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Chapter 6: Problem 34

For Exercises \(21-36,\) write as a decimal number. $$76 \frac{5}{6}$$

Short Answer

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Question: Convert the mixed number \(76 \frac{5}{6}\) into a decimal. Answer: The decimal form of the mixed number \(76 \frac{5}{6}\) is approximately \(76.8333\).

Step by step solution

01

Identify the mixed number

We are given the mixed number \(76 \frac{5}{6}\). The integer part is 76 and the fractional part is \(\frac{5}{6}\).
02

Convert the fractional part into a decimal

To convert the fractional part \(\frac{5}{6}\) into a decimal, divide the numerator by the denominator. In this case, divide 5 by 6: $$\frac{5}{6} \approx 0.8333$$
03

Combine the integer and decimal parts

Now that we've converted the fractional part into a decimal, we add it to the integer part: $$76 + 0.8333 \approx 76.8333$$
04

Final Answer

The decimal form of the mixed number \(76 \frac{5}{6}\) is approximately \(76.8333\).

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Key Concepts

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

Mixed Numbers
Mixed numbers are quite simple once you break them down. A mixed number is a combination of a whole number and a fraction. In our exercise, we worked with the mixed number \(76 \frac{5}{6}\). It's important to recognize the two parts:
  • The whole number, which is 76 in our case.
  • The fraction, which here is \(\frac{5}{6}\).
Mixed numbers are often used in everyday situations like cooking or crafting, where measurements might naturally split into whole units and fractions. By understanding mixed numbers, you can easily switch between fractions and their mixed number forms, making calculations or estimates much simpler.
Take a deep breath and remember, breaking things down into their components is always a great first step in tackling any math challenge.
Decimal Conversion
Converting fractions to decimals is an essential skill in math. It requires a little division magic, but once you get the hang of it, it'll feel like second nature. To convert the fraction \(\frac{5}{6}\) into a decimal, you'll need to divide 5 by 6. This means you perform the division operation \(5 \div 6\). Here's a peek into how it unfolds:
  • The division of 5 by 6 results in a decimal of approximately 0.8333.
  • This result is a repeating decimal, meaning after a certain point, it will keep following the same pattern.
Understanding decimal conversion helps in many real-life scenarios, like dealing with money or measurements, allowing for more precision. Anytime you need to know the exact value or place a value on a number line, converting to a decimal is the way to go!
Mathematical Operations
Mathematical operations are the building blocks of all mathematical concepts. When working with mixed numbers, the key operation is
  • division, to convert the fraction part into a decimal.
  • addition, to sum up the whole number and the resulting decimal.
In our example, the mixed number \(76 \frac{5}{6}\) was broken down into 76 and \(0.8333\), which are then added together. Addition, in this context, is straightforward: you just line up the numbers by their decimal point and add them together digit by digit. Having a strong grasp on these operations ensures you can manipulate numbers in various forms, whether they're in equations, graphs, or measurement systems. This foundational knowledge will serve you well in all math-related tasks.
Division in Fractions
Division in fractions is a key step when converting a fraction to a decimal. To find out how much has been "hidden" in a fraction, you split, or divide, the numerator by the denominator. Let鈥檚 break it down using our example of dividing 5 by 6:
  • Start by setting up the division: 5 divided by 6.
  • You may notice that 5 is less than 6, so you are dealing with a proper fraction. Your result will be less than 1.
  • Perform the division operation either by hand or using a calculator to get approximately 0.8333.
This process allows us to see the true size of the fraction compared to the whole, transforming it into a more familiar and manageable decimal format. Getting comfortable with division in fractions is incredibly useful when working in areas like statistics, finance, or engineering, where precision is critical.

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