Problem 1

A mixture is obtained by mixing four items of following weights; 132.45 grams, 220.11 grams, 128.62 grams and 140 grams. What is the total weight of the mixture?

Solution

Step 1:

The first items weight = 132.45 grams

The second items weight = 220.11 grams

The third items weight = 128.62 grams

The fourth items weight = 140 grams

Step 2:

The total weight of the four items

= 132.45 + 220.11 + 128.62 + 140

= 621.18 grams

Problem 2

Phil saved 142.12,136.72, 330.27and250 in four months. Find the total amount Phil saved during those four months.

Solution

Step 1:

Amount saved in first month = $142.12

Amount saved in first month = $136.72

Amount saved in first month = $330.27

Amount saved in first month = $250

Step 2:

The total amount saved in four months

= 142.12+136.72 + 330.27+250

= $859.11

Problem 1

If Rita is given 2 checks, one for 39.99,anotherfor18.49, how much is the total of the 2 checks?

Solution

Step 1:

The first checks value = $39.99

The second checks value = $18.49

Step 2:

The sum of the two checks = 39.99+18.49 = $58.48

Problem 2

If the rain for the year at a town is expected to be 36.48 inches and it has already rained 26.52 inches, how many more inches of rain are expected?

Solution

Step 1:

Expected rain = 36.48 inches

Fallen rain = 26.52 inches

Step 2:

The amount of expected rain = 36.48 26.52 = 9.96 inches

Problem 3

During two days, Dave drives 23.9 miles and 31.5 miles. How many miles does Dave drive during those two days?

Solution

Step 1:

First distance driven = 23.9 miles

Second distance driven = 31.5 miles

Step 2:

The total distance driven in two days = 23.9 + 31.5 = 55.4 miles

Introduction

Subtraction of money in dollars and cents is same as the subtraction of decimal numbers.

Rules for subtraction with money

• The money amounts to be subtracted are lined up vertically with the decimal points aligned one above the other.
• The digits in the rightmost column are first subtracted.
• Then the digits in all columns are subtracted one by one till we get the difference of the money amounts.
• We bring down the decimal point and the dollar sign at the right places.

Problem 1

Subtract 187.1893.49

Solution

Step 1:

The money amounts to be subtracted are lined up vertically with the decimal points and dollar signs aligned one above the other.

Step 2:

We begin at the right most column 8 < 9, so we borrow 1 from left; 1 becomes 0 and 18 9 = 9, next 0 > 4, so we borrow from left; 7 becomes 6 and 10 4 = 6; next 6 3 = 3; and 8 < 9, so we borrow from left, and we have 18 9 = 9.

Step 3:

So we get the final difference of the money amounts as $ 93.69

Problem 2

Subtract 246.69176.75

Solution

Step 1:

The money amounts to be subtracted are lined up vertically with the decimal points and dollar signs aligned one above the other.

Step 2:

We begin at the right most column 9 5 = 4; 6 < 7, so we borrow 1 from left; 6 becomes 5 and 16 7 = 9, next 5 < 6, so we borrow 1 from left; 4 becomes 3 and 15 6 = 9; 3 < 7, so we borrow 1 from left; 2 becomes 1 and we have 13 7 = 6; next 1 1 = 0

Step 3:

So we get the final difference of the money amounts as $ 69.94

Problem 1

Estimate the sum after rounding each number to the nearest tenth

98.09 + 23.41 11.30 27.85

Solution

Step 1

Rounding each term to nearest tenth, the expression becomes

= 98.09 + 23.41 11.30 27.85

= 98.1 +23.4 11.3 27.9

= 121.5 39.2 = 82.3

Step 2

So the estimated sum after rounding each number to the nearest tenth

= 98.09 + 23.41 11.30 27.85 = 82.3

Problem 2

Estimate the difference after rounding each number to the nearest tenth/hundredth 69.07 + 15.41 8.30 7.85

Solution

Step 1

Rounding each term to nearest tenth, the expression becomes

= 69.07 + 15.41 8.30 7.85

= 69.1 +15.4 8.3 7.9

= 84.5 16.2 = 68.3

Step 2

So the estimated sum after rounding each number to the nearest tenth

= 69.07 + 15.41 8.30 7.85 = 68.3

Introduction

Basic subtraction of decimals is similar to subtraction of whole numbers without borrowing.

Rules for Decimal Subtraction

• First the decimals are written in such a way that digits with same place values are vertically aligned.
• We then add zeros to the right of decimal numbers where ever necessary so that all numbers have the same number of digits after the decimal point.
• We begin with the rightmost column and start subtracting the digits. Then we keep moving to the left till all columns are subtracted.

Problem 1

Subtract 38.48 16.3

Solution

Step 1

The decimals are aligned as shown. A zero is added to the right of 16.3 as the maximum number of decimal places is 2.

Step 2

We start with the right most column. Subtract 8 0 = 8; then moving to left column 4 3 = 1; again moving left 8 6 = 2; next 3 1 = 2;

Step 3

So the difference of the decimals is 12.18

Problem 2

Subtract 29.58 16.46

Solution

Step 1

The decimals are aligned as shown.

