MCQ (with Solutions): Rational Numbers

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

The LCM 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, add 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