Add Or Subtract The Fractions.$ \begin{array}{rr} \frac{3}{7} & \frac{9}{10} \ +\frac{1}{3} & -\frac{2}{3} \ \hline \end{array} }$Solve The Following 1. { (2+3) \times (6-2) =$ $2. ${ 4.5 \times 10^2 =\$}
Introduction
Fractions are an essential part of mathematics, and understanding how to add and subtract them is crucial for solving various mathematical problems. In this article, we will delve into the world of fractions and explore the steps involved in adding and subtracting them. We will also discuss some real-world applications of fractions and provide examples to help you understand the concepts better.
What are Fractions?
A fraction is a way of expressing a part of a whole as a ratio of two numbers. It consists of a numerator (the top number) and a denominator (the bottom number). The numerator represents the number of equal parts we have, while the denominator represents the total number of parts the whole is divided into.
Adding Fractions
Adding fractions involves combining two or more fractions with the same denominator. To add fractions, we simply add the numerators and keep the denominator the same.
Example 1:
{ \begin{array}{rr} \frac{3}{7} & \frac{9}{10} \\ +\frac{1}{3} & -\frac{2}{3} \\ \hline \end{array} \}
To add the fractions in the above example, we need to find a common denominator. The least common multiple (LCM) of 7, 10, and 3 is 210. We can rewrite each fraction with the denominator 210.
{ \frac{3}{7} = \frac{3 \times 30}{7 \times 30} = \frac{90}{210} \}
{ \frac{9}{10} = \frac{9 \times 21}{10 \times 21} = \frac{189}{210} \}
{ \frac{1}{3} = \frac{1 \times 70}{3 \times 70} = \frac{70}{210} \}
{ -\frac{2}{3} = -\frac{2 \times 70}{3 \times 70} = -\frac{140}{210} \}
Now that we have the fractions with the same denominator, we can add them.
{ \frac{90}{210} + \frac{189}{210} + \frac{70}{210} - \frac{140}{210} = \frac{109}{210} \}
Example 2:
{ (2+3) \times (6-2) = \}
To solve this problem, we need to follow the order of operations (PEMDAS).
- Evaluate the expressions inside the parentheses: and .
- Multiply the results: .
Therefore, the solution to the problem is .
Example 3:
{ 4.5 \times 10^2 = \}
To solve this problem, we need to multiply by .
{ 4.5 \times 10^2 = 4500 \}
Subtracting Fractions
Subtracting fractions involves finding the difference between two fractions with the same denominator. To subtract fractions, we simply subtract the numerators and keep the denominator the same.
Example 1:
{ \frac{3}{7} - \frac{2}{7} = \}
To subtract the fractions in the above example, we can simply subtract the numerators and keep the denominator the same.
{ \frac{3}{7} - \frac{2}{7} = \frac{3-2}{7} = \frac{1}{7} \}
Example 2:
{ \frac{9}{10} - \frac{4}{10} = \}
To subtract the fractions in the above example, we can simply subtract the numerators and keep the denominator the same.
{ \frac{9}{10} - \frac{4}{10} = \frac{9-4}{10} = \frac{5}{10} = \frac{1}{2} \}
Real-World Applications of Fractions
Fractions have numerous real-world applications. Here are a few examples:
- Cooking: Fractions are used in cooking to measure ingredients. For example, a recipe might call for 1/4 cup of sugar or 3/4 cup of flour.
- Building: Fractions are used in building to measure materials. For example, a carpenter might need to cut a piece of wood into 1/2 inch thick pieces.
- Science: Fractions are used in science to measure quantities. For example, a scientist might need to measure the concentration of a solution in 1/10th of a gram per liter.
Conclusion
In conclusion, adding and subtracting fractions is a crucial part of mathematics. By understanding how to add and subtract fractions, we can solve a wide range of mathematical problems. We hope this article has provided you with a comprehensive guide to adding and subtracting fractions and has helped you to understand the concepts better.
Final Tips
- Practice, practice, practice: The more you practice adding and subtracting fractions, the more comfortable you will become with the concepts.