Step 2

We start with the right most column. Subtract 8 6 = 2; then moving to left column 5 4 = 1; again moving left 9 6 = 3; next 2 1 = 1;

Step 3

So the difference of the decimals is 13.12

Introduction

Decimals have to be aligned so that digits with same place values are placed one above the other. Such decimals are aligned decimals. The decimals have to be aligned before subtraction is done. Subtraction of aligned decimals is similar to subtraction of whole numbers.

Rules for Subtraction of Aligned Decimals

• First the decimals are aligned so that digits of same place values are placed above and below each other.
• We then add zeros to the right of decimal numbers where ever necessary so that all numbers have the same number of digits after the decimal point.
• We begin with the rightmost column and start subtracting the digits.
• Then we keep moving to the left till all columns are subtracted.

Problem 1

Subtract 18.48 6.3

Solution

Step 1:

The decimals are aligned as shown. A zero is added to the right of 6.3 as the maximum number of decimal places is 2.

Step 2:

We start with the right most column. Subtract 8 0 = 8; then moving to left column 4 3 = 1; again moving left 8 6 = 2; next 1 0 = 1;

Step 3:

So the difference of the decimals is 12.18

Problem 2

Subtract 39.876 26.45

Solution

Step 1:

The decimals are aligned as shown. A zero is added to the right of 26.45 as the maximum number of decimal places is 3.

Step 2:

We start with the right most column. Subtract 6 0 = 6; then moving to left column 7 5 = 2; again 8 4 = 4; next 9 6 = 3.; 3 2 = 1

Step 3:

So the difference of the decimals is 13.426

Introduction

Addition of three decimals is similar to addition of two decimals.

Rules for decimal addition with 3 numbers

• The decimals are first aligned vertically so that digits of same place value are added.
• Zeros are added to the right of decimal numbers where ever necessary so that all numbers have the same number of digits after the decimal point.

Problem 1

Add 67.07 + 13.41 + 7.30

Solution

Step 1:

The decimals are aligned vertically above one another as shown.

Step 2:

We begin at the rightmost column 7 + 1 + 0 = 8; moving left 0 + 4 + 3 = 7; then

7 + 3 + 7 = 17. We bring down 7 and carry 1 to next column where 6 + 1 + 1 = 8.

Step 3:

We bring down 8 and get the final sum as shown.

Problem 2

Add 83.19 + 33.41 + 19.62

Solution

Step 1:

The decimals are aligned vertically above one another as shown.

Step 2:

We begin at the rightmost column 9 + 1 + 2 = 12; We bring down 2 and carry 1 to next column; moving left 1 + 4 + 6 + 1 = 12; We bring down 2 and carry 1 to next column; next 3 + 3 + 9 + 1 = 16. We bring down 6 and carry 1 to next column where 8 + 3 + 1 + 1 = 13.

Step 3:

We bring down 13 and get the final sum as shown.

Definition

The decimals are aligned so that the digits of same place values are above and below each other. Such decimals are aligned decimals. It is necessary that the decimals are aligned before addition. Addition of aligned decimals is similar to addition of whole numbers.

Rules of decimal addition

• Aligning the decimal numbers so that digits of same place values are lined up vertically one above the other
• Adding zeros to the right of the decimal numbers where ever necessary.

So, at first the decimals are aligned so that the digits of same place values are above and below each other. Then zeros are added to the right of decimal numbers as required. We begin with the rightmost column and start adding the digits. Then we keep moving to the left till all columns are added.

Problem 1

Add 12.53 + 6.32

Solution

Step 1:

The decimals are aligned as shown.

Step 2:

We start with the right most column. Add 3 + 2 = 5; then moving to left column 5 + 3 = 8; again 2 + 6 = 8; next 1 + 0 = 1.

Step 3:

So the sum of the decimals is 18.85

Problem 2

Add 13.41 + 7.309

Solution

Step 1:

The decimals are aligned as shown. A zero is added to the right of 13.41 as the maximum number of decimal places is 3.

Step 2:

We start with the right most column. Add 0 + 9 = 9; then moving left 1 + 0 = 1; again 4 + 3 = 7; next 3 + 7 = 10 we bring down 0; carry 1 to next column. 1 + 1 = 2;

Step 3:

So the sum of the decimals is 20.719

This tutorial provides comprehensive coverage of adding and subtracting of decimals based on Common Core CCSS and State Standards and its prerequisites. Students can navigate learning paths based on their level of readiness. Institutional users may customize the scope and sequence to meet curricular needs. This simple tutorial uses appropriate examples to help you understand adding and subtracting of decimals in a general and quick way.

Audience

This tutorial has been prepared for beginners to help them understand the basics of adding and subtracting of decimals. After completing this tutorial, you will find yourself at a moderate level of expertise in adding and subtracting of decimals, from where you can advance further.

Prerequisites

Before proceeding with this tutorial, you need a basic knowledge of elementary math concepts such number sense, addition, subtraction, place values of whole numbers, place value chart, definition of decimal numbers and so on.