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Chapter 5: Problem 171

In the following exercises, simplify. $$18 \div(0.75+0.15)$$

Short Answer

Expert verified
The simplified expression is 20.

Step by step solution

01

Identify the components of the expression

The given expression is \(18 \div(0.75+0.15)\). First, notice that the division is the main operation, with a sum inside the parentheses.
02

Simplify the expression inside the parentheses

Add the numbers inside the parentheses: \(0.75 + 0.15 = 0.90\). Now the expression becomes \(18 \div 0.90\).
03

Perform the division

Divide 18 by 0.90. To simplify this, consider converting the decimal division into a whole number division by moving the decimal point two places to the right for both numbers: \(18 \div 0.90 = 1800 \div 90 = 20\).

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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 essential operations in arithmetic. It allows us to split a number into equal parts. For the given exercise, we have to divide 18 by the sum of 0.75 and 0.15. Start by simplifying inside the parentheses, as per the order of operations. Once the addition inside the parentheses is complete, move to the division step. Remember, when working with decimals, you can simplify the operation by converting them into whole numbers. This makes the calculation easier. In our problem, after adding 0.75 and 0.15, convert 0.90 to a whole number by moving the decimal two places to the right, along with 18. This simplifies the division greatly.
Decimals
Decimals represent fractions or parts of a whole number. Understanding how to handle them is crucial in arithmetic operations. In the exercise, you encounter decimals inside the parentheses: 0.75 and 0.15. When adding decimals, align the decimal points and perform the addition as usual. Here, 0.75 + 0.15 = 0.90. When moving to division involving decimals, a useful trick is to convert the decimals into whole numbers by shifting the decimal point to the right. For example, 18 divided by 0.90 becomes simpler when you think of it as 1800 divided by 90.
Basic Arithmetic
Basic arithmetic includes operations like addition, subtraction, multiplication, and division. These fundamental skills are built upon in more advanced math topics. In this exercise, we start with addition: 0.75 + 0.15, then proceed to division: 18 divided by 0.90. To handle arithmetic with decimals, ensure to align decimal points in addition and convert decimals to whole numbers for easier division. These basic operations will aid in simplifying complex expressions efficiently. Remember to follow the order of operations: parentheses first, then division. Practice these steps regularly to build a strong arithmetic foundation.

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