Calculate The Following:1. $35 \times 3 =$2. $73 \times 27 =$3. $ 908 × 68 = 908 \times 68 = 908 × 68 = [/tex]4. $946 \times 362 =$5. $51 \div 9 =$
Mathematical Calculations: Multiplication and Division
In mathematics, calculations are an essential part of problem-solving and understanding various mathematical concepts. In this article, we will focus on calculating the given mathematical expressions involving multiplication and division.
Multiplication Calculations
Multiplication is a fundamental operation in mathematics that involves finding the product of two or more numbers. It is denoted by the symbol × or *. In the following calculations, we will use the × symbol to represent multiplication.
1. 35 × 3
To calculate 35 × 3, we need to multiply 35 by 3. This can be done by multiplying the numbers together and then adding the results of the partial products.
35 × 3 = (30 + 5) × 3 = 30 × 3 + 5 × 3 = 90 + 15 = 105
Therefore, the result of 35 × 3 is 105.
2. 73 × 27
To calculate 73 × 27, we need to multiply 73 by 27. This can be done by multiplying the numbers together and then adding the results of the partial products.
73 × 27 = (70 + 3) × 27 = 70 × 27 + 3 × 27 = 1890 + 81 = 1971
Therefore, the result of 73 × 27 is 1971.
3. 908 × 68
To calculate 908 × 68, we need to multiply 908 by 68. This can be done by multiplying the numbers together and then adding the results of the partial products.
908 × 68 = (900 + 8) × 68 = 900 × 68 + 8 × 68 = 61200 + 544 = 61744
Therefore, the result of 908 × 68 is 61744.
4. 946 × 362
To calculate 946 × 362, we need to multiply 946 by 362. This can be done by multiplying the numbers together and then adding the results of the partial products.
946 × 362 = (900 + 46) × 362 = 900 × 362 + 46 × 362 = 326200 + 16612 = 342812
Therefore, the result of 946 × 362 is 342812.
Division Calculation
Division is another fundamental operation in mathematics that involves finding the quotient of two numbers. It is denoted by the symbol ÷ or /. In the following calculation, we will use the ÷ symbol to represent division.
5. 51 ÷ 9
To calculate 51 ÷ 9, we need to divide 51 by 9. This can be done by finding the quotient of 51 and 9.
51 ÷ 9 = 5.67 (rounded to two decimal places)
Therefore, the result of 51 ÷ 9 is 5.67.
Conclusion
In this article, we have calculated the given mathematical expressions involving multiplication and division. We have used the × symbol to represent multiplication and the ÷ symbol to represent division. The results of the calculations are as follows:
- 35 × 3 = 105
- 73 × 27 = 1971
- 908 × 68 = 61744
- 946 × 362 = 342812
- 51 ÷ 9 = 5.67
These calculations demonstrate the importance of understanding mathematical operations and how to apply them to solve problems.
Mathematical Calculations: Multiplication and Division - Q&A
In our previous article, we calculated various mathematical expressions involving multiplication and division. In this article, we will address some frequently asked questions related to these calculations.
Q: What is the difference between multiplication and division?
A: Multiplication and division are two fundamental operations in mathematics that involve finding the product and quotient of two numbers, respectively. Multiplication is denoted by the symbol × or * and involves finding the product of two or more numbers, while division is denoted by the symbol ÷ or / and involves finding the quotient of two numbers.
Q: How do I calculate a multiplication problem?
A: To calculate a multiplication problem, you need to multiply the numbers together and then add the results of the partial products. For example, to calculate 35 × 3, you would multiply 35 by 3 and then add the results of the partial products: (30 + 5) × 3 = 30 × 3 + 5 × 3 = 90 + 15 = 105.
Q: How do I calculate a division problem?
A: To calculate a division problem, you need to find the quotient of the two numbers. For example, to calculate 51 ÷ 9, you would divide 51 by 9 and find the quotient: 51 ÷ 9 = 5.67 (rounded to two decimal places).
Q: What is the order of operations in mathematics?
A: The order of operations in mathematics is a set of rules that dictate the order in which mathematical operations should be performed. The order of operations is as follows:
- Parentheses: Evaluate expressions inside parentheses first.
- Exponents: Evaluate any exponential expressions next.
- Multiplication and Division: Evaluate any 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 handle decimal numbers in multiplication and division problems?
A: When working with decimal numbers in multiplication and division problems, you need to follow the same rules as with whole numbers. For example, to calculate 3.5 × 2.7, you would multiply the numbers together and then add the results of the partial products: (3 + 0.5) × (2 + 0.7) = 3 × 2 + 0.5 × 2 + 3 × 0.7 + 0.5 × 0.7 = 6 + 1 + 2.1 + 0.35 = 9.45.
Q: How do I handle negative numbers in multiplication and division problems?
A: When working with negative numbers in multiplication and division problems, you need to follow the same rules as with positive numbers. For example, to calculate -3 × -2, you would multiply the numbers together and then add the results of the partial products: (-3 + 3) × (-2 + 2) = 0 × 0 = 0.
Q: What are some common mistakes to avoid when working with multiplication and division problems?
A: Some common mistakes to avoid when working with multiplication and division problems include:
- Forgetting to multiply or divide numbers correctly
- Not following the order of operations
- Not handling decimal numbers or negative numbers correctly
- Not checking your work for errors
Conclusion
In this article, we have addressed some frequently asked questions related to multiplication and division problems. We have covered topics such as the difference between multiplication and division, how to calculate multiplication and division problems, and how to handle decimal numbers and negative numbers. By following the rules and guidelines outlined in this article, you can avoid common mistakes and become more confident in your ability to solve multiplication and division problems.