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Chapter 2: Q6. (page 72)

Evaluate the expression using the distributive property and mental math.

3  (  97)

Short Answer

Expert verified

3  (  97)  =291.

Step by step solution

01

Step-1 – What are real numbers? 

Real numbers are simply the combination of Whole numbers, Integers, Rational and Irrational numbers in the number system.

02

Step-2 – Distributive Property of Multiplication 

Suppose a, b, and c is three real numbers.

Distributive Property of Multiplication

Property: a  (b  -  c  )  =  a  ·  b  -  a  ·  c  

Example: 8 (12  -  4  )  =   8  ·  12  -  8  ·  4  =  96  -  32  =  64

03

Step-3:  Evaluate the expression using the distributive property and mental math.        

We can write 97 as 100 – 3, to evaluate the expression 3(97), we can use the distributive method of multiplication.

Distributive Property of Multiplication

Property: a  (b  -  c  )  =  a  ·  b  -  a  ·  c  

3  (  97)  =  3 (100  −  3  )  =   3  ·  100  −  3  ·  3  =  300  −  9  =  2913  (  97)  =291

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