Find the ratio of each of the in simplest form :
1 m 44 cm to 2 m 40 cm

Answer

To find the ratio of 1 m 44 cm to 2 m 40 cm in simplest form, we can follow these steps:

### Step 1: Convert meters to centimeters
First, we convert both measurements from meters and centimeters to just centimeters.

1 meter = 100 centimeters

- For 1 m 44 cm:
\[ 1 \text{ m} = 100 \text{ cm} \implies 1 \text{ m} 44 \text{ cm} = 100 \text{ cm} + 44 \text{ cm} = 144 \text{ cm} \]

- For 2 m 40 cm:
\[ 2 \text{ m} = 200 \text{ cm} \implies 2 \text{ m} 40 \text{ cm} = 200 \text{ cm} + 40 \text{ cm} = 240 \text{ cm} \]

### Step 2: Write the ratio
Now we can write the ratio of the two measurements in centimeters:
\[ \text{Ratio} = \frac{144 \text{ cm}}{240 \text{ cm}} \]

### Step 3: Simplify the ratio
Next, we simplify the fraction \(\frac{144}{240}\).

1. Find the greatest common divisor (GCD) of 144 and 240.
- Both numbers can be divided by 12:
\[ \frac{144 \div 12}{240 \div 12} = \frac{12}{20} \]

2. We can simplify \(\frac{12}{20}\) further by dividing both the numerator and denominator by 4:
\[ \frac{12 \div 4}{20 \div 4} = \frac{3}{5} \]

### Final Answer
Thus, the ratio of 1 m 44 cm to 2 m 40 cm in simplest form is:
\[ \text{Ratio} = 3 : 5 \]

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