Grade 4
  1. Numbers and Place Value  1.1. Understanding Place Value  1.2. Reading and Writing Large Numbers  1.3. Comparing and Ordering Numbers  1.4. Rounding Numbers  1.5. Understanding Odd and Even Numbers  1.6. Number Patterns and Sequences
  2. Addition and Subtraction  2.1. Addition of Large Numbers  2.2. Subtraction of Large Numbers  2.3. Estimation in Addition and Subtraction  2.4. Word Problems on Addition and Subtraction
  3. Multiplication and Division  3.1. Understanding Multiplication  3.2. Multiplying Multi-Digit Numbers  3.3. Understanding Division  3.4. Dividing Multi-Digit Numbers  3.5. Multiplication and Division Facts  3.6. Word Problems on Multiplication and Division
  4. Factors and Multiples  4.1. Understanding Factors  4.2. Finding Common Factors  4.3. Understanding Multiples  4.4. Finding Common Multiples  4.5. Prime and Composite Numbers  4.6. Prime Factorization  4.7. Greatest Common Factor  4.8. Least Common Multiple
  5. Fractions  5.1. Understanding Fractions  5.2. Equivalent Fractions  5.3. Simplifying Fractions  5.4. Comparing and Ordering Fractions  5.5. Addition of Fractions  5.6. Subtraction of Fractions  5.7. Mixed Numbers and Improper Fractions  5.8. Converting Mixed Numbers to Improper Fractions  5.9. Word Problems on Fractions
  6. Decimals  6.1. Understanding Decimals  6.2. Reading and Writing Decimals  6.3. Comparing and Ordering Decimals  6.4. Rounding Decimals  6.5. Addition of Decimals  6.6. Subtraction of Decimals  6.7. Converting Decimals to Fractions  6.8. Converting Fractions to Decimals  6.9. Word Problems on Decimals
  7. Measurement  7.1. Length  7.1.1. Units of Length  7.1.2. Converting Units of Length  7.1.3. Perimeter  7.1.4. Area  7.1.5. Word Problems on Length  7.2. Weight  7.2.1. Units of Weight  7.2.2. Converting Units of Weight  7.2.3. Word Problems on Weight  7.3. Volume and Capacity  7.3.1. Units of Volume  7.3.2. Converting Units of Volume  7.3.3. Estimating Volume and Capacity  7.3.4. Word Problems on Volume and Capacity  7.4. Time  7.4.1. Reading Time  7.4.2. Units of Time  7.4.3. Converting Units of Time  7.4.4. Calculating Elapsed Time  7.4.5. Word Problems on Time
  8. Geometry  8.1. Properties of Shapes  8.1.1. Types of Angles  8.1.2. Types of Triangles  8.1.4. Symmetry  8.1.5. Lines of Symmetry  8.2. Perimeter and Area  8.2.1. Perimeter of Rectangles  8.2.2. Perimeter of Other Shapes  8.2.3. Area of Rectangles  8.2.4. Area of Other Shapes  8.2.5. Area of Irregular Shapes  8.3. Coordinate Geometry  8.3.1. Understanding Coordinates  8.3.2. Plotting Points on a Grid  8.3.3. Identifying Shapes on a Grid
  9. Data and Graphs  9.1. Types of Data  9.2. Organizing Data  9.3. Reading Bar Graphs  9.4. Drawing Bar Graphs  9.5. Line Plots  9.7. Reading and Interpreting Line Graphs  9.8. Word Problems on Graphs
  10. Money  10.1. Understanding Money  10.2. Addition and Subtraction with Money  10.3. Making Change  10.4. Multiplying and Dividing Money  10.5. Word Problems on Money

Grade 4 → Decimals ↓


Word Problems on Decimals


Decimals are a fundamental part of math that represent a portion of a whole number. They are used in a variety of daily life situations, such as dealing with money, measurement, and more. Decimals are important to understand, and grade 4 math curriculum often includes word problems on decimals to help students learn them better.

In this article, we're going to explore word problems on decimals. We'll explain what decimals are, how to solve problems involving decimals, and give plenty of examples to show what these problems look like and how they can be solved.

What are decimals?

A decimal is a number that has a point called a decimal point. This point separates the integer part from the fractional part. For example, in the number 3.75, the point (or decimal point) separates 3 (the integer part) from 75 (the fractional part).

3.75 Whole Part: 3 Fractional Part: 75

Decimal numbers can be used to represent values that are less than an integer, as well as values that are greater than an integer. For example, 0.5 is less than one, while 2.45 is greater than two. The position of a digit relative to the decimal point determines its value. This is known as the place value.

Place value in decimal

The value of each place in a decimal number is ten times greater than the value of the place to its right. From left to right, next to the decimal point, the values increase to tenths, hundredths, thousandths, and so on.

