Question

using appropriate property find teb value of -2/3×5/6 -2/3×4/7​

Answer 1

Step-by-step explanation:

-2 × 5 - 2 × 4

3. 6. 3. 7

= -1 × 5 - 8

3. 3. 21

= - 5 - 8 = 105 - 72 = 33 = 11

9. 21. 189 189. 63

Answer 2

➤ Correct Question :-

Find the value of the statement using appropriate property

${\sf \leadsto \dfrac{(-2)}{3} \times \dfrac{5}{6} + \dfrac{(-2)}{3} \times \dfrac{4}{7}}$

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★ How to do :-

Here, we are given with four fractions in which we are asked to solve them using an appropriate property. We can see that we are given with two of the mathematical signs those are the multiplication and addition. We can also see that, in those four fractions the two fractions are common i.e, they are same. So, when we are given with addition and multiplication and in those two fractions are common then we should use the property called as the distributive property. In this property we group the non-common fractions or integers in the bracket and then we multiply the common fraction with the sum of those two non-common fractions. In the place of the addition sign the subtraction sign can also be there but division cannot include in this property. So, let's solve!!

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➤ Solution :-

${\sf \leadsto \dfrac{(-2)}{3} \times \dfrac{5}{6} + \dfrac{(-2)}{3} \times \dfrac{4}{7}}$

Write the fractions in the form of distributive property.

${\sf \leadsto \dfrac{(-2)}{3} \times \bigg( \dfrac{5}{6} + \dfrac{4}{7} \bigg)}$

Firstly, solve the fractions in bracket.

LCM of 6 and 7 is 42.

${\sf \leadsto \dfrac{(-2)}{3} \times \bigg( \dfrac{5 \times 7}{6 \times 7} + \dfrac{4 \times 6}{7 \times 6} \bigg)}$

Multiply the numerators and denominators of fractions in bracket.

${\sf \leadsto \dfrac{(-2)}{3} \times \bigg( \dfrac{35}{42} + \dfrac{24}{42} \bigg)}$

Write both numerators with a common denominator.

${\sf \leadsto \dfrac{(-2)}{3} \times \bigg( \dfrac{35 + 24}{42} \bigg)}$

Add the numerators.

${\sf \leadsto \dfrac{(-2)}{3} \times \dfrac{59}{42}}$

Write the fraction in lowest form by cancellation method.

${\sf \leadsto \dfrac{\cancel{(-2)} \times 59}{3 \times \cancel{42}} = \dfrac{(-1) \times 59}{3 \times 24}}$

Multiply the remaining numbers.

${\sf \leadsto \dfrac{(-59)}{72}}$

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${\red{\underline{\boxed{\bf So, \: the \: answer \: of \: the \: statement \: is \: \dfrac{(-59)}{72}.}}}}$