Problem 77 Find the value of each expressio... [FREE SOLUTION]

Chapter 5: Problem 77

Find the value of each expression. Give the result as a decimal. $$ \frac{1}{4}(-9.6-5.2) $$

Short Answer

Expert verified

The expression evaluates to -3.7.

Step by step solution

Calculate the expression inside the parentheses

First, look at the expression inside the parentheses: $-9.6 - 5.2$. Subtract 5.2 from -9.6. The calculation is:\[ -9.6 - 5.2 = -14.8 \].So, the result inside the parentheses is $-14.8$.

Multiply by the fraction outside the parentheses

Now, multiply $-14.8$ by $\frac{1}{4}$ which is equivalent to dividing by 4:\[ \frac{1}{4}(-14.8) = -14.8 \times \frac{1}{4} = -3.7 \].So, the final result is $-3.7$.

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Key Concepts

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

Fractions

Fractions are a way of representing parts of a whole. They consist of a numerator, which is the number on top, and a denominator, the number on the bottom. The numerator indicates how many parts we have, while the denominator shows how many equal parts the whole is divided into. For example, in the fraction $\frac{1}{4}$, the numerator is 1 and the denominator is 4, which means we have one part out of four equal parts.

A fraction like $\frac{1}{4}$ can be thought of as one quarter, which is also equivalent to 0.25 in decimal form.
When multiplying a fraction by a number, you can multiply the numerator directly by the number or divide the number by the denominator. Both methods will give you the same result.

In the original exercise, we multiplied $\frac{1}{4}$ by $-14.8$, which can be efficiently done by taking $-14.8$ and dividing it by 4. This is a practical example of applying fractions in calculations.

Decimals

Decimals are another way of representing fractions, but they use a base-10 system. They consist of a whole number part and a fractional part, separated by a decimal point. For example, 0.5 is a decimal, where 0 is the whole number part and 5 is after the decimal point.

Each digit after the decimal represents a power of ten. For instance, in 0.25, the 2 is in the tenths place, and the 5 is in the hundredths place.
Decimals are especially useful for calculations involving money, measurements, and more, as they allow for easy addition and subtraction.

In the problem, the terms $-9.6$ and $-5.2$ are decimals. We subtracted these values, resulting in $-14.8$, which can be further combined with fractions during multiplication, making computations more precise and straightforward.

Order of Operations

The order of operations is a set of rules to follow when evaluating mathematical expressions. It ensures that everyone calculates the same result for an expression. The acronym PEMDAS helps remember the order: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

Start by solving any calculations within parentheses.
Next, handle any exponents.
Perform multiplication and division as they appear from left to right.
Complete any addition and subtraction in order from left to right.

In the exercise, we first worked on the expression inside the parentheses $-9.6 - 5.2$, which follows the rule to address parentheses initially. Then, the result was multiplied by $\frac{1}{4}$, highlighting the sequence of operations crucial for reaching the correct solution.

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91影视

Find the value of each expression. Give the result as a decimal. $$ \frac{1}{4}(-9.6-5.2) $$

Short Answer

Step by step solution

Calculate the expression inside the parentheses

Multiply by the fraction outside the parentheses

Key Concepts

Fractions

Decimals

Order of Operations

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