Subtract. Write Your Answer As A Fraction Or As A Whole Or Mixed Number.

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Introduction to Subtraction

Subtraction is a fundamental operation in mathematics that involves finding the difference between two numbers. It is a crucial concept in arithmetic and is used extensively in various mathematical operations, including addition, multiplication, and division. In this article, we will delve into the concept of subtraction, explore its various forms, and provide step-by-step solutions to subtraction problems.

Understanding the Order of Operations

Before we dive into the world of subtraction, it is essential to understand the order of operations. The order of operations is a set of rules that dictates the order in which mathematical operations should be performed when there are multiple operations in an expression. The order of operations is often remembered using the acronym PEMDAS, which stands for:

  1. Parentheses: Evaluate expressions inside parentheses first.
  2. Exponents: Evaluate any exponential expressions next.
  3. Multiplication and Division: Evaluate multiplication and division operations from left to right.
  4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Subtracting Whole Numbers

Subtracting whole numbers involves finding the difference between two whole numbers. The process of subtraction is similar to addition, but with a twist. When subtracting whole numbers, we need to borrow or regroup numbers to make the subtraction process easier.

Example 1: Subtracting Whole Numbers

To solve this problem, we need to subtract 8 from 11. However, since 8 is greater than 11, we need to borrow from the next place value. We can borrow 10 from the tens place, making the subtraction process easier.

11 (borrow 10) = 1 11 (borrow 10) = 1 5 (borrow 10) = 15

Now, we can subtract 8 from 11:

11 - 8 = 3 15 - 1 = 14

Therefore, the result of the subtraction problem is:

3 14

Example 2: Subtracting Whole Numbers with Regrouping

To solve this problem, we need to subtract 9 from 5. However, since 9 is greater than 5, we need to borrow from the next place value. We can borrow 10 from the tens place, making the subtraction process easier.

5 (borrow 10) = 15 2 (borrow 10) = 12 7 (borrow 10) = 17

Now, we can subtract 9 from 5:

5 - 9 = -4 17 - 3 = 14

Therefore, the result of the subtraction problem is:

-4 14

Subtracting Decimals

Subtracting decimals involves finding the difference between two decimal numbers. The process of subtraction is similar to whole numbers, but with a twist. When subtracting decimals, we need to line up the decimal points and subtract the numbers accordingly.

Example 1: Subtracting Decimals

To solve this problem, we need to subtract 2.1 from 5.2. We can line up the decimal points and subtract the numbers accordingly.

Subtracting the numbers, we get:

5.2 - 2.1 = 3.1 3.5 - 1.8 = 1.7

Therefore, the result of the subtraction problem is:

3.1 1.7

Example 2: Subtracting Decimals with Regrouping

To solve this problem, we need to subtract 3.2 from 2.5. However, since 3.2 is greater than 2.5, we need to borrow from the next place value. We can borrow 10 from the tens place, making the subtraction process easier.

2.5 (borrow 10) = 25 1.9 (borrow 10) = 19 4.1 (borrow 10) = 41

Now, we can subtract 3.2 from 2.5:

2.5 - 3.2 = -0.7 41 - 19 = 22

Therefore, the result of the subtraction problem is:

-0.7 22

Subtracting Fractions

Subtracting fractions involves finding the difference between two fractional numbers. The process of subtraction is similar to whole numbers, but with a twist. When subtracting fractions, we need to find a common denominator and subtract the fractions accordingly.

Example 1: Subtracting Fractions

To solve this problem, we need to subtract 3/4 from 1/2. We can find a common denominator, which is 4. We can rewrite the fractions as:

1/2 = 2/4 1/4 = 1/4 3/4 = 3/4

Now, we can subtract the fractions:

2/4 - 3/4 = -1/4 1/4 - 1/4 = 0

Therefore, the result of the subtraction problem is:

-1/4 0

Example 2: Subtracting Fractions with Regrouping

To solve this problem, we need to subtract 5/6 from 3/4. However, since 5/6 is greater than 3/4, we need to borrow from the next place value. We can borrow 10 from the tens place, making the subtraction process easier.

