Are the ratios 45 g: 60 g and 36 kg : 48 kg in proportion?

Answer

To determine if the ratios 45 g : 60 g and 36 kg : 48 kg are in proportion, we will follow these steps:

### Step 1: Convert both ratios to the same unit
The first ratio is given in grams (g), while the second ratio is given in kilograms (kg). To compare them, we need to convert the kilograms to grams.

- **Conversion**:
- 1 kg = 1000 g
- Therefore, 36 kg = 36 × 1000 g = 36000 g
- And 48 kg = 48 × 1000 g = 48000 g

### Step 2: Write the ratios
Now we can write both ratios in grams:
- First ratio: 45 g : 60 g
- Second ratio: 36000 g : 48000 g

### Step 3: Set up the fractions
We can express these ratios as fractions:
- First ratio as a fraction: \( \frac{45}{60} \)
- Second ratio as a fraction: \( \frac{36000}{48000} \)

### Step 4: Cross-multiply to check for proportion
To check if these two fractions are equal, we will cross-multiply:
- \( 45 \times 48000 \) and \( 60 \times 36000 \)

Calculating each:
- \( 45 \times 48000 = 2160000 \)
- \( 60 \times 36000 = 2160000 \)

### Step 5: Compare the results
Since both products are equal:
- \( 2160000 = 2160000 \)

### Conclusion
Since the cross-products are equal, we can conclude that the ratios 45 g : 60 g and 36 kg : 48 kg are indeed in proportion.

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