UPSKILL MATH PLUS
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The distributive property states that multiplying a sum by a number gives the same result as multiplying each added by the number and then adding the products together.
For any number \(a\), \(b\) and \(c\), we have \(a × b + c = a × b + a × c\).
Consider the number \(4\), \(3\) and \(2\) we have
\(4 × 3 + 2 = 4 × 3 + 4 × 2\). (LHS \(=\) RHS)
LHS: \(4 × 2 + 3 = 4 × 5\)
\(= 20\).
RHS: \(4 × 3 + 4 × 2\)
\(= 12 + 8\)
\(= 20\).
Thus, \(4 × 3 + 2 = 4 × 3 + 4 × 2\). (LHS \(=\) RHS)
For any three rational numbers , and , we have: \(×\) \(=\) \(+\) .
Consider the rational numbers , and we have
\(×\) \(=\) \(+\) . (LHS \(=\) RHS)
LHS: \(×\)
\(×\)
\(=\) \(×\) (LCM was taken to get the same denominator)
\(=\) \(×\)
\(=\) \(×\) \(=\) \(=\) .
RHS: \(+\) :
\(=\) \(=\) \(=\) .
And \(=\) .
Therefore \(+\)
\(=\) \(+\)
\(=\) \(+\) (LCM was taken to get the same denominator)
\(=\)
\(=\) .
Thus, \(×\) \(=\) \(+\) . (LHS \(=\) RHS)