Learning Resource Type

Classroom Resource

Multiplying and Dividing with Negatives

Subject Area

Mathematics

Grade(s)

7

Overview

Deepen your understanding of multiplication and division of rational numbers. This interactive exercise focuses on the rules for finding the products and quotients of positive numbers, negative numbers, and fractions and then finding the solutions on a number line.

    Mathematics (2019) Grade(s): 7

    MA19.7.4

    Apply and extend knowledge of operations of whole numbers, fractions, and decimals to add, subtract, multiply, and divide rational numbers including integers, signed fractions, and decimals.

    Unpacked Content

    UP:MA19.7.4

    Vocabulary

    • Integers
    • Rational numbers
    • Additive inverses
    • opposite quantities
    • Absolute value
    • Terminating decimals
    • Repeating decimals

    Knowledge

    Students know:
    • a number and its opposite have a sum of 0.
    • A number and its opposite are called additive inverses.
    • Strategies for adding and subtracting two or more numbers.
    • Absolute value represents distance on a number line, therefore it is always non-negative.
    • Strategies for multiplying signed numbers.
    • 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).
    • The decimal form of a rational number terminates or eventually repeats.

    Skills

    Students are able to:
    • add rational numbers.
    • Subtract rational numbers.
    • Represent addition and subtraction on a number line diagram.
    • Describe situations in which opposite quantities combine to make 0.
    • Find the opposite of a number.
    • Interpret sums of rational numbers by describing real-world contexts.
    • Show that the distance between two rational numbers on the number line is the absolute value of their difference.
    • Use absolute value in real-world contexts involving distances.
    • Multiply and divide rational numbers.
    • Convert a rational number to a decimal using long division.

    Understanding

    Students understand that:
    • finding sums and differences of rational numbers (negative and positive) involves determining direction and distance on the number line.
    • Subtraction of rational numbers is the same as adding the additive inverse, p - q = p + (-q).
    • If a factor is multiplied by a number greater than one, the answer is larger than that factor.
    • If a factor is multiplied by a number between 0 and 1, the answer is smaller than that factor.
    • Multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers.
    • Integers can be divided, provided that the divisor is not zero.
    Link to Resource

    CR Resource Type

    Interactive/Game

    Resource Provider

    PBS
    Accessibility
    License

    License Type

    PD
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