Quotients of Signed Numbers
Quotients of Signed Numbers establishes the sign rules for division: dividing two numbers with opposite signs gives a negative result, and dividing two numbers with the same sign gives a positive result. Taught in Yoshiwara Elementary Algebra Chapter 2: Linear Equations, these rules mirror the rules for multiplying signed numbers and are fundamental for Grade 6 students working with negative numbers in equations, fractions, and algebra. The special cases 0/a = 0 and a/0 is undefined are also established.
Key Concepts
Property The quotient of two numbers with opposite signs is a negative number. The quotient of two numbers with the same sign is a positive number. If $a$ is any nonzero number, then $$\frac{0}{a} = 0 \quad \text{and} \quad \frac{a}{0} \text{ is undefined.}$$.
Examples The quotient of two numbers with the same sign is positive: $\frac{ 45}{ 9} = 5$.
The quotient of two numbers with opposite signs is negative: $32 \div ( 4) = 8$.
Common Questions
What is the sign rule for dividing negative numbers?
If both numbers have the same sign, the quotient is positive. If they have opposite signs, the quotient is negative. For example, (-12)/3 = -4, and (-12)/(-3) = 4.
What is 0 divided by a nonzero number?
Zero divided by any nonzero number equals 0. For example, 0/7 = 0.
What is a number divided by 0?
Division by zero is undefined. You cannot divide any number by 0.
Where are quotients of signed numbers in Yoshiwara Elementary Algebra?
This topic is covered in Chapter 2: Linear Equations of Yoshiwara Elementary Algebra.
Do the same sign rules apply to multiplication?
Yes. Multiplication and division share the same sign rules: same signs give positive results, opposite signs give negative results.