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Chapter 1: Problem 599

Divide. $$ 1.44 \div(-0.3) $$

Short Answer

Expert verified
-4.8

Step by step solution

01

Convert to a Fraction

Convert the division into fraction form: \(\frac{1.44}{-0.3}\).
02

Simplify the Fraction

Make the denominator a whole number by moving the decimal point one place to the right in both the numerator and the denominator: \(\frac{1.44 \times 10}{-0.3 \times 10} = \frac{14.4}{-3}\).
03

Perform the Division

Divide the numerator by the denominator: \(\frac{14.4}{-3} = -4.8\).
04

Consider the Sign

Since you are dividing a positive number by a negative number, the result must be negative: \(\frac{14.4}{-3} = -4.8\).

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Key Concepts

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

Converting Decimals to Fractions
Understanding how to convert decimals into fractions is a key skill in math. To start, take the decimal number and place it over 1. For example, with 1.44, it becomes \( \frac{1.44}{1} \).
Next, you need to remove the decimal by multiplying both the numerator and the denominator by a power of 10. Since 1.44 has two decimal places, you multiply by 100:
\( \frac{1.44 \times 100}{1 \times 100} = \frac{144}{100} \).
At this point, the decimal has been converted to a fraction. Remember, always multiply by 10, 100, or 1,000 based on the number of decimal places in order to clear the decimal.
Simplifying Fractions
Once the decimal is converted to a fraction, it's essential to simplify it. Simplifying means finding the simplest form where the numerator and denominator have no common factors other than 1.
For the fraction \( \frac{144}{100} \), both 144 and 100 can be divided by their greatest common divisor, which is 4.
First, do the division: \( \frac{144 \div 4}{100 \div 4} = \frac{36}{25} \).
Checking the result, \( \frac{36}{25} \) is already in its simplest form because 36 and 25 share no common prime factors. Simplifying fractions in this way makes calculations easier and more streamlined.
Division Rules for Negative and Positive Numbers
When dividing numbers, it's important to keep track of their signs. Positive and negative numbers follow specific rules.
  • If both numbers are positive or both are negative, the result is positive.
  • If one number is positive and the other one is negative, the result is negative.
In our problem, 1.44 is positive, and -0.3 is negative.
According to the division rules, a positive divided by a negative results in a negative number:
Thus, \( \frac{1.44}{-0.3} = -4.8 \).
Always remember to note the signs of numbers to ensure the correct result in your calculations.

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