Add And Subtract Rationals - Instruction - Level GFind $3 - 5 \frac{1}{3}$.Model The Expression On The Number Line.What Is The Difference?$3 - 5 \frac{1}{3} =

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Understanding Rational Numbers

Rational numbers are a type of real number that can be expressed as the quotient or fraction of two integers, where the denominator is non-zero. In other words, rational numbers are numbers that can be written in the form of a/b, where a and b are integers and b is not equal to zero. Rational numbers include all integers, fractions, and decimals that can be expressed as a finite decimal or fraction.

Modeling Rational Numbers on the Number Line

The number line is a visual representation of the real number system, where each point on the line corresponds to a real number. Rational numbers can be modeled on the number line by plotting the corresponding point for each rational number. For example, the rational number 3 can be plotted on the number line at the point 3 units to the right of zero.

Modeling the Expression on the Number Line

To model the expression 3 - 5 1/3 on the number line, we need to first convert the mixed number 5 1/3 to an improper fraction. The mixed number 5 1/3 can be converted to an improper fraction by multiplying the whole number part (5) by the denominator (3) and then adding the numerator (1). This gives us 16/3.

Now, we can model the expression 3 - 16/3 on the number line. To do this, we need to find a common denominator for the two rational numbers. In this case, the common denominator is 3. We can then rewrite the rational number 3 as 9/3.

Now, we can subtract the two rational numbers: 9/3 - 16/3. To do this, we need to subtract the numerators while keeping the denominator the same. This gives us (9-16)/3 = -7/3.

The Difference

The difference between 3 and 5 1/3 is -7/3. This means that 3 is 7/3 units less than 5 1/3.

Step-by-Step Solution

  1. Convert the mixed number 5 1/3 to an improper fraction: 16/3.
  2. Model the expression 3 - 16/3 on the number line.
  3. Find a common denominator for the two rational numbers: 3.
  4. Rewrite the rational number 3 as 9/3.
  5. Subtract the two rational numbers: 9/3 - 16/3.
  6. Simplify the result: (9-16)/3 = -7/3.

Conclusion

In this article, we have learned how to add and subtract rational numbers. We have also learned how to model rational numbers on the number line and how to find the difference between two rational numbers. By following the step-by-step solution, we can easily find the difference between two rational numbers.

Common Mistakes to Avoid

  • Not converting the mixed number to an improper fraction before subtracting.
  • Not finding a common denominator before subtracting.
  • Not simplifying the result after subtracting.

Practice Problems

  1. Find the difference between 2 and 3 1/4.
  2. Find the difference between 4 and 2 3/4.
  3. Find the difference between 1 and 2 1/2.

Answer Key

  1. -11/4
  2. 1 1/4
  3. 1/2
    Add and Subtract Rationals - Q&A =====================================

Frequently Asked Questions

Q: What is the difference between adding and subtracting rational numbers?

A: Adding and subtracting rational numbers involves combining or comparing two or more rational numbers. When adding rational numbers, we combine the numerators while keeping the denominator the same. When subtracting rational numbers, we subtract the numerators while keeping the denominator the same.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and then add the numerator. For example, to convert 5 1/3 to an improper fraction, multiply 5 by 3 and add 1, which gives us 16/3.

Q: What is the common denominator?

A: The common denominator is the smallest number that both denominators can divide into evenly. For example, if we have two rational numbers with denominators 3 and 6, the common denominator is 6.

Q: How do I find the common denominator?

A: To find the common denominator, we need to find the least common multiple (LCM) of the two denominators. The LCM is the smallest number that both denominators can divide into evenly.

Q: What is the least common multiple (LCM)?

A: The least common multiple (LCM) is the smallest number that both numbers can divide into evenly. For example, the LCM of 3 and 6 is 6.

Q: How do I simplify a rational number?

A: To simplify a rational number, we need to find the greatest common divisor (GCD) of the numerator and denominator and divide both numbers by the GCD.

Q: What is the greatest common divisor (GCD)?

A: The greatest common divisor (GCD) is the largest number that both numbers can divide into evenly. For example, the GCD of 12 and 18 is 6.

Q: How do I add rational numbers with different denominators?

A: To add rational numbers with different denominators, we need to find the common denominator and then add the numerators while keeping the denominator the same.

Q: How do I subtract rational numbers with different denominators?

A: To subtract rational numbers with different denominators, we need to find the common denominator and then subtract the numerators while keeping the denominator the same.

Q: What is the difference between a rational number and an irrational number?

A: A rational number is a number that can be expressed as a fraction or ratio of two integers, while an irrational number is a number that cannot be expressed as a fraction or ratio of two integers.

Q: Can you give me some examples of rational numbers?

A: Yes, here are some examples of rational numbers: 3/4, 2/3, 1/2, 3/5, etc.

Q: Can you give me some examples of irrational numbers?

A: Yes, here are some examples of irrational numbers: √2, π, e, etc.

Conclusion

In this article, we have answered some frequently asked questions about adding and subtracting rational numbers. We have also covered some important concepts such as converting mixed numbers to improper fractions, finding the common denominator, simplifying rational numbers, and adding and subtracting rational numbers with different denominators.

Practice Problems

  1. Find the difference between 2 and 3 1/4.
  2. Find the difference between 4 and 2 3/4.
  3. Find the difference between 1 and 2 1/2.

Answer Key

  1. -11/4
  2. 1 1/4
  3. 1/2