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Chapter 1: Q70. (page 17)

CRITICAL THINKING

Is the Distributive Property also true for division? In other words, does b+ca=ba+ca,a鈮�0? If so, give an example and explain why it is true. If not true, give a counterexample.

Short Answer

Expert verified

Yes, Distributive property is true for division.

One example is 4+62=42+62

Example is true because on simplifying left hand side and right hand side separately each terms gives same result

LHS

RHS


4+62=102=5


42+62=2+3=5


Step by step solution

01

- Check Distributive Property is true for division of not

Let a,b,andcbe real numbers with a鈮�0such that a divides sum of bandc

Since, denominator of a fraction can be separated with each term of numerator so distributive property is true for division.

02

- Substitution for exapmle

To give an example substitute 2 for a, 4 for b and 6 for c into expression

b+ca=ba+ca

03

- Verify 4+62=42+62

First evaluate left hand side by adding terms of numerator then dividing it by denominator as shown below

4+62=102=5

Now to evaluate right hand side, first simplify both fractions then add the resultant terms

42+62=2+3=5

Thus, 4+62=42+62

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