Learn on PengiReveal Math, AcceleratedUnit 5: Solve Problems Involving Operations with Integers and Rational Numbers

Lesson 5-5: Divide Integers and Rational Numbers

In this Grade 7 lesson from Reveal Math, Accelerated, students learn how to divide integers and rational numbers, including how to determine the sign of a quotient based on whether the dividend and divisor have the same or different signs. The lesson covers dividing a positive by a negative, a negative by a positive, and two negatives, using number lines, algebra tiles, and standard division. Students also practice placing the negative sign in equivalent positions within a fraction and apply these skills to real-world problems involving money and other contexts.

Section 1

Rules for Dividing Signed Numbers

Property

  1. The quotient of two numbers with the same sign is positive.
  2. The quotient of two numbers with opposite signs is negative.
  3. Zero divided by any number (except zero) is zero.
  4. The quotient of any number divided by zero is undefined.

Examples

  • The quotient of two numbers with opposite signs is negative: 32÷(−8)=−432 \div (-8) = -4.
  • The quotient of two numbers with the same sign is positive: −45−9=5\frac{-45}{-9} = 5.
  • Division by zero is undefined, but zero divided by a non-zero number is zero: −140\frac{-14}{0} is undefined, while 07=0\frac{0}{7} = 0.

Explanation

Division is the inverse of multiplication, so its sign rules are the same. Since 3×(−4)=−123 \times (-4) = -12, it follows that −12÷(−4)=3-12 \div (-4) = 3. Division by zero is undefined because no number can multiply by zero to get a non-zero result.

Section 2

Placement of the Negative Sign in Division

Property

For any integers aa and bb (with b≠0b \neq 0):

−ab=−ab=a−b-\frac{a}{b} = \frac{-a}{b} = \frac{a}{-b}

Examples

Section 3

Dividing Rational Numbers in Different Forms

Property

To divide rational numbers that are in different forms, first convert them to the same form (usually fractions) and then divide.

  • If the signs are the same (both positive or both negative), the quotient is positive
  • If the signs are different (one positive, one negative), the quotient is negative

Examples

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Rules for Dividing Signed Numbers

Property

  1. The quotient of two numbers with the same sign is positive.
  2. The quotient of two numbers with opposite signs is negative.
  3. Zero divided by any number (except zero) is zero.
  4. The quotient of any number divided by zero is undefined.

Examples

  • The quotient of two numbers with opposite signs is negative: 32÷(−8)=−432 \div (-8) = -4.
  • The quotient of two numbers with the same sign is positive: −45−9=5\frac{-45}{-9} = 5.
  • Division by zero is undefined, but zero divided by a non-zero number is zero: −140\frac{-14}{0} is undefined, while 07=0\frac{0}{7} = 0.

Explanation

Division is the inverse of multiplication, so its sign rules are the same. Since 3×(−4)=−123 \times (-4) = -12, it follows that −12÷(−4)=3-12 \div (-4) = 3. Division by zero is undefined because no number can multiply by zero to get a non-zero result.

Section 2

Placement of the Negative Sign in Division

Property

For any integers aa and bb (with b≠0b \neq 0):

−ab=−ab=a−b-\frac{a}{b} = \frac{-a}{b} = \frac{a}{-b}

Examples

Section 3

Dividing Rational Numbers in Different Forms

Property

To divide rational numbers that are in different forms, first convert them to the same form (usually fractions) and then divide.

  • If the signs are the same (both positive or both negative), the quotient is positive
  • If the signs are different (one positive, one negative), the quotient is negative

Examples