3/4 (borrow 10) = 30/40 2/3 (borrow 10) = 20/30 1/2 (borrow 10) = 10/20

Now, we can subtract 5/6 from 3/4:

30/40 - 25/40 = 5/40 20/30 - 15/30 = 5/30 10/20 - 5/20 = 5/20

Therefore, the result of the subtraction problem is:

5/40 5/30 5/20

Conclusion

Subtraction is a fundamental operation in mathematics that involves finding the difference between two numbers. It is a crucial concept in arithmetic and is used extensively in various mathematical operations, including addition, multiplication, and division. In this article, we have explored the concept of subtraction, including subtracting whole numbers, decimals, and fractions. We have also provided step-by-step solutions to subtraction problems, including examples with regrouping. By understanding the concept of subtraction and practicing the various forms of subtraction, you can become proficient in solving subtraction problems and excel in mathematics.

Introduction

In our previous article, we explored the concept of subtraction, including subtracting whole numbers, decimals, and fractions. We also provided step-by-step solutions to subtraction problems, including examples with regrouping. In this article, we will answer some of the most frequently asked questions about subtraction.

Q&A

Q: What is the difference between subtraction and addition?

A: Subtraction and addition are two fundamental operations in mathematics that involve finding the difference or sum of two numbers. While addition involves finding the sum of two numbers, subtraction involves finding the difference between two numbers.

Q: How do I subtract a negative number from a positive number?

A: When subtracting a negative number from a positive number, you can simply add the positive number to the absolute value of the negative number. For example, 5 - (-3) = 5 + 3 = 8.

Q: How do I subtract a fraction from a whole number?

A: When subtracting a fraction from a whole number, you need to find a common denominator and subtract the fraction accordingly. For example, 2 - 1/4 = 2 - 1/4 = 7/4.

Q: How do I subtract a decimal from a whole number?

A: When subtracting a decimal from a whole number, you need to line up the decimal points and subtract the numbers accordingly. For example, 5.2 - 1.8 = 3.4.

Q: What is the difference between subtracting and regrouping?

A: Subtracting and regrouping are two related concepts in mathematics. Subtracting involves finding the difference between two numbers, while regrouping involves borrowing or carrying numbers to make the subtraction process easier.

Q: How do I regroup numbers when subtracting?

A: When regrouping numbers when subtracting, you need to borrow or carry numbers from the next place value to make the subtraction process easier. For example, 5 - 8 = 5 (borrow 10) = 15, 15 - 8 = 7.

Q: What is the difference between subtracting fractions and subtracting decimals?

A: Subtracting fractions and subtracting decimals are two related concepts in mathematics. Subtracting fractions involves finding the difference between two fractional numbers, while subtracting decimals involves finding the difference between two decimal numbers.

Q: How do I subtract fractions with different denominators?

A: When subtracting fractions with different denominators, you need to find a common denominator and subtract the fractions accordingly. For example, 1/2 - 1/3 = 3/6 - 2/6 = 1/6.

Q: How do I subtract decimals with different decimal places?

A: When subtracting decimals with different decimal places, you need to line up the decimal points and subtract the numbers accordingly. For example, 5.2 - 1.8 = 3.4.

Q: What is the difference between subtracting and dividing?

A: Subtracting and dividing are two related concepts in mathematics. Subtracting involves finding the difference between two numbers, while dividing involves finding the quotient of two numbers.

Q: How do I subtract a number from a quotient?

A: When subtracting a number from a quotient, you need to divide the number by the quotient and subtract the result. For example, 12 ÷ 4 = 3, 3 - 2 = 1.

Conclusion

In this article, we have answered some of the most frequently asked questions about subtraction. We have explored the concept of subtraction, including subtracting whole numbers, decimals, and fractions, and provided step-by-step solutions to subtraction problems, including examples with regrouping. By understanding the concept of subtraction and practicing the various forms of subtraction, you can become proficient in solving subtraction problems and excel in mathematics.

Additional Resources

Final Thoughts

Subtraction is a fundamental operation in mathematics that involves finding the difference between two numbers. It is a crucial concept in arithmetic and is used extensively in various mathematical operations, including addition, multiplication, and division. By understanding the concept of subtraction and practicing the various forms of subtraction, you can become proficient in solving subtraction problems and excel in mathematics.