Calculating Fractions and Decimals

Learn how to use the commutative, associative, and distributive laws to simplify calculations with fractions and decimals. Let’s get started! 🚀

Calculating Fractions and Decimals - introduction visual

Video Lesson

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Flashcards

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Showing the commutative law (a + b = b + a), associative law (a + (b + c) = (a + b) + c), and distributive law (a × (b + c) = ab + ac)Example of the commutative and associative laws in addition with decimals and fractions, showing rearrangement and grouping of numbers.Commutative and associative laws in multiplication shown with a worked example involving fractions, decimals, and whole numbers.Distributive law example, showing step-by-step calculation with decimals and fractions, ending with 8.8.Explanation of distributive law applied to fractions and decimals, showing step-by-step simplification example.

🛎️ Properties of Arithmetic

  • The commutative law means the order does not matter: a+b=b+aa+b=b+a and a×b=b×aa\times b=b\times a.
  • The associative law means grouping does not matter: a+(b+c)=(a+b)+ca+(b+c)=(a+b)+c and a×(b×c)=(a×b)×ca\times(b\times c)=(a\times b)\times c.

🛎️ Commutative Law

  • You can swap the order of numbers when adding or multiplying.
  • The answer stays the same.

🛎️ Associative Law

  • You can change the brackets when adding or multiplying.
  • The grouping changes, but the answer stays the same.

🛎️ Using Laws to Simplify Multiplication

  • When multiplying decimals and fractions, rearrange the numbers.
  • Group fractions together and decimals together to calculate more easily.

🛎️ Distributive Law with More Terms

  • Factor out the common factor first.
  • Simplify what is inside the brackets, then find the final answer.

Practice Questions

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Interactive Activity

Calculating fractions and decimals

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