Problem 257 - Prealgebra

Question

In the following exercises, multiply. $$(79)(5)$$

Step-by-Step Solution

Answer

395

Step 1: Set Up the Multiplication

Write the numbers you want to multiply. Here, the numbers are 79 and 5.

Step 2: Multiply the Units Digit

Multiply the units digit of 79 (which is 9) by 5. \[9 \times 5 = 45\]Keep the 5 in the units place and carry over the 4.

Step 3: Multiply the Tens Digit

Multiply the tens digit of 79 (which is 7) by 5. \[7 \times 5 = 35\]Add the carry over 4 from the previous step. \[35 + 4 = 39\]

Step 4: Combine the Results

Place the result from the multiplication of tens digit (39) next to the result of the units digit (5). The result is 395.

Key Concepts

multiplication process

Multiplication is one of the basic arithmetic operations that everyone needs to master. It involves combining groups of numbers to find a total amount. For instance, multiplying 79 and 5 means you are adding 79 to itself 5 times. This can be broken down into an easier step-by-step process.
By understanding each step, you can multiply any two numbers more easily and accurately. Ensure all numbers are properly aligned before you start to avoid mistakes.

carrying over in multiplication

One important concept in multiplication is 'carrying over'. When the product of two digits is greater than 9, we write down the units digit and carry over the tens digit to the next column.
This carry over must be added in the next multiplication step. For example, when we multiply 9 by 5, we get 45. Here, we write down 5 and carry over 4. In the next step, this 4 will be added to the product of the tens digit and the multiplier.

step-by-step multiplication

Breaking down each step of multiplication into smaller parts helps in better understanding.
Here’s how you multiply 79 by 5 step-by-step:

Step 1: Write the numbers 79 and 5, one below the other.

Step 2: Multiply the units digit of 79 (which is 9) by 5. \[9 \times 5 = 45\]
Write 5 in the units place and carry over the 4.

Step 3: Multiply the tens digit of 79 (which is 7) by 5. \[7 \times 5= 35\]
Then add the carry over 4 from the previous step, resulting in \[35 + 4 = 39\].

Step 4: Combine the results. Place the result from the multiplication of the tens digit (39) next to the result of the units digit (5).
The final answer is 395.
This method ensures you do not miss any part, and your multiplications are always accurate.