Add the following rational numbers: - 5 7 and 3 7

Given, - 5 7 and 3 7 Hence, adding the numbers, we get: - 5 7 + 3 7 = - 5 + 3 7 = - 2 7 (Since denominators are same, we will just add the numerators and write the fraction keeping the denominator same.) Hence, the addition of the given rational numbers gives - 2 7 .

What should be added to 1 2 + 1 3 + 1 5 to get 3 ?

1 2 + 1 3 + 1 5 = 15 30 + 10 30 + 6 30 = 31 30 (L.C.M of 2 , 3 , 5 = 30 ) Consider the number to be added as x . According to the question, 1 2 + 1 3 + 1 5 + x = 3 ⇒ x = 3 - ( 15 × 1 15 × 2 + 10 × 1 10 × 3 + 6 × 1 6 × 5 ) ⇒ x = 3 - ( 15 × 1 + 10 × 1 + 6 × 1 ) 30 ⇒ x = 3 × 30 1 × 30 - 31 30 ⇒ x = 90 30 - 31 30 ⇒ x = 59 30 Hence, the required number = 59 30

Add and express the sum as a mixed fraction: - 31 6 + - 27 8

Given, - 31 6 + - 27 8 = - 31 × 4 6 × 4 + - 27 × 3 8 × 3 ( LCM of 6 and 8 is 24 ) = - 124 24 + - 81 24 = - 124 - 81 24 = - 205 24 A mixed Fraction is a whole number and a proper fraction combined. Divide the numerator by denominator to obtain quotient, remainder. Write it in the form q r d (where q is quotient, r is remainder, and d is divisor). Hence, the required mixed fraction is - 8 13 24 .

Add and express the sum as a mixed fraction: 24 7 + - 11 4

Given, 24 7 + - 11 4 = 24 × 4 7 × 4 + - 11 × 7 4 × 7 ( LCM of 7 and 4 is 28 ) = 96 28 + - 77 28 = 19 28 A mixed Fraction is a whole number and a proper fraction combined. Here, the numerator is smaller than the denominator. The given fraction is a proper fraction, and proper fractions cannot be converted into a mixed fraction.

What should be added to - 7 8 to get 5 9 ?

Consider the number to be added to be x Putting the question into the equation form, we get - 7 8 + x = 5 9 ⇒ x = 5 9 - - 7 8 ⇒ x = 5 9 + 7 8 ⇒ x = 5 × 8 9 × 8 + 7 × 9 8 × 9 ⇒ x = 40 72 + 63 72 ⇒ x = 40 + 63 72 ⇒ x = 103 72 So, the other number is 103 72 .

What should be added to - 5 11 to get 26 33 ?

Consider the number to be added to be x Putting the question into the equation form, we get - 5 11 + x = 26 33 ⇒ x = 26 33 - - 5 11 ⇒ x = 26 33 - - 5 11 We need to find the L.C.M. of the denominators to make the denominators same. L.C.M of 33 , 11 is 33 . ⇒ x = 26 × 1 33 × 1 - - 5 × 3 11 × 3 ⇒ x = 26 - ( - 15 ) 33 ⇒ x = 41 33 So, the other number is 41 33 .

What number should be subtracted from - 5 3 to get 5 6 ?

Consider the number to be subtracted to be x Putting the question into the equation form, we get - 5 3 - x = 5 6 ⇒ - x = 5 6 + 5 3 ⇒ - x = 5 6 + 5 × 2 3 × 2 ⇒ - x = 5 6 + 10 6 ⇒ - x = 5 + 10 6 ⇒ - x = 15 6 ⇒ x = - 15 6 ⇒ x = - 5 2 Hence, the number to be subtracted = - 5 2 .

Add and express the sum as a mixed fraction: - 12 5 + 43 10

Given, - 12 5 + 43 10 = - 12 × 2 5 × 2 + 43 × 1 10 × 1 ( LCM of 5 and 10 is 10 ) = - 24 10 + 43 10 (Since denominators are same, we will just add the numerators and write the fraction keeping the denominator same.) = - 24 + 43 10 = 19 10 A Mixed Fraction is a whole number and a proper fraction combined. Now, divide the numerator by denominator to obtain quotient, remainder and divisor. (where q is quotient, r is remainder, and d is divisor). Write it in the form q r d . Hence, the mixed fraction obtained is 1 9 10 .

The sum of two numbers is - 4 3 . If one of the numbers is - 5 , find the other.

Consider the unknown number to be x Putting the question into the equation form, we get: - 5 + x = - 4 3 ⇒ x = - 4 3 - ( - 5 ) ⇒ x = - 4 3 + 5 1 ⇒ x = - 4 3 + 5 × 3 1 × 3 ⇒ x = - 4 + 15 3 ⇒ x = 11 3 So, the other number is 11 3 .

What should be added to 2 3 + 3 5 to get - 2 15 ?

Consider the number to be added as x . Putting the question into the equation form, we get 2 3 + 3 5 + x = - 2 15 ⇒ x = - 2 15 - 2 3 + 3 5 ⇒ x = - 2 15 - 2 × 5 3 × 5 + 3 × 3 5 × 3 ⇒ x = - 2 15 - 10 15 + 9 15 ⇒ x = - 2 15 - 10 + 9 15 ⇒ x = - 2 15 - 19 15 ⇒ x = - 2 - 19 15 ⇒ x = - 21 15 ⇒ x = - 7 5 Hence, the required number = - 7 5

What number should be added to - 5 7 to get - 2 3 ?

Consider the number to be added to be x . Putting the question into the equation form, we get: - 5 7 + x = - 2 3 ⇒ x = - 2 3 - - 5 7 ⇒ x = - 2 3 + 5 7 ⇒ x = - 2 × 7 3 × 7 + 5 × 3 7 × 3 ⇒ x = - 14 21 + 15 21 ⇒ x = - 14 + 15 21 ⇒ x = 1 21 Hence, the other number is 1 21 .

What number should be subtracted from 3 7 to get 5 4 ?

Consider the number to be subtracted to be x . Putting the question into the equation form, we get 3 7 - x = 5 4 ⇒ - x = 5 4 - 3 7 ⇒ - x = 5 × 7 4 × 7 - 3 × 4 7 × 4 ⇒ - x = 35 28 - 12 28 ⇒ - x = 35 - 12 28 = 23 28 ⇒ x = - 23 28 Hence, the required number = - 23 28