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Chapter 5: Problem 266

Simplify. Give the answer as a decimal. 5.1\(\left(\frac{12}{5}-3.91\right)\)

Short Answer

Expert verified
-7.701

Step by step solution

01

- Simplify the fraction

Calculate the value of the fraction \ \frac{12}{5}.\ \[ \frac{12}{5} = 2.4 \]
02

- Subtract the decimal

Subtract 3.91 from 2.4. \ \[ 2.4 - 3.91 = -1.51 \]
03

- Multiply by 5.1

Multiply the result from step 2 by 5.1. \ \[ 5.1 \times -1.51 = -7.701 \]

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Key Concepts

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

fraction simplification
When you need to simplify a fraction, you break it down to its simplest form. In our exercise, we have the fraction \(\frac{12}{5}\). Here, 12 is the numerator, and 5 is the denominator. To simplify it, divide the numerator by the denominator.

So, \(\frac{12}{5} = 2.4\).

Now, the fraction is converted to a decimal, making it easier to work with in further calculations.
decimal subtraction
Subtracting decimals seems complex, but it becomes easy with a step-by-step approach. First, write the numbers in a column, aligning the decimal points.

In our example, subtract 3.91 from 2.4. It is easier to align the numbers like this:

2.40

-3.91

When you subtract 3.91 from 2.40, remember to borrow where needed. The result is \(-1.51\).

Decimal subtraction can sometimes yield negative results, especially when a smaller number is subtracted by a larger one.
multiplication with decimals
Multiplying decimals involves a few easy steps. First, ignore the decimal points and multiply the numbers as if they were whole. In our problem, we are multiplying 5.1 and -1.51.

Ignoring the decimals, multiply 51 by 151. After calculating, place the decimal in the product by counting the total number of decimal places in both original numbers combined.

For 5.1 (one decimal place) and -1.51 (two decimal places), the product will have three decimal places. Therefore, 51 times 151 gives 7701.

When you place the decimal back, it becomes \(-7.701\).

Remember, a negative multiplied by a positive gives a negative result.

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