Problem 32
Question
Simplify. $$ 10 \cdot 5+1 \cdot 1 $$
Step-by-Step Solution
Verified Answer
51
1Step 1: Multiply 10 and 5
Perform the multiplication of the first two numbers. Multiply 10 by 5 to get 50. \(10 \times 5 = 50\)
2Step 2: Multiply 1 and 1
Perform the multiplication of the last two numbers. Multiply 1 by 1 to get 1. \(1 \times 1 = 1\)
3Step 3: Add the Results
Add the results from Step 1 and Step 2 together. \(50 + 1 = 51\)
Key Concepts
MultiplicationAdditionOrder of Operations
Multiplication
In algebra, multiplication is combining two numbers to get a product. We use the multiplication sign (\(\times\)) or sometimes a dot (\(\cdot\)).
In the given problem, there are two multiplication steps:
* First, we multiply 10 by 5. This is pretty straightforward. We take 10, and add it to itself five times: \(10 \times 5 = 50\).
* Next, we have a smaller multiplication: 1 times 1. This means adding 1 to itself once, which returns 1: \(1 \times 1 = 1\).
Practicing these simple multiplications is important. It builds the foundation for more complex algebraic manipulations later on.
In the given problem, there are two multiplication steps:
* First, we multiply 10 by 5. This is pretty straightforward. We take 10, and add it to itself five times: \(10 \times 5 = 50\).
* Next, we have a smaller multiplication: 1 times 1. This means adding 1 to itself once, which returns 1: \(1 \times 1 = 1\).
Practicing these simple multiplications is important. It builds the foundation for more complex algebraic manipulations later on.
Addition
Addition is the process of combining two or more numbers to get a sum. It's denoted by the plus sign (\(+\)).
In our problem, once the multiplications are done, we need to add the results: the product of 10 and 5, which is 50, and the product of 1 and 1, which is 1.
Mathematically, it looks like this: \(50 + 1 = 51\).
Addition might seem simple, but it’s important to get comfortable with it. Adding numbers correctly is crucial, especially when combining results from earlier multiplicative steps.
In our problem, once the multiplications are done, we need to add the results: the product of 10 and 5, which is 50, and the product of 1 and 1, which is 1.
Mathematically, it looks like this: \(50 + 1 = 51\).
Addition might seem simple, but it’s important to get comfortable with it. Adding numbers correctly is crucial, especially when combining results from earlier multiplicative steps.
Order of Operations
The order of operations in mathematics (PEMDAS/BODMAS) tells us the correct sequence to evaluate a mathematical expression.
Here's the breakdown:
1. Multiply 10 by 5: \(10 \times 5 = 50\).
2. Multiply 1 by 1: \(1 \times 1 = 1\).
3. Lastly, add the results: \(50 + 1 = 51\).
Always follow these rules to ensure correct outcomes in algebra.
Here's the breakdown:
- P/B: Parentheses/Brackets first.
- E/O: Exponents/Orders (squares, cubes, etc.).
- MD/DM: Multiplication and Division (left to right).
- AS: Addition and Subtraction (left to right).
1. Multiply 10 by 5: \(10 \times 5 = 50\).
2. Multiply 1 by 1: \(1 \times 1 = 1\).
3. Lastly, add the results: \(50 + 1 = 51\).
Always follow these rules to ensure correct outcomes in algebra.
Other exercises in this chapter
Problem 31
Write decimal notation for each number. $$ \frac{2}{3} $$
View solution Problem 31
Find the prime factorization of each number. If the number is prime, state this. $$ 210 $$
View solution Problem 32
Find \(-(-x)\) when \(x\) is each of the following. $$ -9.1 $$
View solution Problem 32
Add. Do not use the number line except as a check. \(11+(-9)\)
View solution