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

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Calculating Fractions and Decimals poster

Flashcards

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Commutative, associative, and distributive law formulas for simplifying fractions and decimalsCommutative and associative laws applied to addition with decimals and fractions, showing regroupingAssociative law in multiplication with fractions, decimals, and whole numbers worked exampleDistributive law applied to multiply and simplify fractions and decimals with step-by-step worked exampleDistributive law with multiple terms: factoring out common fractions and simplifying decimals step by step

🛎️ 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.

🛎️ What Is the Commutative Law?

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

🛎️ What Is the Associative Law?

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

🛎️ How to Simplify Multiplication with Fractions and Decimals?

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

🛎️ How Does the Distributive Law Work with Multiple Terms?

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

Practice Questions

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Calculating fractions and decimals

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