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Chapter 4: Problem 20

Eight quarts of oil cost \(\$ 14.00 .\) How much do 5 qt of oil cost? $$ 4^{0}+2^{0} $$

Short Answer

Expert verified
5 quarts cost \$8.75. The expression evaluates to 2.

Step by step solution

01

Understand Relationship Between Quarts and Cost

First, determine the cost per quart by dividing the total cost by the number of quarts: \[ \text{Cost per quart} = \frac{14.00}{8} \]
02

Calculate Cost per Quart

Perform the division: \[ \text{Cost per quart} = 1.75 \]
03

Determine Cost for 5 Quarts

Multiply the cost per quart by the number of quarts you want to find: \[ \text{Cost for 5 quarts} = 1.75 \times 5 = 8.75 \]
04

Simplify the Mathematical Expression

Evaluate the expression \(4^{0}+2^{0}\) by solving each term: \[ 4^{0} = 1 \text{ and } 2^{0} = 1 \]Adding these results, we get: \[ 1 + 1 = 2 \]

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Key Concepts

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

division
Division is one of the fundamental operations in mathematics. It is basically splitting a number into equal parts. For example, in the given problem, we need to find the cost per quart when eight quarts of oil cost \(14.00. To find the cost of one quart, we divide the total cost by the number of quarts: Cost per quart = \[ \frac{14.00}{8} \] This tells us how much one quart costs. After performing the division, we see that Cost per quart = \)1.75. Here are some key points about division:
  • It distributes a large quantity into smaller, equal parts.
  • It's the inverse of multiplication.
  • Dividing by zero is undefined because it does not have a real number solution.
Understanding division is essential for solving problems that involve ratios, rates, and proportions.
multiplication
Multiplication is another basic operation in math. It essentially means adding a number to itself a certain number of times. When you multiply two numbers, one of them can be seen as the total number of groups, and the other as the size of each group. In our problem, we used multiplication to determine the total cost for 5 quarts of oil. Once we know the cost per quart, we multiply it by the number of quarts we need: Cost for 5 quarts = \[ 1.75 \times 5 = 8.75 \] Key points about multiplication include:
  • It can be thought of as repeated addition.
  • Multiplying by 1 leaves the number unchanged (called the identity property).
  • Multiplying by 0 always results in 0 (this is the zero property).
  • Order of multiplication does not matter (commutative property).
Multiplication helps us quickly find the total of several equal groups, making it crucial for solving proportion problems.
mathematical expressions
Mathematical expressions are combinations of numbers, variables, and operations that represent a value. In the problem, we had the expression: \[ 4{^0} + 2{^0} \] To solve this, understanding the concept of exponents is essential. Here,
  • Any number raised to the power of 0 is 1.
So: 4{^0} = 1 and 2{^0} = 1 Adding these together: 1 + 1 = 2. Mathematical expressions can be simple, like the ones in our example, or more complex. Important things to remember about expressions:
  • They do not contain equality signs like equations do.
  • They can be simplified or evaluated by carrying out operations.
By simplifying expressions, we can make complex problems easier to understand and solve.

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Most popular questions from this chapter

In \(2006,\) national expenditures for health care reached 2,106,000,000,000 dollars. Using 300 million as the population of the United States, about how much, to the nearest dollar, was spent on health care person in \(2006 ?\) (Source: U.S. Centers for Medicare and Medicaid Services.)

Perform each indicated operation. Find the difference between the sum of \(5 x^{2}+2 x-3\) and \(x^{2}-8 x+2\) and the sum of \(7 x^{2}-3 x+6\) and \(-x^{2}+4 x-6\)

Subtract. See Example \(\boldsymbol{\delta}\) $$ \begin{array}{l} {12 m^{3}-8 m^{2}+6 m+7} \\ {-3 m^{3}+5 m^{2}-2 m-4} \\ \hline \end{array} $$

Evaluate. $$ 1000(1.53) $$

Explain how to multiply a number by a positive power of 10. Then explain how to multiply a number by a negative power of 10.
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