Division Relationship Explained

The question provides a division fact and asks us to find the result of a similar division problem where the numbers involved have different decimal placements.

• Given: $2994 \div 14.5 = 172$
• To find: $29.94 \div 1.45 = ?$

Decimal Shift Effect Analysis

Let's analyze how the dividend and divisor change from the given information to the problem we need to solve:

• The dividend changes from $2994$ to $29.94$. This means the original dividend has been divided by $100$ (or the decimal point shifted 2 places to the left).
• The divisor changes from $14.5$ to $1.45$. This means the original divisor has been divided by $10$ (or the decimal point shifted 1 place to the left).

We can express the division we need to solve in terms of the original numbers:

$29.94 \div 1.45 = \frac{29.94}{1.45}$

Now, let's rewrite the numerator and denominator using the original numbers:

Numerator: $29.94 = \frac{2994}{100}$

Denominator: $1.45 = \frac{14.5}{10}$

Substitute these back into the fraction:

$\frac{29.94}{1.45} = \frac{\frac{2994}{100}}{\frac{14.5}{10}}$

To simplify this complex fraction, we multiply the numerator by the reciprocal of the denominator:

$= \frac{2994}{100} \times \frac{10}{14.5}$

Rearrange the terms to group the known division:

$= \left(\frac{2994}{14.5}\right) \times \left(\frac{10}{100}\right)$

Calculation Steps

We know from the given information that $\frac{2994}{14.5} = 172$. Let's substitute this value:

$= 172 \times \left(\frac{10}{100}\right)$

Simplify the fraction $\frac{10}{100}$:

$= 172 \times \frac{1}{10}$

Now, perform the final multiplication:

$= \frac{172}{10}$

$= 17.2$

Therefore, $29.94 \div 1.45 = 17.2$.