The calculation of negative 13 divided by 3 is a straightforward mathematical operation. To solve this problem, we can follow the standard rules of arithmetic. First, we need to understand that dividing by a number is the same as multiplying by its reciprocal. Therefore, negative 13 divided by 3 can be rewritten as negative 13 multiplied by the reciprocal of 3, which is 1/3.
Step-by-Step Calculation
To calculate negative 13 divided by 3, we proceed as follows: we multiply -13 by 1⁄3. This operation involves multiplying the numerator (-13) by 1 and then dividing the result by the denominator (3). The calculation can be represented as: (-13) * (1⁄3) = -13⁄3.
Simplifying the Fraction
The fraction -13⁄3 can be simplified by dividing the numerator by the denominator. Since 13 divided by 3 equals 4 with a remainder of 1, we can express -13⁄3 as -4 and 1⁄3. This is because -13 divided by 3 gives us -4 as the quotient and -1 as the remainder, which can be represented as a fraction: -4 - 1⁄3. However, in decimal form, -13⁄3 is approximately -4.33.
| Operation | Result |
|---|---|
| -13 divided by 3 | -4.33 (approximate decimal form) |
| -13 multiplied by 1/3 | -13/3 (exact fraction form) |
| Simplified form of -13/3 | -4 and 1/3 (mixed number form) |
In mathematical terms, the division of two numbers is defined as the multiplication of the first number by the reciprocal of the second. Applying this definition to our problem, we find that -13 divided by 3 is equivalent to -13 times 1/3, which yields -13/3. This fraction, when simplified or converted to a decimal, provides the final answer to the calculation.
Understanding the Concept of Negative Numbers in Division
Negative numbers are an integral part of the number system and play a crucial role in various mathematical operations, including division. When dividing a negative number by a positive number, the result is always negative. This rule applies to the calculation of -13 divided by 3, where the negative sign of the dividend (-13) determines the negative outcome of the division.
Importance of Sign Rules in Mathematics
In mathematics, sign rules are essential for performing arithmetic operations correctly. For division, the rule states that if the signs of the two numbers are different (one positive and one negative), the result will be negative. This principle guides the calculation of -13 divided by 3, ensuring that the outcome is negative due to the difference in signs between the dividend and the divisor.
The calculation of negative 13 divided by 3 is a fundamental mathematical operation that demonstrates the application of division rules and the handling of negative numbers. By following the standard procedures for division and applying the rules for negative numbers, we can determine that -13 divided by 3 equals -4.33 (approximately) or -13/3 in fraction form.
What is the result of dividing a negative number by a positive number?
+The result of dividing a negative number by a positive number is always negative. For example, -13 divided by 3 equals -4.33, which is negative.
How do you simplify a fraction like -13⁄3?
+To simplify a fraction like -13⁄3, you divide the numerator (-13) by the denominator (3). This gives you -4 with a remainder of -1, which can be represented as -4 and 1⁄3 in mixed number form or approximately -4.33 in decimal form.