For example, in the decimal number 4.576:

4.576 - 4 is the whole number part - 5 is in the tenths place (0.5 or 5/10) - 7 is in the hundredths place (0.07 or 7/100) - 6 is in the thousandths place (0.006 or 6/1000)

Understanding word problems on decimals

Understanding word problems on decimals involves two main tasks. First, you must understand the problem statement, and second, you must translate it into a mathematical sentence that you can solve.

1. Understanding

Read the problem carefully. Identify important numbers and keywords. Look for words that indicate the operations you need to perform, such as addition, subtraction, multiplication, or division.

2. Translation

Once you understand the problem, translate the words into a mathematical expression using numbers and decimal places as needed. Then, solve the equation or calculation to find the answer.

Let us understand this process with some examples:

Example 1: Shopping scenario

Problem: Sarah bought a book for $15.75 and a pen for $2.30. How much money did she spend in total?

Solution:

  1. Recognize the important numbers: $15.75 and $2.30.
  2. Here the required operation is addition, as we have to find out the total amount spent.
$15.75 +$2.30 ------ $18.05

Answer: Sarah spent a total of $18.05.

Example 2: Distance problem

Question: A car traveled 250.6 km on the first day and 182.4 km on the second day. How many kilometers did it travel in total?

Solution:

  1. Identify the important numbers: 250.6 km and 182.4 km.
  2. The operation required to find the total travel distance is addition.
250.6 +182.4 ------- 433.0

Answer: The car traveled a total of 433.0 km.

Example 3: Subtraction scenario

Problem: Emily had $120.50 in her bank account. She withdrew $45.75. How much money is left in her account now?

Solution:

  1. Recognize the important numbers: $120.50 and $45.75.
  2. Here the process of subtraction is required to find the remaining amount.
$120.50 -$45.75 --------- $74.75

Answer: Emily has a balance of $74.75 in her account.

Example 4: Multiplication by decimals

Problem: A bottle of juice costs $1.25. How much will 8 bottles cost?

Solution:

  1. Identify the important numbers: $1.25 (cost per bottle) and 8 (number of bottles).
  2. The required operation is multiplication.
$1.25 times 8 = $10.00

Answer: 8 bottles of juice would cost $10.00.

Example 5: Division by decimals

Problem: If 3.2 liters of milk is divided equally among 4 children, how much milk will each child get?

Solution:

  1. Identify the important numbers: 3.2 liters of milk and 4 children.
  2. The operation required to find the amount of milk each child receives is division.
3.2 div 4 = 0.8

Answer: Each child gets 0.8 litres of milk.

Visual examples of decimal arithmetic

Add:

1.25 2.50 3.75

This represents the simple addition of 1.25 and 2.50 which results in 3.75.

Subtraction:

5.00 2.15 2.85

This represents a subtraction process where subtracting 2.15 from 5.00 gives the result 2.85.

Multiplication:

1.5 X 3 4.5

In this example, 1.5 multiplied by 3 gives the result 4.5.

Division:

9.0 , 3 3.0

This represents division where 9.0 divided by 3 gives 3.0.

Word problems on decimals can vary in complexity, and grade 4 students should practice regularly to improve their skills and confidence. The key to understanding these problems is to carefully extract the necessary information, determine the correct operation, and then complete the math needed to find the solution.

Additional practice problems and their solutions are given below to help reinforce the concepts:

Practice problems

Problem 1: A bottle contains 2.5 liters of juice. If Tim removes 0.75 liters of juice, how much juice will be left in the bottle?

Solution:

2.5 - 0.75 = 1.75

Answer: 1.75 litres of juice is left.

Problem 2: The length of a ribbon is 12.35 m. If 4.6 m is cut off, how much ribbon will remain?

Solution:

12.35 - 4.6 = 7.75

Answer: 7.75 meters of ribbon remains.

Problem 3: A family spends $52.40 on groceries each week. How much do they spend in three weeks?

Solution:

$52.40 times 3 = $157.20

Answer: They spend $157.20 on groceries in three weeks.

Problem 4: A piece of cloth is 9.6 m long and needs to be divided into 4 equal pieces. How long is each piece?

Solution:

9.6 div 4 = 2.4

Answer: Each piece is 2.4 meters long.

Conclusion

Decimals are an essential part of mathematics and play a vital role in daily life calculations. Word problems on decimals help in understanding how to apply the theoretical knowledge of decimals in practical scenarios. Practice is important to master decimal calculations, and the examples given in this lesson serve as a guide to solve these problems effectively.

Remember, the key steps are to read the problem carefully, identify the numbers and operations, turn the words into a mathematical equation, and then solve it. As students become more comfortable with these steps, solving word problems with decimals becomes easier and faster.

Continue exploring and practicing more and more problems, and decimals will soon become a familiar and manageable part of math for students in Grade 4 and beyond.


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Word Problems on Decimals

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