How do I solve 33.8 / 32.5

How do I solve 33.8 / 32.5, quickly and easily.

The correct answer and explanation is:

To solve $33.8 \div 32.5$ quickly and easily, you can use a few mental math tricks or a straightforward calculator approach. Let’s go through both.

Quick Calculation:

1. Estimate first:
   Notice that 33.8 and 32.5 are close in value. So, $\frac{33.8}{32.5}$ will be a little more than 1.
2. Rewrite as a fraction: $$
   \frac{33.8}{32.5}
   $$
3. Make the divisor a whole number:
   Multiply numerator and denominator by 10 to eliminate the decimals: $$
   \frac{33.8 \times 10}{32.5 \times 10} = \frac{338}{325}
   $$
4. Divide numerator by denominator:
   Use long division or a calculator: $$
   338 \div 325 \approx 1.04
   $$

So, the answer is approximately 1.04.

Explanation in 300 Words:

Dividing decimals like 33.8 by 32.5 can be tricky at first glance, but there’s a simple trick to make it easier: eliminate the decimals by multiplying both numbers by the same power of 10. Since both numbers have one decimal place, multiplying both by 10 converts them into whole numbers without changing their ratio.

This method simplifies the division problem because working with whole numbers is more straightforward than working with decimals directly. So, $33.8 / 32.5$ becomes $338 / 325$.

Next, you perform the division of these whole numbers. 338 divided by 325 is slightly greater than 1 because 338 is just a bit larger than 325. To get a precise answer, you can do long division or use a calculator.

The quotient is about 1.04, which means 33.8 is approximately 1.04 times 32.5.

Another mental math tip is to approximate first: Since 33.8 is close to 32.5, the ratio should be close to 1. Then, by noting the difference (33.8 – 32.5 = 1.3), you can estimate the fraction $1.3 / 32.5 \approx 0.04$, which supports the final result of about 1.04.

This method is useful not only here but for any division involving decimals — always try to convert to whole numbers first, then divide.