**Adding rational numbers with the same sign :**

To add rational numbers with the same sign, add the absolute values of the rational numbers and use the sign of the rational numbers for the sum.

**Example 1 : **

Add : (-2/3) + (-1/3)

**Solution : **

**Step 1 : **

Find the absolute values.

|-2/3| = 2/3 and |-1/3| = 1/3

**Step 2 : **

Find the sum of the absolute values :

2/3 + 1/3 = (2+1) / 3

2/3 + 1/3 = 3/3

2/3 + 1/3 = 1

**Step 3 : **

Use the sign of the rational numbers to write the sum.

(-2/3) + (-1/3) = -1

**Example 2 : **

Add : (+2/5) + (+1/5)

**Solution : **

**Step 1 : **

Find the absolute values.

|+2/5| = 2/5 and |+1/5| = 1/5

**Step 2 : **

Find the sum of the absolute values :

2/5 + 1/5 = (2+1)/5

2/5 + 1/5 = 3/5

**Step 3 : **

Use the sign of the rational numbers to write the sum.

(+2/5) + (+1/5) = +3/5

**Example 3 : **

Malachi hikes for 2.5 miles and stops for lunch. Then he hikes for 1.5 more miles. How many miles did he hike altogether?

**Solution : **

**Step 1 : **

Use positive numbers to represent the distance Malachi hiked.

**Step 2 : **

Find 2.5 + 1.5.

Let us use the real number line to add 2.5 and 1.5.

**Step 3 : **

Start at 2.5.

**Step 4 : **

Move 1.5 units to the right because the second addend is positive.

The result is 4.

Malachi hiked 4 miles.

**Example 4 : **

Kyle pours out 3/4 liter of liquid from a beaker. Then he pours out another 1/2 liter of liquid. What is the overall change in the amount of liquid in the beaker?

**Solution : **

**Step 1 : **

Use negative numbers to represent amounts the change each time Kyle pours liquid from the beaker.

**Step 2 : **

Find -3/4 + (-1/2).

Let us use the real number line to add -3/4 and -1/2.

**Step 3 : **

Start at -3/4.

**Step 4 : **

Move | -1/2 | = 1/2 unit to the left because the second addend is negative.

The result is -1 1/4.

The amount of liquid in the beaker has decreased by 1 1/4 liters.

After having gone through the stuff given above, we hope that the students would have understood "How to add rational numbers with the same sign".

Apart from the stuff given above, if you want to know more about "Adding rational numbers with the same sign", please click here

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here.

HTML Comment Box is loading comments...

**WORD PROBLEMS**

**HCF and LCM word problems**

**Word problems on simple equations **

**Word problems on linear equations **

**Word problems on quadratic equations**

**Area and perimeter word problems**

**Word problems on direct variation and inverse variation **

**Word problems on comparing rates**

**Converting customary units word problems **

**Converting metric units word problems**

**Word problems on simple interest**

**Word problems on compound interest**

**Word problems on types of angles **

**Complementary and supplementary angles word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**One step equation word problems**

**Linear inequalities word problems**

**Ratio and proportion word problems**

**Word problems on sets and venn diagrams**

**Pythagorean theorem word problems**

**Percent of a number word problems**

**Word problems on constant speed**

**Word problems on average speed **

**Word problems on sum of the angles of a triangle is 180 degree**

**OTHER TOPICS **

**Time, speed and distance shortcuts**

**Ratio and proportion shortcuts**

**Domain and range of rational functions**

**Domain and range of rational functions with holes**

**Graphing rational functions with holes**

**Converting repeating decimals in to fractions**

**Decimal representation of rational numbers**

**Finding square root using long division**

**L.C.M method to solve time and work problems**

**Translating the word problems in to algebraic expressions**

**Remainder when 2 power 256 is divided by 17**

**Remainder when 17 power 23 is divided by 16**

**Sum of all three digit numbers divisible by 6**

**Sum of all three digit numbers divisible by 7**

**Sum of all three digit numbers divisible by 8**

**Sum of all three digit numbers formed using 1, 3, 4**

**Sum of all three four digit numbers formed with non zero digits**