Introduction:
Integer is defined as a number which can be positive or negative but it should be a whole number and not a fraction or decimal. There are two types of integers, they are, i) positive integer and ii) negative integer. It can be positive or as well as negative integer. The sum or the product of the algebraic integers is also an algebraic integer. Integers are closed under the arithmetic operations of addition and multiplication. Mixed integers represent the mixed numbers with basic arithmetic operations. In this article, we are going to see about solving mixed integers. Integers are not closed under exponentiation while natural numbers closed under exponentiation.
Solving mixed integers with same denominators:
Solving mixed integers with same denominators Example 1:
Solve the mixed integers: 2 2/3 - 4 2/3
Solution:
Here, we need to convert the given mixed number or improper number and then to perform the arithmetic operation.
On solving this,
2 2/3 = (2 * 2 + 2) / 3
= (4 + 2)/3
converting 2 2/3 to improper number we get,
= 6/3
4 2/3 = (4 * 3 + 2) / 3
= (12 + 2)/3
converting 4 2/3 to improper number we get,
= 14/3
= 6/3 – 14/3
Now subtracting,
= (6 – 14) / 3
= -8/3
The answer is given as -8/3.
Solving mixed integers with same denominators Example 2:
Solve the mixed integers: 3 4/7 - 2 3/7
Solution:
Here, we need to convert the given mixed number or improper number and then to perform the arithmetic operation.
On solving this,
3 4/7 = (3 * 7 + 4) / 7
= (21 + 4)/7
converting 3 4/7 to improper number we get,
= 25/7
2 3/7 = (2* 7 + 3) / 7
= (14 + 3)/7
converting 2 3/7 to improper number we get,
= 17/7
= 25/7 – 17/7
Now subtracting,
= (25 – 17) / 7
= 8/7
The answer is given as 8/7.
Solving mixed integers with different denominators:
Solving mixed integers with different denominators Example 1:
Solve the mixed integers: 1 2/3 - 1 5/7
Solution:
Here, we need to convert the given mixed number or improper number and then to perform the arithmetic operation.
On solving this,
1 2/3 = (1 * 3 + 2) / 3
= (3 + 2)/3
converting 1 2/3 to improper number we get,
= 5/3
1 5/7 = (1* 7 + 5) / 7
= (7 + 5)/7
converting 1 5/7 to improper number we get,
= 12/7
= 5/3 – 12/7
Take the LCD,
LCD = 3 * 7
= 21
On solving this we get,
= (5 (7) – 12(3)) / 21
= (35 – 36) / 21
= - 1/ 21
The answer is given as -1/21.
