Easy method for solving decimal by whole number word problems Grade 5

📚 Understanding Decimal by Whole Number Word Problems

Decimal by whole number word problems involve multiplying a number that has a decimal point (like 2.5) by a whole number (like 3). These problems often show up in everyday situations, like calculating the total cost of multiple items or figuring out how much of an ingredient you need when scaling up a recipe.

📜 A Brief History of Decimals

Decimals weren't always around! The concept of decimal fractions was developed over centuries. Early forms can be traced back to ancient China, but the modern decimal notation we use today was popularized in Europe during the 16th and 17th centuries, largely due to the work of mathematicians like Simon Stevin. Using decimals made calculations easier and more accurate, which was crucial for advancements in science, engineering, and commerce.

🔑 Key Principles for Solving Decimal Word Problems

• 🔢 Identify the Operation: Read the problem carefully to determine if you need to multiply. Look for keywords like "each," "per," "times," or "total."
• 📝 Set Up the Problem: Write the decimal number and the whole number, aligning them as if you were multiplying whole numbers.
• ➗ Ignore the Decimal (Temporarily): Multiply the numbers as if the decimal point wasn't there.
• 📍 Place the Decimal: Count the number of decimal places in the original decimal number. In the answer, count that many places from right to left and place the decimal point.
• ✅ Check Your Answer: Does the answer make sense in the context of the problem? Estimate to see if your answer is reasonable.

🗓️ Real-World Examples

Let's look at some common examples:

1. Example 1: Sarah buys 4 notebooks. Each notebook costs $2.25. How much does she spend in total?

Solution: $2.25 \times 4 = $9.00. Sarah spends $9.00.

2. Example 2: A recipe calls for 0.5 cups of sugar per cake. If you want to bake 3 cakes, how much sugar do you need?

Solution: $0.5 \times 3 = 1.5$. You need 1.5 cups of sugar.

3. Example 3: John runs 1.7 miles each day. How many miles does he run in 5 days?

Solution: $1.7 \times 5 = 8.5$. John runs 8.5 miles.

✍🏽 Step-by-Step Method

Here's a detailed method you can follow:

1. Step 1: Read and Understand: Read the word problem carefully. What is the problem asking you to find? What information are you given?
2. Step 2: Identify the Operation: Determine whether multiplication is required based on the context of the problem.
3. Step 3: Set Up the Equation: Write down the equation. For example, if you are multiplying 2.5 by 3, write it as $2.5 \times 3$.
4. Step 4: Multiply: Multiply the numbers without considering the decimal point. In our example, $25 \times 3 = 75$.
5. Step 5: Place the Decimal: Count the number of decimal places in the original decimal number (in our example, 2.5 has one decimal place). Place the decimal point in your answer so that it has the same number of decimal places. So, 75 becomes 7.5.
6. Step 6: Write the Answer: Write the answer with the correct units. For example, "The total cost is $7.50."

💡 Tips and Tricks

• ✅ Estimation: Before you start multiplying, estimate what the answer should be. This can help you check if your final answer is reasonable. For example, if you are multiplying 2.8 by 4, you know that 2.8 is close to 3, so the answer should be close to $3 \times 4 = 12$.
• 🧐 Decimal Placement: Pay close attention to where you put the decimal point. This is the most common mistake when multiplying decimals.
• ✍🏾 Practice: The more you practice, the better you'll become at solving these problems.

🎯 Practice Quiz

1. A candy bar costs $1.35. How much will 6 candy bars cost?
2. A bottle of juice contains 1.2 liters. How many liters are in 3 bottles?
3. A piece of ribbon is 2.4 inches long. How long will 8 pieces be?
4. A pen costs $0.75. How much will 5 pens cost?
5. A bag of chips weighs 0.6 pounds. How much will 7 bags weigh?
6. A small toy car costs $3.50. How much will 2 toy cars cost?
7. A water bottle holds 0.8 liters of water. How much water can 4 bottles hold?

🏆 Solutions to Practice Quiz

1. $1.35 \times 6 = $8.10
2. $1.2 \times 3 = 3.6$ liters
3. $2.4 \times 8 = 19.2$ inches
4. $0.75 \times 5 = $3.75
5. $0.6 \times 7 = 4.2$ pounds
6. $3.50 \times 2 = $7.00
7. $0.8 \times 4 = 3.2$ liters

📝 Conclusion

Solving decimal by whole number word problems becomes easy with the right approach. Remember to read carefully, set up the problem correctly, and double-check your decimal placement. Practice makes perfect! Keep practicing and you'll become a pro in no time!