Problem 292 - Prealgebra

Question

In the following exercises, translate and simplify. forty-eight times seventy-one

Step-by-Step Solution

Answer

3408

Step 1 - Translate the words into a mathematical expression

First, translate 'forty-eight times seventy-one' into a mathematical expression. 'Times' is a keyword that indicates multiplication. This can be written as: \(48 \times 71\)

Step 2 - Perform the multiplication

Next, calculate the product of 48 and 71. The multiplication can be done directly or by breaking it down into smaller steps. Let's do it directly: \(48 \times 71 = 3408\)

Step 3 - Final simplification

Since the multiplication operation gives us a single number, no further simplification is needed. The final answer is 3408.

Key Concepts

math translation

Math translation is the process of converting words into mathematical expressions or symbols. In our exercise, 'forty-eight times seventy-one' needs to be put in a form that we can work with mathematically. The word 'times' tells us to use multiplication. So we translate it as follows:

'forty-eight' becomes 48
'times' becomes \(\times\)
'seventy-one' becomes 71

Hence, the phrase 'forty-eight times seventy-one' translates to \(48 \times 71\). This makes it much easier to find the solution, as now it's just a multiplication problem.

multiplication problems

Once we have our expression \(48 \times 71\), we need to perform the multiplication. Multiplication problems involve calculating the product of two or more numbers. Here, we can directly multiply 48 and 71, though sometimes breaking down into smaller parts helps manage complex calculations.

Let's do the direct multiplication:
\(48 \times 71 = 3408\).

Alternatively, you can break it down using distributive property:
First, split 71 into 70 and 1:
\(48 \times 71 = 48 \times (70 + 1)\)
Now distribute 48 over the sum:
\((48 \times 70) + (48 \times 1)\)
Calculate each part:
\(48 \times 70 = 3360\) and \(48 \times 1 = 48\)
Add the results:
\(3360 + 48 = 3408\).

So, no matter how we do it, the product remains the same.

simplification steps

Simplification steps are crucial to make complex expressions easier to understand and solve. In this exercise, since multiplication already simplifies the problem to its final answer, the steps focus on making the process clear. We began with translating words into a mathematical expression, then moved on to solving the multiplication.

Here, we went from a word problem to \(48 \times 71\), and then calculated it to find 3408.
In this case, there are no additional simplification steps needed. If the problem had included further operations like addition or subtraction, we would continue simplifying until we get the final simple form.

Remember, simplification is all about reducing a problem to its easiest-to-understand form, so whether you're doing multiplication or any other operation, always look for ways to break it down step-by-step.