8/5+1/2x3/4-7/5÷3/4+10/3
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Introduction
When it comes to solving mathematical expressions, it's essential to follow the correct order of operations. This includes parentheses, exponents, multiplication and division (from left to right), and addition and subtraction (from left to right). In this article, we will break down the expression 8/5+1/2x3/4-7/5÷3/4+10/3 and solve it step by step.
Step 1: Evaluate the Multiplication and Division Operations
The expression contains multiplication and division operations. We need to follow the order of operations and evaluate these operations from left to right.
- Multiplication: 1/2 x 3/4
- Division: 7/5 ÷ 3/4
To evaluate the multiplication, we multiply the numerators and denominators separately.
1/2 x 3/4 = (1 x 3) / (2 x 4) = 3/8
To evaluate the division, we divide the numerator by the denominator.
7/5 ÷ 3/4 = (7 ÷ 3) / (5 ÷ 4) = 7/15 ÷ 5/4 = (7 ÷ 5) / (3 ÷ 4) = 7/5 ÷ 3/4 = (7 x 4) / (5 x 3) = 28/15
Step 2: Substitute the Results Back into the Expression
Now that we have evaluated the multiplication and division operations, we can substitute the results back into the expression.
8/5 + 3/8 - 28/15 + 10/3
Step 3: Find a Common Denominator
To add and subtract fractions, we need to have a common denominator. The least common multiple (LCM) of 5, 8, 15, and 3 is 120.
Step 4: Convert Each Fraction to Have a Common Denominator
We will convert each fraction to have a denominator of 120.
- 8/5: Multiply the numerator and denominator by 24.
- 3/8: Multiply the numerator and denominator by 15.
- 28/15: Multiply the numerator and denominator by 8.
- 10/3: Multiply the numerator and denominator by 40.
8/5 = (8 x 24) / (5 x 24) = 192/120 3/8 = (3 x 15) / (8 x 15) = 45/120 28/15 = (28 x 8) / (15 x 8) = 224/120 10/3 = (10 x 40) / (3 x 40) = 400/120
Step 5: Add and Subtract the Fractions
Now that we have a common denominator, we can add and subtract the fractions.
192/120 + 45/120 - 224/120 + 400/120
To add and subtract fractions, we add or subtract the numerators while keeping the denominator the same.
(192 + 45 - 224 + 400) / 120 = 113 / 120
Step 6: Simplify the Result
The fraction 113/120 cannot be simplified further.
Conclusion
In this article, we broke down the expression 8/5+1/2x3/4-7/5÷3/4+10/3 and solved it step by step. We evaluated the multiplication and division operations, substituted the results back into the expression, found a common denominator, converted each fraction to have a common denominator, added and subtracted the fractions, and simplified the result. The final answer is 113/120.
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Introduction
In our previous article, we broke down the expression 8/5+1/2x3/4-7/5÷3/4+10/3 and solved it step by step. In this article, we will provide a Q&A section to help you better understand the solution and address any questions you may have.
Q&A
Q: What is the order of operations in mathematics?
A: The order of operations in mathematics is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The order of operations is:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate multiplication and division operations from left to right.
- Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.
Q: How do I evaluate the multiplication and division operations in the expression 8/5+1/2x3/4-7/5÷3/4+10/3?
A: To evaluate the multiplication and division operations, we need to follow the order of operations. We will evaluate the multiplication operation first, which is 1/2 x 3/4. Then, we will evaluate the division operation, which is 7/5 ÷ 3/4.
Q: What is the result of the multiplication operation 1/2 x 3/4?
A: To evaluate the multiplication operation, we multiply the numerators and denominators separately.
1/2 x 3/4 = (1 x 3) / (2 x 4) = 3/8
Q: What is the result of the division operation 7/5 ÷ 3/4?
A: To evaluate the division operation, we divide the numerator by the denominator.
7/5 ÷ 3/4 = (7 ÷ 3) / (5 ÷ 4) = 7/15 ÷ 5/4 = (7 ÷ 5) / (3 ÷ 4) = 7/5 ÷ 3/4 = (7 x 4) / (5 x 3) = 28/15
Q: How do I substitute the results back into the expression 8/5+1/2x3/4-7/5÷3/4+10/3?
A: Now that we have evaluated the multiplication and division operations, we can substitute the results back into the expression.
8/5 + 3/8 - 28/15 + 10/3
Q: What is the least common multiple (LCM) of 5, 8, 15, and 3?
A: The least common multiple (LCM) of 5, 8, 15, and 3 is 120.
Q: How do I convert each fraction to have a common denominator of 120?
A: To convert each fraction to have a common denominator of 120, we will multiply the numerator and denominator of each fraction by the necessary factor.
- 8/5: Multiply the numerator and denominator by 24.
- 3/8: Multiply the numerator and denominator by 15.
- 28/15: Multiply the numerator and denominator by 8.
- 10/3: Multiply the numerator and denominator by 40.
8/5 = (8 x 24) / (5 x 24) = 192/120 3/8 = (3 x 15) / (8 x 15) = 45/120 28/15 = (28 x 8) / (15 x 8) = 224/120 10/3 = (10 x 40) / (3 x 40) = 400/120
Q: How do I add and subtract the fractions with a common denominator of 120?
A: To add and subtract the fractions, we add or subtract the numerators while keeping the denominator the same.
(192 + 45 - 224 + 400) / 120 = 113 / 120
Q: What is the final answer to the expression 8/5+1/2x3/4-7/5÷3/4+10/3?
A: The final answer to the expression 8/5+1/2x3/4-7/5÷3/4+10/3 is 113/120.
Conclusion
In this article, we provided a Q&A section to help you better understand the solution to the expression 8/5+1/2x3/4-7/5÷3/4+10/3. We covered topics such as the order of operations, evaluating multiplication and division operations, substituting results back into the expression, finding a common denominator, converting fractions to have a common denominator, adding and subtracting fractions, and simplifying the result. We hope this Q&A section has been helpful in clarifying any questions you may have had about the solution.