbers without fractions or decimals. They include 0, 1, 2, 3, and so on. In the problem given, the whole numbers are 4 and 9.

To add whole numbers:
  • Identify the numbers you need to add. In this exercise, they are 4 and 9.
  • Simply add them together: 4 + 9 = 13.

No need to worry about fractions or decimals when working solely with whole numbers.

Whole numbers are straightforward as compared to fractions and mixed numbers.
fractions
Fractions represent parts of a whole. They have a numerator (top number) and a denominator (bottom number). The denominator shows the total number of parts, while the numerator shows how many parts we have. In this exercise, the fractions are \(\frac{5}{8}\) and \(\frac{3}{8}\).

To add fractions:
  • First, make sure the denominators are the same. Here, both denominators are 8.
  • Add the numerators: 5 + 3 = 8.
  • Put the sum over the common denominator: \(\frac{5 + 3}{8} = \frac{8}{8} = 1\).

Adding fractions is simple when they have the same denominator. If not, you would need to find a common denominator first.
mixed numbers
Mixed numbers consist of a whole number and a fraction. Examples include \(4 \frac{5}{8}\) and \(9 \frac{3}{8}\). Mixed numbers can be broken down into their whole number and fractional parts for easier addition.

To add mixed numbers:
  • Add the whole numbers separately. In our example, add 4 and 9, getting 13.
  • Add the fractional parts. Here, it is \(\frac{5}{8} + \frac{3}{8}\), which equals 1.
  • Combine the sums from steps 1 and 2. Our sum is 13 for the whole numbers plus 1 from the fractions, resulting in 14.

Breaking mixed numbers into their components helps simplify the process of addition.

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Most popular questions from this chapter

In the following exercises, simplify. $$ -\frac{22}{25}+\frac{9}{40} $$

In the following exercises, simplify. $$ \frac{2}{d}+\frac{9}{d} $$

In the following exercises, change to equivalent fractions using the given LCD. $$\frac{1}{3}, \frac{3}{4} \text { and } \frac{4}{5}, \quad L C D=60$$

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x+\left(-\frac{11}{12}\right)\) when (a) \(x=\frac{11}{12} \quad\) (b) \(x=\frac{3}{4}\)

In the following exercises, evaluate the given expression. Express your answers in simplified form, using improper fractions if necessary. \(x+\frac{1}{2}\) when (a) \(x=-\frac{1}{8} \quad\) ( b) \(x=-\frac{1}{2}\)
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