MCQ Questions for Class 8 Maths - Rational Numbers

To simplify ²⁄₃ + (-⁴⁄₅) + ⁷⁄₁₅ + (-¹¹⁄₂₀), we first need to find the least common denominator (LCD) for the fractions. The denominators are 3, 5, 15, and 20.

The LCD of 3, 5, 15, and 20 is 60.

Now we express each fraction with a denominator of 60:

• ²⁄₃ = ⁴⁰⁄₆₀
• -⁴⁄₅ = ^-48⁄₆₀
• ⁷⁄₁₅ = ²⁸⁄₆₀
• -¹¹⁄₂₀ = ^-33⁄₆₀

Now, sum the fractions:

⁴⁰⁄₆₀ + ^-48⁄₆₀ + ²⁸⁄₆₀ + ^-33⁄₆₀

Simplifying:

^{40 - 48 + 28 - 33}⁄₆₀ = ^-13⁄₆₀

Thus, the simplified result is: B: −¹³⁄₆₀

The identity element under addition is the number that, when added to any other number, leaves that number unchanged. In other words, for any number x, the identity element e satisfies:

x + e = x

The number that satisfies this property is 0, since:

x + 0 = x

Thus, the correct answer is: C: 0

Both the numerator and denominator have no common divisor other than 1.

Also, both the numerator and denominator is positive

1/2 cannot be simplified further

Therefore, 1/2 is in standard form

The only rational number that is neither positive nor negative is 0, as it does not have a sign.

Thus, the correct answer is:

B: 0.

To find the product of ⁷⁄₈ and ^-2⁄₂₁, we multiply the numerators and denominators:

⁷⁄₈ × ^-2⁄₂₁ = ^{7 × -2}⁄_{8 × 21} = ^-14⁄₁₆₈

Now simplify ^-14⁄₁₆₈:

^-14⁄₁₆₈ = ^{-14 ÷ 14}⁄_{168 ÷ 14} = ^-1⁄₁₂

Thus, the correct answer is: B: −¹⁄₁₂

Let the two rational numbers be x and -15/19.

The sum of the numbers is given by:

x + (-15/19) = -7

Isolate x:

x = -7 + 15/19

Convert -7 to a fraction with denominator 19:

-7 = -133/19

Now, add the fractions:

x = (-133/19) + (15/19) = (-133 + 15) / 19 = -118/19

The correct answer is:

D: -118/19