Distinguishing Opposites and Reciprocals
Distinguishing Opposites and Reciprocals is a Grade 7 math skill in Illustrative Mathematics, Chapter 5: Rational Number Arithmetic. Students learn the difference between a number and its additive inverse (opposite) versus its multiplicative inverse (reciprocal), and how each relates to the operations of addition and multiplication.
Key Concepts
The additive inverse (or opposite) of a number $a$ is $ a$. Their sum is the additive identity, $0$. $$a + ( a) = 0$$ The multiplicative inverse (or reciprocal) of a non zero number $a$ is $\frac{1}{a}$. Their product is the multiplicative identity, $1$. $$a \cdot \frac{1}{a} = 1 \quad (a \neq 0)$$.
Common Questions
What is the opposite of a number?
The opposite of a number is its additive inverse. The opposite of 5 is negative 5, and the opposite of negative 3 is 3. A number and its opposite sum to zero.
What is the reciprocal of a number?
The reciprocal of a number is its multiplicative inverse. The reciprocal of 4 is 1/4, and the reciprocal of 2/3 is 3/2. A number times its reciprocal equals 1.
How do opposites and reciprocals differ?
Opposites involve addition (sum to zero), while reciprocals involve multiplication (product equals 1). Both involve inverting a relationship but through different operations.
What is the reciprocal of a negative number?
The reciprocal of a negative number is also negative. The reciprocal of negative 2 is negative 1/2.
What chapter covers opposites and reciprocals in Illustrative Mathematics Grade 7?
Distinguishing opposites and reciprocals is covered in Chapter 5: Rational Number Arithmetic in Illustrative Mathematics Grade 7.