Rational and Irrational Sums Rational
Irrational
-4 +23
2/3 + 1/2
-1/4 + 12
2/5 + 15
-3/5 + 6/7
TL + 4
-V3+ 5/8
3.25 +4.17

Rational

Rational

Rational

Rational

Rational

Irrational

Irrational

Rational

Step-by-step explanation:

First we need to establish what a rational, and a irrational numbers are.  A rational number are basically integers that can be written as fractions which means any of the options that are integers or fractions are in fact rational numbers. A irrational number are basically numbers that cannot be written as a fraction which means things like repeating decimals or just numbers that cannot be expressed as a fraction of two other whole numbers.

First option:

19 is a rational number because it can be expressed as two integers which are 1 and 19

Second option:

Both are fractions which means the sum will be a fraction which also means it is a rational number since we previously established that every fraction is a rational number.

Third option:

You can write 12 as a fraction which is 12/1 and then solve which the sum will also be a fraction which means it will also be a rational number.

Fourth Option:

15 can be written as 15/1 which means it is a rational number which also means the sum of the two fractions will also be a rational number.

Fifth option:

Adding fractions, fractions are rational numbers which means the sum will also be a rational number

Sixth option:

Pie is a infinite decimal number which means it is irrational because it cannot be written as a fraction.

Seventh option:

/3 cannot be written as a fraction which means the entire equation is irrational because a rational plus a irrational number will always equal a irrational number.

Eighth option:

Since how these decimals are not repeating they are both rational numbers.

Hope this helps.

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