Video: Evaluating Numerical Expressions of Rational Numbers Using the Properties of Multiplication

Evaluate (−2/5) × 15 + (−2/5) × 25 using the properties of multiplication.

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Video Transcript

Evaluate negative two-fifths multiplied by 15 plus negative two-fifths multiplied by 25 using the properties of multiplication.

In this example, we can use the distributive property of multiplication over addition. This states that 𝑎𝑏 plus 𝑎𝑐 can be rewritten as 𝑎 multiplied by 𝑏 plus 𝑐.

In our example, negative two-fifths is a common factor. This means that we can rewrite the calculation as negative two-fifths multiplied by 15 plus 25. 15 plus 25 is equal to 40.

Therefore, we have negative two-fifths multiplied by 40. One-fifth of 40 is equal to eight. Therefore, negative two-fifths multiplied by 40 is negative 16.

Negative two-fifths multiplied by 15 plus negative two-fifths multiplied by 25 is equal to negative 16.

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