Question

Verify ;i)3/4×(-⅓+⅚)={3/4×(-⅓)}+(3/4×5/6)​

Answer 1

★ How to do :-

Here, we are given with three fractions on LHS and the same three fractions on the RHS of the statement. We are asked to verify that the both sides of the statement are equal to each other. As we can see that on LHS we are given with one bracket and on the RHS, we are given with two different brackets to solve with. In this case, this property is known as the distributive property. This can be used for addition and multiplication of fractions or integers. As in this question, we are given with multiplication and addition, we can use the same rule to solve this question. If we get the results of both sides as equal to each other, then the statement given to us will be verified. So, let's solve!!

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★ How to do :-

${\sf \leadsto \dfrac{3}{4} \times \bigg( \dfrac{(-1)}{3} + \dfrac{5}{6} \bigg) = \bigg( \dfrac{3}{4} \times \dfrac{(-1)}{3} \bigg) + \bigg( \dfrac{3}{4} \times \dfrac{5}{6} \bigg)}$

Let's solve the LHS and RHS separately.

LHS :-

${\sf \leadsto \dfrac{3}{4} \times \bigg( \dfrac{(-1)}{3} + \dfrac{5}{6} \bigg)}$

LCM of 3 and 6 is 6.

${\sf \leadsto \dfrac{3}{4} \times \bigg( \dfrac{(-1) \times 2}{3 \times 2} + \dfrac{5}{6} \bigg)}$

Multiply the numerators and denominators of first fraction.

${\sf \leadsto \dfrac{3}{4} \times \bigg( \dfrac{(-2)}{6} + \dfrac{5}{6} \bigg)}$

Now, write both numerators with a common denominator.

${\sf \leadsto \dfrac{3}{4} \times \bigg( \dfrac{(-2) + 5}{6} \bigg)}$

Add the numerators.

${\sf \leadsto \dfrac{3}{4} \times \dfrac{3}{6}}$

Multiply the fractions.

${\sf \leadsto \dfrac{3 \times 3}{4 \times 6} = \dfrac{9}{24}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \cancel \dfrac{9}{24} = \dfrac{3}{8} \: --- LHS}$

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RHS :-

${\sf \leadsto \bigg( \dfrac{3}{4} \times \dfrac{(-1)}{3} \bigg) + \bigg( \dfrac{3}{4} \times \dfrac{5}{6} \bigg)}$

Write both numerators and denominators with a common fraction in both brackets.

${\sf \leadsto \bigg( \dfrac{3 \times (-1)}{4 \times 3} \bigg) + \bigg( \dfrac{3 \times 5}{4 \times 6} \bigg)}$

Multiply the numerators and denominators.

${\sf \leadsto \dfrac{(-3)}{12} + \dfrac{15}{24}}$

Write the fractions in lowest form by cancellation method.

${\sf \leadsto \dfrac{(-1)}{4} + \dfrac{5}{8}}$

LCM of 4 and 8 is 8.

${\sf \leadsto \dfrac{(-1) \times 2}{4 \times 2} + \dfrac{5}{8}}$

Multiply the numerators and denominators of first fraction.

${\sf \leadsto \dfrac{(-2)}{8} + \dfrac{5}{8} = \dfrac{(-2) + 5}{8}}$

Add the numbers to get the value of RHS.

${\sf \leadsto \dfrac{3}{8} \: --- RHS}$

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Let's compare the results now.

Comparison :-

${\sf \leadsto \dfrac{3}{8} \: and \: \dfrac{3}{8}}$

As we can see that they are equal. So,

${\sf \leadsto \dfrac{3}{8} = \dfrac{3}{8}}$

So,

${\sf \leadsto LHS = RHS}$

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Hence verified !!

Answer 2

Answer

Answer:

i) = -3/4*(-4/5+6/7)

= (-3/4* -4/5)+(-3/4*6/7)

ii) =4/5*(-5/6-7/8)

=(4/5*-5/6) - (4/5* -7/6)

Answer

Hope its help u