- Use visual aids: Visual aids such as diagrams and charts can help you to understand the concepts better.
- Break down complex problems: Break down complex problems into smaller, more manageable parts to make them easier to solve.
Q: What is the difference between adding and subtracting fractions?
A: Adding fractions involves combining two or more fractions with the same denominator, while subtracting fractions involves finding the difference between two fractions with the same denominator.
Q: How do I add fractions with different denominators?
A: To add fractions with different denominators, you need to find a common denominator. The least common multiple (LCM) of the denominators is the smallest number that both denominators can divide into evenly. Once you have the common denominator, you can rewrite each fraction with the common denominator and then add them.
Q: How do I subtract fractions with different denominators?
A: To subtract fractions with different denominators, you need to find a common denominator. The least common multiple (LCM) of the denominators is the smallest number that both denominators can divide into evenly. Once you have the common denominator, you can rewrite each fraction with the common denominator and then subtract them.
Q: What is the least common multiple (LCM)?
A: The least common multiple (LCM) is the smallest number that two or more numbers can divide into evenly. For example, the LCM of 4 and 6 is 12, because 12 is the smallest number that both 4 and 6 can divide into evenly.
Q: How do I find the LCM of two numbers?
A: To find the LCM of two numbers, you can list the multiples of each number and find the smallest number that appears in both lists. Alternatively, you can use the following formula:
LCM(a, b) = (a × b) / GCD(a, b)
where GCD(a, b) is the greatest common divisor of a and b.
Q: What is the greatest common divisor (GCD)?
A: The greatest common divisor (GCD) is the largest number that two or more numbers can divide into evenly. For example, the GCD of 12 and 18 is 6, because 6 is the largest number that both 12 and 18 can divide into evenly.
Q: How do I find the GCD of two numbers?
A: To find the GCD of two numbers, you can list the factors of each number and find the largest number that appears in both lists. Alternatively, you can use the following formula:
GCD(a, b) = (a × b) / LCM(a, b)
Q: Can I add or subtract fractions with unlike denominators?
A: Yes, you can add or subtract fractions with unlike denominators by finding a common denominator and then adding or subtracting the fractions.
Q: What is the difference between adding and subtracting mixed numbers?
A: Adding mixed numbers involves combining the whole numbers and fractions separately, while subtracting mixed numbers involves finding the difference between the whole numbers and fractions separately.
Q: How do I add mixed numbers?
A: To add mixed numbers, you need to add the whole numbers and fractions separately. For example:
2 1/2 + 3 1/4 = (2 + 3) + (1/2 + 1/4)
Q: How do I subtract mixed numbers?
A: To subtract mixed numbers, you need to subtract the whole numbers and fractions separately. For example:
3 1/2 - 2 1/4 = (3 - 2) + (1/2 - 1/4)
Q: Can I add or subtract fractions with decimals?
A: Yes, you can add or subtract fractions with decimals by converting the decimals to fractions and then adding or subtracting the fractions.
Q: How do I convert decimals to fractions?
A: To convert decimals to fractions, you can use the following formula:
a/b = c/d
where a/b is the decimal and c/d is the fraction.
For example:
0.5 = 1/2
Q: Can I add or subtract fractions with negative numbers?
A: Yes, you can add or subtract fractions with negative numbers by following the same rules as adding and subtracting positive fractions.
Q: How do I add or subtract fractions with negative numbers?
A: To add or subtract fractions with negative numbers, you need to follow the same rules as adding and subtracting positive fractions. For example:
-1/2 + 1/2 = 0
-1/2 - 1/2 = -1
Q: Can I add or subtract fractions with variables?
A: Yes, you can add or subtract fractions with variables by following the same rules as adding and subtracting fractions with constants.
Q: How do I add or subtract fractions with variables?
A: To add or subtract fractions with variables, you need to follow the same rules as adding and subtracting fractions with constants. For example:
x/2 + 1/2 = (x + 1)/2
x/2 - 1/2 = (x - 1)/2
We hope this article has been helpful in answering your questions about adding and subtracting fractions. If you have any further questions or need further clarification, please don't hesitate to ask.