Problem 32 - Elementary Algebra

Question

Evaluate \(12 \mathrm{~kg}+54 \mathrm{~g}\). Write the answer in grams.

Step-by-Step Solution

Answer

12054 g

Step 1: Understand the Units

The given weights are in kilograms (kg) and grams (g). The final answer should be in grams (g).

Step 2: Convert Kilograms to Grams

Since 1 kg equals 1000 g, multiply 12 kg by 1000.i.e., \[ 12 \text{ kg} = 12 \times 1000 \text{ g} = 12000 \text{ g} \]

Step 3: Add the Gram Values

Now add the converted grams (12000 g) to the given grams (54 g).i.e., \[ 12000 \text{ g} + 54 \text{ g} = 12054 \text{ g} \]

Key Concepts

kilograms to grams conversion

To solve this problem, we start by converting kilograms (kg) to grams (g). This is a simple unit conversion that you need to know. The conversion factor is straightforward: 1 kilogram is equal to 1000 grams. This means for every kilogram, you multiply by 1000 to get the amount in grams.

For example, if we have 12 kg, we convert it by:
\[ 12 \text{ kg} \times 1000 = 12000 \text{ g} \]
Now we have converted 12 kilograms into 12,000 grams, making further addition easier.

addition of weights

After converting the units, the next step is to add the weights together. Addition is a fundamental arithmetic operation where you combine values.

In this exercise, you have the converted grams from kilograms, which is 12,000 g, and an additional weight already in grams, which is 54 g. Now you simply add the two values together:
\[ 12,000 \text{ g} + 54 \text{ g} = 12,054 \text{ g} \]
Addition here is straightforward, making sure both weights are in the same unit (grams) first, so they can be added directly. The total weight in grams gives us the complete answer.

elementary algebra

This problem involves basic arithmetic and algebraic skills. Elementary algebra includes operations like addition, subtraction, multiplication, and division. Here, understanding how to properly convert units and add weights falls under these basic skills.

First, we multiplied to convert kilograms to grams, which is an elementary algebraic operation:
\[ 12 \times 1000 = 12000 \]
Then, we added two numbers together, which is another fundamental operation:
\[ 12000 + 54 = 12054 \]
These steps use elementary algebra to transform and combine values, ensuring you have the correct final answer.