A box of candies weighs `640 (1)/(2)` g. If each candy weighs `45 (3)/(4)`g, how many candies are there in the box?

Answer

To find the number of candies in the box, we need to divide the total weight of the box of candies by the weight of each candy. Let's break this down step by step.

### Step 1: Convert Mixed Numbers to Improper Fractions
The weight of the box is given as \( 640 \frac{1}{2} \) grams. We need to convert this mixed number into an improper fraction.

1. Multiply the whole number (640) by the denominator (2):
\[ 640 \times 2 = 1280 \]
2. Add the numerator (1) to this result:
\[ 1280 + 1 = 1281 \]
3. So, \( 640 \frac{1}{2} \) can be written as:
\[ \frac{1281}{2} \]

### Step 2: Convert the Weight of Each Candy to an Improper Fraction
The weight of each candy is given as \( 45 \frac{3}{4} \) grams. We will convert this mixed number into an improper fraction as well.

1. Multiply the whole number (45) by the denominator (4):
\[ 45 \times 4 = 180 \]
2. Add the numerator (3) to this result:
\[ 180 + 3 = 183 \]
3. So, \( 45 \frac{3}{4} \) can be written as:
\[ \frac{183}{4} \]

### Step 3: Set Up the Division
Now we need to find the total number of candies by dividing the weight of the box by the weight of each candy:
\[ \text{Number of candies} = \frac{1281/2}{183/4} \]

### Step 4: Apply the Rule for Dividing Fractions
When dividing fractions, we multiply by the reciprocal of the divisor:
\[ \frac{1281}{2} \div \frac{183}{4} = \frac{1281}{2} \times \frac{4}{183} \]

### Step 5: Simplify the Expression
Now we can simplify this expression:
\[ = \frac{1281 \times 4}{2 \times 183} \]
Calculating the numerator:
\[ 1281 \times 4 = 5124 \]
Calculating the denominator:
\[ 2 \times 183 = 366 \]
So we have:
\[ \frac{5124}{366} \]

### Step 6: Simplify the Fraction
Now we can simplify \( \frac{5124}{366} \):
1. Divide both the numerator and the denominator by 2:
\[ \frac{5124 \div 2}{366 \div 2} = \frac{2562}{183} \]

### Step 7: Perform the Division
Now we can perform the division:
\[ 2562 \div 183 = 14 \]
This means the total number of candies is 14.

### Final Answer
The total number of candies in the box is **14**.

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