Divide Rational Numbers

Examples, solutions, worksheets, videos, and lessons to help Grade 7 students learn how to apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non-zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real-world contexts.

Common Core: 7.NS.2b

Suggested Learning Targets

• I can use the division rules for integers and apply them to dividing decimals and fractions.
• I can explain that integers can be divided provided that the divisor is not zero.
• I can explain and recognize that a negative fraction can be written as a negative numerator and positive denominator or as a positive numerator and negative denominator.
• I can interpret quotients of rational numbers in real world contexts.
• I can create an equivalent mathematical expression when given an expression by using the properties of operations.
• I can identify equivalent expressions when given two or more expressions.

Understanding division of rational numbers (Common Core Standard 7.NS.2b)

Dividing Rational Numbers
How to divide rational numbers (fractions and decimals)?

Division of Rational Numbers
Examples:

1. Find the multiplicative inverse of each of the following.
   (a) 100
   (b) 2/8
   (c) - 19/21
   (d) 7
   (e) -z³/(2xy²)
2. Divide the following rational numbers, be sure that your answer is in the simplest form.
   
3. The world’s largest trench digger, “Bagger 288”, moves at 3/8 mph. How long will it take to dig a trench 2/3 mile long?

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