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

Evaluate 9 × (−4/7) + (−4/7) × 17 + 16 × (−4/7) using the properties of multiplication.

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Video Transcript

Evaluate nine multiplied by negative four-sevenths plus negative four-sevenths multiplied by 17 plus 16 multiplied by negative four-sevenths using the properties of multiplication.

The three terms have a common factor — negative four-sevenths. So we can use the distributive property of multiplication. Factorizing out negative four-sevenths gives us negative four-sevenths multiplied by nine plus 17 plus 16. As nine plus 17 plus 16 is equal to 42, we are left with negative four-sevenths multiplied by 42. Negative four multiplied by 42 is negative 168. So we are left with negative 168 divided by seven. This is equal to negative 24.

Therefore, nine multiplied by negative four-sevenths plus negative four-sevenths multiplied by 17 plus 16 multiplied by negative four-sevenths is equal to negative 24.

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