In this Grade 7 lesson from enVision Mathematics, students learn how to multiply rational numbers, including fractions, decimals, and mixed numbers that are positive or negative. The lesson covers the sign rules for multiplication — positive times negative yields a negative product, and negative times negative yields a positive product — extending the integer multiplication rules to all rational numbers. Students apply these skills through real-world contexts such as changes in elevation and bank account balances.
Section 1
Modeling Multiplication of Signed Numbers on a Number Line
The multiplication can be modeled on a number line.
The expression represents groups of size . Start at 0 and make jumps of size .
If is positive, the final position is in the same direction as the jumps.
If is negative, the final position is in the opposite direction of the jumps.
Section 2
Multiplying Different Forms of Rational Numbers
To multiply rational numbers in different forms, such as a decimal and a fraction, first convert them to a common form. You can either convert the decimal to a fraction or the fraction to a decimal before multiplying.
Expand to review the lesson summary and core properties.
Section 1
Modeling Multiplication of Signed Numbers on a Number Line
The multiplication can be modeled on a number line.
The expression represents groups of size . Start at 0 and make jumps of size .
If is positive, the final position is in the same direction as the jumps.
If is negative, the final position is in the opposite direction of the jumps.
Section 2
Multiplying Different Forms of Rational Numbers
To multiply rational numbers in different forms, such as a decimal and a fraction, first convert them to a common form. You can either convert the decimal to a fraction or the fraction to a decimal before multiplying.