Question

Verify (1/2+4/5)-6/7=1/2+(4/5-6/7)the property and name the property

Answer 1

Answer:

$\left(\frac{1}{2}+\frac{4}{5}\right)-\frac{6}{7}=\frac{1}{2}+\left(\frac{4}{5}-\frac{6}{7}\right)$

(Associative property )

[(A+B)+C = A+(B+C)]

Step-by-step explanation:

$LHS = \left(\frac{1}{2}+\frac{4}{5}\right)-\frac{6}{7}\\=\left(\frac{5+8}{10}\right)-\frac{6}{7}\\=\frac{13}{10}-\frac{6}{7}\\=\frac{91-60}{70}\\=\frac{31}{70}\:---(1)$

$RHS=\frac{1}{2}+\left(\frac{4}{5}-\frac{6}{7}\right)\\=\frac{1}{2}+\left(\frac{28-30}{35}\right)\\=\frac{1}{2}+\left(\frac{-2}{35}\right)\\=\frac{35-4}{70}\\=\frac{31}{70}\:---(2)$

LHS = RHS

Therefore,

$\left(\frac{1}{2}+\frac{4}{5}\right)-\frac{6}{7}=\frac{1}{2}+\left(\frac{4}{5}-\frac{6}{7}\right)$

(Associative property )

[(A+B)+C = A+(B+C)]

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