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Chapter 6: Problem 19

Perform each operation. $$ 3 \frac{1}{8}+2.325 $$

Short Answer

Expert verified
5.450

Step by step solution

01

Convert Mixed Number to Improper Fraction

The mixed number \(3 \frac{1}{8}\) needs to be converted to either an improper fraction or a decimal for easy addition. \(3 \frac{1}{8}\) is equivalent to \(\frac{25}{8}\) because \(3 \times 8 + 1 = 25\).
02

Convert Improper Fraction to Decimal

Convert \(\frac{25}{8}\) to a decimal. Divide 25 by 8 to get \(3.125\).
03

Add the Decimals

Now add the two decimals: \(3.125 + 2.325\). Align the decimals and perform the addition: \(3.125 + 2.325 = 5.450\).

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Key Concepts

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

Mixed Numbers
Mixed numbers consist of a whole number and a fraction combined into one entity. For instance, in the original exercise, we have the mixed number \(3 \frac{1}{8}\). This number signifies three whole parts and one-eighth of another part.
  • The whole number part gives us a clearer picture of the size of the value.
  • The fractional part adds detail to indicate portions smaller than a whole.
Mixed numbers are quite common in daily life, like when measuring time or cooking. To perform operations like addition or subtraction seamlessly, it鈥檚 often necessary to convert mixed numbers to improper fractions or decimals as seen in our exercise.
Improper Fractions
An improper fraction occurs when the numerator (top number) is greater than or equal to the denominator (bottom number). In the exercise, we converted the mixed number \(3 \frac{1}{8}\) to an improper fraction \(\frac{25}{8}\).
  • To convert a mixed number to an improper fraction, multiply the whole number by the fraction's denominator and add the numerator. This gives the new numerator.
  • For \(3 \frac{1}{8}\), multiply 3 and 8: \(3 \times 8 = 24\). Then, add 1: \(24 + 1 = 25\). Thus, \(\frac{25}{8}\).
Improper fractions can simplify complex calculations, especially when dealing with operations like addition and subtraction, because they represent a singular number.
Fraction to Decimal Conversion
Converting fractions to decimals is a crucial skill that aids in various mathematical operations. In the problem, once we have the improper fraction \(\frac{25}{8}\), the next task is to turn it into a decimal.
  • To convert a fraction to a decimal, simply perform the division: divide the numerator by the denominator.
  • Dividing 25 by 8 gives you 3.125, which represents the same value in decimal form.
Decimals are often easier to work with, especially in addition and subtraction, as they allow straightforward alignment and calculation. This conversion helps in simplifying problems and achieving accurate results.

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Most popular questions from this chapter

Round each decimal to the specified position. 4.087 to the nearest tenth.

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Round 0.0652 to the nearest hundredth.
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