Multiplying Decimals Made Easy!

Summary

This instructional video script teaches viewers how to multiply numbers with decimals. It begins with a simple example, explaining the process of multiplying 4.6 by 7, emphasizing the importance of carrying over numbers and placing the correct number of digits to the right of the decimal point in the final answer. The script progresses to more complex examples, such as multiplying 3.9 by 5.6 and 12.9 by 3.7, detailing each step of the multiplication process. It concludes with multiplying 14.56 by 8 and 13.79 by 5.46, highlighting the need to add zeros when moving to a new line and ensuring the total number of decimal places in the answer matches the sum of decimal places in the original numbers.

Takeaways

• 🔢 Multiplying decimals involves treating them like whole numbers until the end of the calculation.
• 📐 When multiplying, remember to carry over numbers as you would in whole number multiplication.
• 📝 After multiplying, align the decimal point in the product with the sum of the decimal places in the factors.
• 📈 For example, in 4.6 * 7, the product should have one digit after the decimal (since 4.6 has one).
• 📉 When multiplying larger numbers with decimals, like 3.9 * 5.6, you must account for all decimal places in the factors.
• 🔄 Carrying over is crucial; for instance, in 3.9 * 5.6, carrying over affects the next digit's calculation.
• 📑 When multiplying by a whole number followed by a decimal, like 12 * 3.7, treat the whole number as part of the decimal.
• 🔄 Always remember to add zeros when moving to a new line in the multiplication process.
• 📉 In problems with percentages, like 14.56% * 8, convert the percentage to a decimal before multiplying.
• 🔎 The final position of the decimal point in the product is determined by the total number of decimal places in the factors.
• 📐 For complex multiplications, like 13.79 * 5.46, ensure each step is clear and carry overs are accurately accounted for.

Q & A

What is the product of 4.6 and 7 according to the video?

The product of 4.6 and 7 is 32.2. The calculation involves multiplying 6 by 7 to get 42, then carrying over the 4, and multiplying 4 by 7 to get 28, adding the carried over 4 to get 32, and finally placing the decimal point one place to the right as there is one number to the right of the decimal in the original numbers.

How do you multiply 3.9 by 5.6 as demonstrated in the video?

To multiply 3.9 by 5.6, you first multiply the digits without considering the decimal points (9*6=54, write down 4 and carry over 5; 3*6=18, add 5 to get 23; 5*9=45, write down 5 and carry over 4; 5*3=15, add 4 to get 19). Then, align the decimal points according to the total number of decimal places in the original numbers (two in 3.9 and one in 5.6, so three in total), resulting in 21.84.

What is the final step when multiplying decimals as shown in the video?

The final step when multiplying decimals is to ensure that the number of digits to the right of the decimal point in your answer matches the total number of digits to the right of the decimal points in the original numbers.

Can you explain the process of multiplying 12.9 by 3.7 as described in the video?

To multiply 12.9 by 3.7, you multiply each digit of 12.9 by each digit of 3.7, carrying over as necessary (9*7=63, write down 3 and carry over 6; 2*7=14, add 6 to get 20, write down 0 and carry over 2; 1*7=7, add 2 to get 9; 3*9=27, carry over 2; 2*3=6, add 2 to get 8; 1*3=3). Then, add all the results together and place the decimal point two places to the right since there are two numbers to the right of the decimal point in total in the original numbers.

What is the significance of adding zeros when carrying over in decimal multiplication as explained in the video?

Adding zeros when carrying over in decimal multiplication is important for aligning the decimal places correctly. For each new line of multiplication, you add a zero to the end of the partial product to ensure the decimal point is placed accurately in the final result.

How does the video script guide you to multiply 14.56 by 8?

To multiply 14.56 by 8, you multiply each digit of 14.56 by 8 (8*6=48, carry over 4; 8*5=40, add 4 to get 44; 8*4=32, add 4 to get 36; 8*1=8, add 3 to get 11). Then, add all the partial products together, and place the decimal point three places to the right as the original numbers have a total of three digits to the right of the decimal point.

What is the product of 13.79 and 5.46 as shown in the video?

The product of 13.79 and 5.46 is 75.2934. This is calculated by multiplying each digit of 13.79 by each digit of 5.46, carrying over as necessary, and ensuring the final answer has four digits to the right of the decimal point, as both original numbers have two digits to the right of the decimal point.

How does the video emphasize the importance of decimal placement in multiplication?

The video emphasizes the importance of decimal placement by showing that the number of digits to the right of the decimal point in the final answer must match the total number of digits to the right of the decimal points in the original numbers being multiplied.

What is the rule for placing the decimal point in the final answer when multiplying decimals as per the video?

The rule for placing the decimal point in the final answer when multiplying decimals is to count the total number of digits to the right of the decimal points in both original numbers and place the decimal point in the answer with that many digits to the right.

Can you describe the step-by-step process of multiplying decimals as outlined in the video?

The step-by-step process of multiplying decimals involves: 1) Ignoring the decimal points and multiplying the numbers as whole numbers. 2) Carrying over as necessary during multiplication. 3) Adding zeros for each new line of multiplication. 4) Adding all partial products together. 5) Placing the decimal point in the final answer according to the total number of decimal places in the original numbers.