If a, b, c are integers and b ≠ 0 then, a × (b - c) = a × b - a × c

Solution:

The given terms are, if a, b, c are integers and b ≠ 0 then, a × (b - c) = a × b - a × c. To prove whether the given statement is true or false let us consider some integer values for a, b and c.

Consider a = 1, b = 2 and c = 3. On substituting the values of a, b, and c in the expression a × (b - c) = a × b - a × c we have

1 × (2 - 3) = 1 × 2 - 1 × 3

-1 = -1

Therefore, after using integer rules and simplifying the expression we observed that the statement ‘if a, b, c are integers and b ≠ 0 then, a × (b - c) = a × b - a × c’ is true.

✦ Try This: State whether the statement is true or false. 4 × (5 - 6) = 4 × 5 - 4 × 6.

We can apply integer rules and the order of operations to identify whether 4 × (5 - 6) = 4 × 5 - 4 × 6 is true or false

☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 1

NCERT Exemplar Class 7 Maths Chapter 1 Exercise Problem 97

If a, b, c are integers and b ≠ 0 then, a × (b - c) = a × b - a × c

Summary:

After applying the integer rules along with considering an illustration we examined that if a, b, c are integers and b ≠ 0 then, a × (b - c) = a × b - a × c is a true statement

☛ Related Questions:

• Multiplication is not commutative for integers
• (-1) is not a multiplicative identity of integers
• 99 × 101 can be written as (100 - 1) × (100 + 1)