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Chapter 5: Problem 174

In the following exercises, simplify. $$(1.5-0.06) \div(0.12+0.24)$$

Short Answer

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Step by step solution

01

Simplify the numerator

Simplify the expression in the numerator: \(1.5 - 0.06 \) Subtract 0.06 from 1.5: \[ 1.5 - 0.06 = 1.44 \]
02

Simplify the denominator

Simplify the expression in the denominator: \(0.12 + 0.24 \) Add 0.12 and 0.24: \[ 0.12 + 0.24 = 0.36 \]
03

Divide the simplified numerator by the simplified denominator

Now divide the simplified numerator by the simplified denominator: \( 1.44 \div 0.36 \) Perform the division: \[ 1.44 \div 0.36 = 4 \]

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Key Concepts

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

Numerator and Denominator Simplification
Understanding how to simplify the numerator and denominator of an expression is crucial. In this exercise, we start by simplifying each part of the expression before performing the division.

The numerator here is the expression on top: \(1.5 - 0.06\). To simplify it, we subtract \0.06\ from \1.5\. This gives us \1.44\.

Next, we simplify the denominator, which is the expression on the bottom: \(0.12 + 0.24\). Adding these numbers together results in \0.36\.

When both the numerator and denominator are simplified, we can move on to the next step. Simplifying parts of the expression first makes the final calculation more manageable and accurate.
Basic Arithmetic Operations
In mathematics, basic arithmetic operations include addition, subtraction, multiplication, and division. In this exercise, we specifically use subtraction and addition before moving on to division.

First, subtraction is used to simplify the numerator: \(1.5 - 0.06 = 1.44\). Subtracting a smaller number (0.06) from a larger number (1.5) results in a positive outcome (1.44).

Then, addition is used for the denominator: \(0.12 + 0.24 = 0.36\). Adding these two positive numbers gives a positive sum (0.36). Lastly, we perform division, which is the core operation for finding how many times one number is contained within another: \(1.44 \div \ 0.36 = 4\).
Step-by-Step Problem Solving
Breaking down problems into smaller, manageable steps helps make the solution clearer. Let's revisit the steps in this particular problem:

  • Step 1: Simplify the numerator. We start by simplifying \(1.5 - 0.06 \). Performing the subtraction gives us \1.44\.

  • Step 2: Simplify the denominator. Next, we simplify \(0.12 + 0.24 \). Performing the addition gives us \0.36\.

  • Step 3: Divide the simplified values. Finally, we divide the simplified numerator by the simplified denominator: \(1.44 \div \ 0.36 = 4\).

By following these steps, each phase of the problem becomes clear. This methodical approach ensures accuracy and promotes a deeper understanding of each operation involved.

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