Question

true or false.

to add two fractions with x's, you add their numerators and denominators.

Answer 1

False.

To add two fractions, you need a common denominator. You don't simply add the numerators and denominators. Here's the correct process:

1. Find the least common denominator (LCD) of the two fractions.
2. Convert each fraction to an equivalent fraction with the LCD as the denominator.
3. Add the numerators of these equivalent fractions.
4. Write the result over the common denominator.

For example, to add the fractions \(\frac{a}{b}\) and \(\frac{c}{d}\), you would do the following:

1. Find the LCD of \(b\) and \(d\), which is \(bd\) if \(b\) and \(d\) are relatively prime.
2. Convert \(\frac{a}{b}\) to \(\frac{a \cdot d}{b \cdot d}\) and \(\frac{c}{d}\) to \(\frac{c \cdot b}{d \cdot b}\).
3. Add the numerators: \(a \cdot d + c \cdot b\).
4. Write the result over the common denominator: \(\frac{a \cdot d + c \cdot b}{b \cdot d}\).