**Modeling decimal addition and subtraction :**

For some real-world problems, we may need to add or subtract two decimals.

Let us see how decimal addition and subtraction can be modeled through the following examples.

**Modeling decimal addition :**

Let us see, how to add the decimals 0.24 and 0.15.

Observe the figure given below.

0.24 and 0.15 are shaded in two different colors. Now the sum of 0.24 and 0.15 is 0.39

That is,

3 tenths and 9 hundredths

**Modeling decimal subtraction :**

Let us see, how to subtract the decimal 0.14 from 0.25.

Observe the figure given below.

0.25 is shaded in green color.

Since, we are subtracting 0.14 from 0.25, let us shade 0.14 in red color in some of the green colored boxes.

Then, we have

To get the result of 0.25 - 0.14, count the number of green colored boxes.

That is, 0.11

Apart from "Modeling decimal addition and subtraction", let us see the other methods used to add and subtract decimals.

Adding decimals is similar to adding wholenumbers. First align the numbers by place value. Start adding at the right and regroup when necessary. Bring down the decimal point into your answer.

Based on the point given above, let us see the other methods to add decimals.

**Method 1 :**

Therefore,

0.24 + 0.15 = 0.39

**Method 2 :**

**Not asaaaaaaaaaaaaaaaaa0 . 2 4 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa+ 0 . 1 5 aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaa0 . 3 9 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------**

Therefore,

0.24 + 0.15 = 0.39

**Note :**

In both the methods, arrange the decimal numbers according to the place values and add them.

Let us see, how to subtract 0.14 from 0.25

**Method 1 :**

Therefore,

0.25 - 0.14 = 0.11

**Method 2 :**

**Not asaaaaaaaaaaaaaaaaa0 . 2 5 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa- 0 . 1 4 aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaa0 . 1 1 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------**

Therefore,

0.25 - 0.14 = 0.11

**Note :**

In both the methods, arrange the decimal numbers according to the place values as we arrange in whole numbers. Then subtract them.

**Problem 1 :**

Add the following decimals

0.75 and 0.5

**Solution :**

**Not asaaaaaaaaaaaaaaaaa0 . 7 5 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa+ 0 . 2 0 aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaaa0 . 9 5 aaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa-----------**

In the above addition of decimals, 0.2 is taken as 0.20, as the first decimal number has two digits on the right side of the decimal point.

**Problem 2 :**

Add the following decimals

28.07, 7.6, 0.008

**Solution :**

**Not asaaaaaaaaaaaaa2 8 . 0 7 0 aaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa+ 7 . 6 0 0aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa0 . 0 0 8aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa------------aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa3 5 . 6 7 8aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaasaaaaaaa-------------**

**In the above addition of decimals, 7.6 is taken as 7.600 and 28.07 is taken as 28.070. Because the last decimal number has 3 digits on the right side of the decimal point. **

**Problem 3 :**

Add the following decimals

14.2, 16, 0.542

**Solution :**

**Not asaaaaaaaaaaaaaa 1 4 . 2 0 0 aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa(+) 1 6 . 0 0 0 aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaa0 . 5 4 2 aaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa---------------aaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaa3 0 . 7 4 2 aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa--------------- aaaaaaaaaaaaaaaaaaaaa **

**In the above addition of decimals, 14.2 is taken as 14.200 and 16 is taken as 16.000. Because the last decimal number has 3 digits on the right side of the decimal point.**

**Problem 4 :**

Add the following decimals

10.653, 0.065, 3

**Solution :**

**Not asaaaaaaaaaaaaaa 1 0 . 6 5 3 aaaaaaaaaaaaaaaaaaaaaas aaaaaaaaaaaaaaaaaa(+)0 0 . 0 6 5 aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaaaa3 . 0 0 0 aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa---------------aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa 1 3 . 7 1 8 aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa-----------------aaaaaaaaaaaaaaaaaaaaaa **** **

**In the above addition of decimals, 3 is taken as 3.000.Because the first and second numbers have 3 digits on the right side of the decimal point.**

**Problem 5 :**

Add the following decimals

38.056, 24.6, 39

**Solution :**

**Not asaaaaaaaaaaaaaa 3 8 . 0 5 6aaaaaaaaaaaaaaaaaaaaaas aaaaaaaaaaaaaaaaaa(+) 2 4 . 6 0 0 aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaaa 3 9 . 0 0 0 aaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaa---------------aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaaaa 1 0 1 . 6 5 6aaaaaaaaaaaaaaaaaaaaaaa aaaaaaaaaaaaaaaaa-----------------aaaaaaaaaaaaaaaaaaaaaa **** **

**In the above addition of decimals, 39 is taken as 39.000. Because the first number has 3 digits on the right side of the decimal point.**

**Problem 6 :**

Find the value of 48.05 - 25.57

**Solution :**

**Problem 7 :**

Find the value of 18 - 6.59

**Solution :**

In the above subtraction of decimals, 18 is taken as 18.00. Because, the second decimal number has 2 digits on the right side of the decimal point.

**Problem 8 :**

Find the value of 8.563 - 3. 54

**Solution :**

In the above subtraction of decimals, 3.54 is taken as 3.540. Because the first number has 3 digits on the right side of the decimal point.

After having gone through the stuff given above, we hope that the students would have understood "Modeling decimal addition and subtraction".

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**Identifying Integers and Their Opposites****Comparing and Ordering Integers****Absolute Value****Greatest Common Factor****Least Common Multiple****Classifying Rational Numbers****Identifying Opposites and Absolute Value of Rational Numbers****Comparing and Ordering Rational Numbers****Applying GCF and LCM to Fraction Operations****Dividing Fractions****Dividing Mixed Numbers****Solving Multistep Problems with Fractions and Mixed Numbers****Dividing Whole Numbers****Adding and Subtracting Decimals****Multiplying Decimals****Dividing Decimals****Applying Operations with Rational Numbers**

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