The Essence of Mass Subtraction | Unraveling the Discrepancy Among Mass Units

Introduction:

In subtraction of mass, we learn how to find the difference between units of mass or weight. We can subtract units of mass like ordinary numbers using two methods – with conversion into grams and without conversion. This article provides worked-out examples and practice questions to help students understand and master subtraction of mass.

Full Article: The Essence of Mass Subtraction | Unraveling the Discrepancy Among Mass Units

In Subtraction of Mass: Finding the Difference Between Units of Mass

In the process of subtraction, it is important to be able to find the difference between units of mass or weight. To do this, we must convert the units of mass, such as kilograms and grams, into grams before performing subtraction. In this article, we will explore two different methods for solving subtraction problems involving units of mass: subtracting units with conversion into grams and subtracting units without conversion.

Method 1: Subtracting Units with Conversion into Grams

To subtract units with conversion into grams, we follow these steps:

1. Convert kilograms (kg) into grams (g) by multiplying by 1000.
2. Add the converted grams to the remaining grams.
3. Perform the subtraction as you would with ordinary numbers.

For example, let’s subtract 11 kg 460 g from 25 kg 765 g:

Step 1: Convert kilograms into grams

• 11 kg 460 g = (11 × 1000) g + 460 g = 11000 g + 460 g = 11460 grams
• 25 kg 765 g = (25 × 1000) g + 765 g = 25000 g + 765 g = 25765 grams

Step 2: Subtract the converted grams

11460 g – 25765 g = 14305 g

Step 3: Convert the result back into kilograms and grams

14305 g = 14 kg 305 g

Therefore, 25 kg 765 g – 11 kg 460 g = 11 kg 305 g

Method 2: Subtracting Units Without Conversion into Grams

To subtract units without conversion into grams, we follow these steps:

1. Arrange the kilograms and grams in separate columns.
2. Subtract the grams column first. If the top number is smaller than the bottom number, borrow from the kilograms column.
3. Subtract the kilograms column.

For example, let’s subtract 24 kg 565 g from 45 kg 225 g:

Step 1: Arrange the kilograms and grams

45 kg 225 g

24 kg 565 g

Step 2: Subtract the grams

225 g – 565 g = 660 ml

Step 3: Subtract the kilograms, borrowing if necessary

45 kg – 24 kg = 20 kg

Therefore, 45 kg 225 g – 24 kg 565 g = 20 kg 660 g

Other Examples

Here are a few more examples of subtraction of mass:

Example 1: Subtract 21 kg 370 g from 37 kg 675 g without conversion

37 kg 675 g

21 kg 370 g

Result: 16 kg 305 g

Example 2: Subtract 44 kg 900 g from 105 kg 60 g

105 kg 60 g – 44 kg 900 g

Result: 60 kg 160 g

Example 3: Subtract 682 kg 541 g from 325 kg 193 g

325 kg 193 g – 682 kg 541 g

Result: 357 kg 348 g

By practicing these problems, students can become proficient in subtracting units of mass. Whether using conversion into grams or subtracting without conversion, these methods will provide a solid foundation for mastering subtraction of mass.

Questions and Answers

Here are a few practice problems to test your skills:

Question 1: Subtract the given weights:

1. 76 kg 142 g – 24 kg 031 g
2. 90 g 622 mg – 48 g 503 mg
3. 62 kg 579 g – 51 kg 560 g
4. 60 g 222 mg – 34 g 083 mg
5. 80 kg 885 g – 47 kg 000 g
6. 100 kg 529 g – 36 kg 610 g
7. 27 g 021 mg – 9 g 300 mg
8. 321 kg 450 g – 50 kg 290 g
9. 560 kg 000 g – 110 kg 850 g

Answers:

1. 52 kg 111 g
2. 42 g 119 mg
3. 11 kg 19 g
4. 26 g 139 mg
5. 33 kg 885 g
6. 63 kg 919 g
7. 17 g 721 mg
8. 271 kg 160 g
9. 449 kg 150 g

Question 2: Subtract the following:

1. 68 kg 97 g – 12 kg 67 g
2. 49 kg 70 g – 26 kg 50 g
3. 17 kg 74 g – 15 kg 30 g
4. 24 kg 60 g – 12 kg 23 g
5. 52 kg 800 g – 19 kg 485 g
6. 73 kg 423 g – 38 kg 365 g
7. 62 kg 125 g – 47 kg 496 g
8. 403 kg 320 g – 304 kg 743 g
9. 247 kg 400 g – 153 kg 575 g
10. 490 kg 200 g – 177 kg 100 g

Answers:

1. 56 kg 30 g
2. 23 kg 20 g
3. 2 kg 44 g
4. 12 kg 37 g
5. 32 kg 315 g
6. 34 kg 58 g
7. 14 kg 629 g
8. 98 kg 577 g
9. 93 kg 825 g
10. 313 kg 100 g

Summary: The Essence of Mass Subtraction | Unraveling the Discrepancy Among Mass Units

Subtraction of mass involves finding the difference between units of mass or weight. We can subtract units of mass like ordinary numbers using two different methods – with conversion into grams and without conversion into grams. Worked-out examples are provided to demonstrate the process. Students can practice both methods to improve their skills.

Frequently Asked Questions

Subtraction of Mass FAQs

1. What is subtraction of mass?

Subtraction of mass is a mathematical operation used to find the difference between two given quantities of mass.

2. How is subtraction of mass performed?

To subtract mass, you can simply subtract the values of the two masses involved. However, ensure that both masses are in the same units before subtraction.

3. What are the units used for measuring mass?

The commonly used units for measuring mass include grams (g), kilograms (kg), pounds (lb), and ounces (oz).

4. Can I subtract masses with different units?

No, it is important to convert the masses to the same units before performing subtraction. For example, if one mass is given in grams and the other in kilograms, convert one of them so that they both have the same unit.

5. Is mass subtraction commutative?

No, mass subtraction is not commutative. The order in which the masses are subtracted affects the result.

6. Can I subtract mass from other physical quantities?

No, mass can only be subtracted from mass. It is not possible to subtract mass from other physical quantities such as length or time.

7. Are there any specific rules or formulas for subtracting mass?

No, there are no specific rules or formulas for subtracting mass. It is a straightforward arithmetic operation.

8. What can be the possible outcomes when subtracting two masses?

The possible outcomes when subtracting two masses are:

• If the first mass is greater than the second mass, the result will be a positive difference.
• If the first mass is equal to the second mass, the result will be zero.
• If the first mass is smaller than the second mass, the result will be a negative difference.

9. Is there any significance to the sign of the difference obtained after mass subtraction?

Yes, the sign of the difference obtained after mass subtraction indicates the direction of the difference. A positive difference suggests an increase or gain in mass, while a negative difference suggests a decrease or loss in mass.