Solve Decimal Division: 2.4 ÷ 5.1 Step-by-Step

To solve this problem, we'll follow these steps:

• Step 1: Convert each decimal number into a fraction
• Step 2: Perform the division of these fractions using multiplication by the reciprocal
• Step 3: Simplify the resulting fraction

Now, let's work through each step:

Step 1: Convert the decimals to fractions.

For the decimal 2.4, notice it is equal to 24 divided by 10, so it can be written as the fraction $\frac{24}{10}$.

For the decimal 5.1, it is equal to 51 divided by 10, so it can be written as the fraction $\frac{51}{10}$.

Step 2: Divide the fractions by multiplying by the reciprocal.

We have the division: $\frac{24}{10} \div \frac{51}{10}$.

Instead of dividing, we multiply by the reciprocal: $\frac{24}{10} \times \frac{10}{51}$.

When multiplying, we multiply the numerators and the denominators:

$\frac{24 \times 10}{10 \times 51} = \frac{240}{510}$.

Step 3: Simplify the resulting fraction.

Both 240 and 510 are divisible by 30:

$\frac{240 \div 30}{510 \div 30} = \frac{8}{17}$.

Thus, the fraction simplifies to $\frac{8}{17}$.

Therefore, the solution to the problem is $\frac{8}{17}$.