Problem 64 Simplify each expression. $$ ... [FREE SOLUTION]

Chapter 5: Problem 64

Simplify each expression. $$ (-2.5)(3)-4.7 $$

Short Answer

Expert verified

The expression simplifies to -12.2.

Step by step solution

Distribute the Multiplication

The expression is \[ (-2.5)(3) - 4.7 \]. First, multiply $-2.5$ by 3.Perform the multiplication: $-2.5 imes 3 = -7.5$.

Perform the Subtraction

Now, substitute $-7.5$ for $(-2.5)(3)$ in the original expression.This gives us \[-7.5 - 4.7\]. Calculate the result by subtracting:$-7.5 - 4.7 = -12.2$.

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Key Concepts

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

Multiplication in Prealgebra

To really simplify and understand prealgebra, you need a grasp of basic multiplication concepts. Multiplication in prealgebra isn't much different than what you're used to from arithmetic. It involves combining equal groups together. In our example, we are multiplying $-2.5$ by $3$. This means we have three groups of $-2.5$, which is essentially the same as adding $-2.5$ three times.

Start by considering the sign: negative times a positive equals a negative result.
Calculate the absolute values: multiply $2.5$ by $3$ to get $7.5$.
Since we initially observed that multiplying a negative by a positive results in a negative, our answer is $-7.5$.

Notice how straightforward this becomes with practice. Keep these rules of signs in mind; they're very helpful to avoid mistakes.

Subtraction in Prealgebra

Subtraction can sometimes be a little trickier than addition, because you have to pay close attention to the signs of the numbers involved. When you perform a subtraction operation in prealgebra, you are taking away one number from another. In our exercise, you'll notice we start with $-7.5$ and subtract $4.7$.

Since both numbers are negative, think of it as moving further left on the number line.
Subtract the absolute values: calculate $7.5 + 4.7 = 12.2$, because we add $4.7$ to $7.5$ when both are negative.
The result remains negative, giving us $-12.2$.

Remember, dealing with negatives requires practice, but once you get used to looking at the signs, these calculations become intuitive.

Step-by-Step Algebra Solutions

Working through problems in algebra step-by-step helps to ensure accuracy and builds confidence. In this problem, we dealt with two main operations: multiplication and subtraction, and each has its crucial place.
Here are some helpful tips when tackling step-by-step solutions:

Always start by looking at the expression as a whole and identify operations involved.
Prioritize operations according to the order of operations鈥攎ultiply before you subtract.
Work slowly, especially when dealing with negative numbers, to avoid simple errors in signs.
Write out each step clearly as you work through it to make tracking your process easier.

Step-by-step problem solving is exactly like following a recipe; stick to the sequence of steps and you'll arrive at the correct solution. In this example, the final answer of $-12.2$ is reached by following the planned series of operations carefully.

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91影视

Simplify each expression. $$ (-2.5)(3)-4.7 $$

Short Answer

Step by step solution

Distribute the Multiplication

Perform the Subtraction

Key Concepts

Multiplication in Prealgebra

Subtraction in Prealgebra

Step-by-Step Algebra Solutions

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