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.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter
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.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter