Step-by-Step Guide to Solving Decimal Multiplication Word Problems
Before learning about the multiplication of decimal numbers, sit back and think about where you saw decimals earlier. Have you seen it while buying your favourite candy? Probably! Have you seen it on the weighing scale while buying potatoes? Maybe! A decimal is a proper fraction whose denominator is a power of 10. Such fractions are represented in the form of numbers, which can be identified by a (.) full stop in between the digits. Let’s learn about decimal numbers and the process of decimal multiplication.
Decimal Numbers
As said above, decimal numbers are numbers that have numbers like 10, 100, and 1000 in the denominator. Have a look below at the image.
Decimal number representation
Let’s learn how to perform the multiplication of such decimal numbers.
Rules to Solve Problems on Multiplication of Decimal Numbers
Solving decimal addition and subtraction is easy, as you do not have to change the decimal place. However, you have to change the place of the decimal when you perform multiplication or division on decimal numbers or numbers. Let’s understand decimal multiplication word problems with a practical example.
Suppose you went to buy your favourite candy, which costs Rs. 0.50 for one piece. You want to buy four candies. So how will you calculate the amount you have to pay the shopkeeper?
Four candies
So, you can calculate the amount by multiplication. You can see that the full stop, or period symbol, between 0 and 5 makes the number decimal. So here, you have to multiply. To perform decimal multiplication, you have to follow certain rules.
Here are the rules you must follow:
First, multiply the number by ignoring the decimal place.
The next step is to place the decimal point in the product after counting the number of digits before the decimal point in the multiplicand.
Let’s solve the candy problem by using these two rules.
The price of one piece = Rs. 0.50
The price of four pieces will be the price of one piece multiplied by 4, which is =$0.50 \times 4$.
First step of decimal multiplication
The next step is to place the decimal point by counting the number of digits before the decimal point in the multiplicand. Here, the multiplicand is 0.50. Hence, we place the decimal point by putting the decimal point after 0 in the product.
Note: Always start from the right side of the digits in the product.
There are two digits in front of the decimal point in the multiplicand. Hence, the result will be Rs. 2.00 as shown below.
Decimal placement after multiplication
So, this is how you can perform multiplication on decimal numbers.
Solved Examples of Decimal Multiplication
Find the product of 12.25 and 2.
Here, the multiplicand contains two digits after the decimal point. So in the solution, the product also has the decimal place after two digits from the right.
Determine the product of 14.3 and 4.
Here, the multiplicand contains two digits after the decimal point. So in the solution, the product also has the decimal place after two digits from the right.
Find the product of 25.5 and 2.
Here, the multiplicand contains one digit after the decimal point. So, in the solution, the product also has the decimal place after one digit from the right.
Decimal Multiplication Worksheet
The questions in the decimal multiplication worksheet given below, along with the answers, will help you practice decimal multiplication much better.
- Find the product of 42.5 and 4
Ans: 170.00
- Find the product of 20.5 and 3
Ans: 61.50
- Find the product of 10.5 and 6
Ans: 63.00
- Find the product of 23.1 and 10
Ans: 231.00
Conclusion
In this article, you have learnt about decimal numbers. The uses of decimals in daily life and the rules that must be followed while performing decimal multiplication. You have learnt that when performing decimal multiplication, you must take care of the number of digits present in front of the decimal point. Apart from these, you have also learnt to solve decimal multiplication questions.
FAQs on Multiplication of Decimals: Word Problem Strategies
1. What is the basic rule for solving word problems on the multiplication of decimals?
The fundamental rule is a two-step process. First, ignore the decimal points and multiply the numbers as if they were whole numbers. Second, count the total number of digits after the decimal point in all the numbers you multiplied. Place the decimal point in your answer so that it has the same number of digits after it, counting from the right.
2. Where are some real-world examples of word problems involving multiplication of decimals?
You encounter multiplication of decimals in many daily situations. Common examples include:
- Calculating the total cost of multiple items, where each item has a price like ₹15.50.
- Finding the area of a rectangular space, like a room with a length of 4.5 metres and a width of 3.2 metres.
- Determining the total distance covered if you travel at a speed of 50.5 km per hour for 2.5 hours.
- Calculating the total weight of a basket containing several fruits, each with a specific weight in kilograms, like 0.25 kg.
3. How do you multiply a decimal number by a whole number in a word problem?
To multiply a decimal by a whole number, you follow a simple method. First, multiply the numbers without considering the decimal point. Then, in the resulting product, place the decimal point by counting the number of decimal places in the original decimal number. For example, to solve 2.5 metres × 3, you first calculate 25 × 3 = 75. Since 2.5 has one decimal place, your answer will be 7.5 metres.
4. How do you determine the correct position for the decimal point when multiplying two decimal numbers?
To find the correct position, you need to add the number of decimal places from both numbers being multiplied. For instance, if you multiply 3.25 (two decimal places) by 1.5 (one decimal place), your final answer must have a total of 2 + 1 = 3 decimal places. After calculating 325 × 15 = 4875, you place the decimal point three places from the right to get 4.875.
5. Why is it so important to solve word problems involving decimal multiplication?
Learning to solve these problems is crucial because decimals are fundamental to understanding concepts of money, measurement, and weight. Real-life scenarios rarely involve only whole numbers. Being able to calculate costs, distances, or quantities accurately using decimals is an essential practical skill that you will use throughout your life, not just in Maths exams.
6. How is multiplying decimals conceptually different from adding or subtracting them?
The main difference lies in how you handle the decimal point. For addition and subtraction, you must align the decimal points vertically before you calculate. For multiplication, you ignore the decimal points during calculation and only place it in the final product based on the total count of decimal places in the original numbers. Aligning them is not necessary for multiplication and would lead to an incorrect answer.
7. Is there a way to estimate the answer to a decimal multiplication problem before solving it?
Yes, estimating is a great strategy to check if your final answer is reasonable. Before you multiply, round the decimal numbers to their nearest whole numbers and multiply them. For example, to solve 4.8 × 2.1, you can estimate by calculating 5 × 2 = 10. Your actual answer (10.08) should be close to this estimate. This helps you catch major errors, especially in placing the decimal point.
