Problem 83 - Algebra 1

Question

find the quotient. $$ 26 \div(-13) $$

Step-by-Step Solution

Answer

The quotient of 26 divided by -13 is -2.

Step 1: Identify the Dividend and the Divisor

The dividend is the number that is being divided, which in this case is 26. The divisor is the number we are dividing by, that is -13.

Step 2: Perform Division

Next, simply perform the division using absolute values only at this point. Thus, 26 divided by 13 equals 2.

Step 3: Apply the Rules of Sign

A positive number divided by a negative number results in a negative number. Therefore, the quotient of 26 divided by -13 is -2.

Key Concepts

Understanding the Quotient

In basic arithmetic, the term "quotient" refers to the result of dividing one number by another. Imagine you have 26 apples and you want to split them evenly among 13 friends. The number each friend gets represents the quotient. More formally, in our exercise, when the number 26 is divided by -13, the quotient is -2. In this scenario, it measures how many times the divisor, -13, can fit into the dividend, 26.
The key here is understanding that division breaks quantities into smaller, equal parts, and the quotient is the size of each part when the set is partitioned.

Rules of Sign in Division

When dividing integers, the signs of the numbers involved can significantly impact the outcome. There are a few simple rules that help us determine the sign of the quotient:

• If both the dividend and divisor have the same sign (both positive or both negative), the quotient will be positive.
• If the dividend and the divisor have different signs (one positive, one negative), the quotient will be negative.

In the problem of 26 divided by -13, the dividend is positive, and the divisor is negative. According to the rules of sign, this results in a negative quotient, hence the answer -2.

Concept of Integer Division

Integer division is a fundamental operation in mathematics where you divide two integers and get another integer as the quotient. In integer division, it's crucial to remember that there will be no fractions or decimals; the result is always a whole number. For example, dividing 26 by -13 gives -2, since 13 fits into 26 two times, but because of the negative sign, the quotient becomes negative.
This is particularly useful in computer science and programming, where operations often require working with whole numbers without including fractional values. Integer division gives a clean, simplified result that can be easily used in further calculations.