Recall that dividing fractions is the same as multiplying the first fraction by the reciprocal of the second fraction.
- 11/6÷ 25/6 ⇔ - 11/6* 6/25
When multiplying real numbers, the product will be positive if the signs are the same and it will be negative if the signs are different.
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Same Sign & Different Signs
(+)(+)=(+) & (+)(-)=(-)
(-)(-)=(+) & (-)(+)=(-)
In our case one number is positive and one number is negative, so the product will be negative.
We can check our answer by finding the product using a calculator. However, most calculators will give the product as a decimal number. Because our answer is a fraction, we need to compare the product of the original fractions to the decimal that is equivalent to the final product that we found. First, let's find the decimal form of our product.
Now we will find the product of the fractions using the calculator. Remember to use parentheses around each of the fractions so that the order of operations is performed correctly! Calculators cannot read our minds, unfortunately.
Because the calculator found the same decimal for both calculations, we know that our answer was correct!
