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Chapter 5: Problem 260

Simplify. Give the answer as a decimal. \(5 \frac{2}{5}-8.75\)

Short Answer

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Step 3

Step by step solution

01

- Convert Mixed Number to Decimal

First, convert the mixed number to a decimal. A mixed number has a whole number and a fraction. Convert the fraction to a decimal and then add the whole number. Given:
02

- Perform the Subtraction

Now, subtract the decimal obtained in Step 1 from 8.75. Arrange the numbers with the larger number on top for easier subtraction.
03

- Simplify the Answer

Perform the subtraction and simplify if necessary to get the final result in decimal form.

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Key Concepts

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

Understanding Mixed Numbers
Mixed numbers are a combination of a whole number and a fraction. For example, in the mixed number 5\(\frac{2}{5}\), 5 is the whole number, and \(\frac{2}{5}\) is the fraction.
To work with these numbers, you often need to convert the fraction part to a decimal. This makes further calculations easier.
For instance, we convert 5\(\frac{2}{5}\) by transforming \(\frac{2}{5}\) into a decimal. To do this, simply divide the numerator (2) by the denominator (5). This gives you 0.4.
Adding this to the whole number 5, we get 5.4.
So, 5\(\frac{2}{5}\) is equal to 5.4 as a decimal.
Decimal Conversion Simplified
Converting other numbers into decimals often helps when performing arithmetic operations like addition, subtraction, multiplication, and division.
To convert a fraction to a decimal, divide the numerator (top number) by the denominator (bottom number).
For example:
  • If you have \(\frac{3}{4}\), divide 3 by 4 to get 0.75.
  • For \(\frac{1}{2}\), dividing 1 by 2 gives you 0.5.
Converting mixed numbers to decimals involves the same steps, but you add the decimal to the whole number. Using these steps makes operations straightforward.
Subtraction of Decimals Made Easy
When subtracting decimals, line up the numbers by their decimal points. This keeps the place values organized.
Let's subtract 8.75 from 5.4. It's easier to arrange the numbers with the larger number on top:
\[\begin{array}{r} 8.75 \- 5.40 \ \end{array}\] Subtract digits in the same place value columns (ones, tenths, hundredths). Borrow if you need to.
In our case, subtracting in each column gives 0.4 - 0.5 in the tenths place, so we need to borrow from the one's place. Always double-check each step.
This approach keeps errors minimal and ensures you get accurate results.
Simplifying Decimals
Once you've completed subtraction, it鈥檚 important to simplify the decimal if needed.
Simplifying involves reducing the number of decimal places for clarity, though sometimes, the decimal is already in its simplest form.
For example, if you get 3.340, you can simplify it to 3.34 by removing the trailing zero. This doesn't change the value, but it makes the number cleaner and easier to read.
Remember: Only remove zeros that don't affect the number value. For instance, 0.400 simplifies to 0.4, but not 0.045.

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Most popular questions from this chapter

In the following exercises, order each of the following pairs of numbers, using < or >. $$-0.1\underline\quad-0.4$$

In the following exercises, round each number to the nearest hundredth. $$0.697$$

In the following exercises, find the unit rate. Round to two decimal places, if necessary. 435 miles on 15 gallons of gas

In the following exercises, round each number to the nearest (a) hundredth (b) tenth (c) whole number. $$1.638$$

In the following exercises, locate each number on a number line. $$-1.6$$
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