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Chapter 5: Problem 76

Find the value of each expression. Give the result as a decimal. $$ \frac{3}{4}-(9.6)(5) $$

Short Answer

Expert verified
-47.25

Step by step solution

01

Multiply 9.6 by 5

First, calculate the product of 9.6 and 5. Multiply them together: \[ 9.6 \times 5 = 48.0 \]
02

Simplify the Expression

Subtract the result from the multiplication in Step 1 from \( \frac{3}{4} \). Convert \( \frac{3}{4} \) to a decimal, which is 0.75, and then subtract 48.0: \[ 0.75 - 48.0 = -47.25 \]
03

Final Result

The expression evaluates to \(-47.25\) when written as a decimal.

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Key Concepts

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

Fractions to Decimals
Converting fractions to decimals is an essential skill, especially when you need to perform operations such as addition, subtraction, multiplication, or division. A fraction represents a part of a whole and is expressed as two numbers separated by a slash.
To convert a fraction like \( \frac{3}{4} \) into a decimal, you need to divide the numerator (3) by the denominator (4).
This means you'd perform a division like this: 3 divided by 4, which gives you 0.75.
Here are a few steps you might follow:
  • Identify the numerator and denominator.
  • Divide the numerator by the denominator using long division or a calculator.
  • Write down the result as a decimal.
Practicing this process helps in getting comfortable with fractions and decimals, allowing you to easily switch between the two forms during calculations.
Multiplication
Multiplication is one of the four basic arithmetic operations and is essential for solving mathematical problems efficiently. The operation is represented by the multiplication symbol, commonly shown as \( \times \) or sometimes as a simple dot \( \cdot \).
In the provided exercise, you need to determine the product of 9.6 and 5.
To multiply decimals:
  • Ignore the decimal points and multiply the numbers as if they were whole numbers. Here, multiply 96 by 5, resulting in 480.
  • Count the total number of decimal places in both numbers being multiplied. In this case, 9.6 has one decimal place.
  • Apply the total count of decimal places to your result. Since there's one decimal place, place the decimal point in 480 to get 48.0.
Understanding and practicing multiplication will aid in performing larger calculations without errors.
Subtraction
Subtraction is used for finding the difference between numbers. It's part of many calculations, such as the one in our exercise where we subtract the product of two numbers from a fraction.
Once you have completed the multiplication: \( 48.0 \), you need to perform the subtraction: \( 0.75 - 48.0 \).
To perform subtraction efficiently, follow these steps:
  • Ensure both numbers are in the same form, typically as decimals in these kinds of problems.
  • Align the decimal points vertically to ensure accuracy when subtracting.
  • Subtract the numbers as you would with whole numbers, borrowing from the left if necessary.
  • Write down the final result, in this case, \(-47.25\).
Mastering subtraction, especially when mixed with multiplication or decimals, strengthens your overall math competency.

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Most popular questions from this chapter

\(1.278 \div 0.3\)

In your own words, describe how to quickly divide a number by a power of 10 such as \(10,100,1000,\) etc.

Divide. \(0.54 \div 12\)

Divide. \(-86.79 \div(-1000)\)

Determine whether the given values are solutions of the given equations. \(\frac{z}{100}=0.8 ; z=8\)
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