`6(1)/(4)` of a weight is 0.25 kg. What is `45%` of this weight?

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Define the weight
Let's assume the weight is \( x \) kg.

### Step 2: Convert the percentage
We know that \( 6 \frac{1}{4} \) percent of the weight \( x \) is equal to 0.25 kg. First, we convert \( 6 \frac{1}{4} \) into an improper fraction:
\[ 6 \frac{1}{4} = \frac{25}{4} \]
So, we can write the equation as:
\[ \frac{25}{4} \% \text{ of } x = 0.25 \text{ kg} \]

### Step 3: Remove the percentage
To remove the percentage, we convert \( \frac{25}{4} \% \) into a fraction:
\[ \frac{25}{4} \% = \frac{25}{4} \times \frac{1}{100} = \frac{25}{400} \]
Thus, we can rewrite our equation as:
\[ \frac{25}{400} \times x = 0.25 \]

### Step 4: Solve for \( x \)
Now we can solve for \( x \):
\[ x = 0.25 \times \frac{400}{25} \]
To simplify, we first convert \( 0.25 \) into a fraction:
\[ 0.25 = \frac{1}{4} \]
So, substituting this in gives:
\[ x = \frac{1}{4} \times \frac{400}{25} \]
Now, simplifying \( \frac{400}{25} \):
\[ \frac{400}{25} = 16 \]
Thus, we have:
\[ x = \frac{1}{4} \times 16 = 4 \text{ kg} \]

### Step 5: Calculate 45% of the weight
Now that we have found \( x = 4 \) kg, we need to find \( 45\% \) of this weight:
\[ 45\% \text{ of } x = \frac{45}{100} \times 4 \]
This simplifies to:
\[ = \frac{45 \times 4}{100} = \frac{180}{100} = 1.8 \text{ kg} \]

### Final Answer
Thus, \( 45\% \) of the weight is \( 1.8 \) kg.

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