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Learning Goal

Part of: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers2 of 3 cluster items

Apply and extend previous understandings of multiplication and division to multiply and divide rational numbers

7.NS.A.2

**7.NS.A.2**: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers. a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts. b. 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. c. Apply properties of operations as strategies to multiply and divide rational numbers. d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

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7.NS.A.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.
a. Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (-1)(-1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real-world contexts.
b. 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.
c. Apply properties of operations as strategies to multiply and divide rational numbers.
d. Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

What you'll learn

  1. Explain why the product of two negative numbers is positive, using the distributive property and patterns in multiplication
  2. Apply rules for multiplying signed numbers: same signs yield a positive product; different signs yield a negative product
  3. Interpret products of rational numbers in real-world contexts, including contexts where the sign of the product has meaning
  4. Divide rational numbers by applying the relationship between multiplication and division, using the fact that -(p/q) = (-p)/q = p/(-q)
  5. Apply properties of operations (commutative, associative, distributive) as strategies to multiply and divide rational numbers efficiently
  6. Convert a rational number to a decimal using long division and identify whether the decimal terminates or repeats

Slides

Interactive presentations perfect for visual learners • 2 slide decks

Slide Video

Watch narrated slides play like a video lesson • Narrated slide playback

Exercises

Practice problems to build fluency and understanding • 1 exercises