1. Find the rational numbers that should be added to \( \frac{2}{9} \) to get -1 . 2. Find the rational numbers that should be subtracted from \( \frac{-2}{3} \) to get \( \frac{-5}{6} \). 3. The sum of two fractions is \( 5 \frac{1}{7} \), one of them is \( 4 \frac{1}{7} \), what is the other fraction 4. Find the rational numbers that should be multiplied with \( \frac{-3}{13} \) to get 39 . \( 5 . \quad \) How is the fractional number for 5 out of 7 written ?

To find the rational number that should be added to \( \frac{2}{9} \) to obtain -1, you can set up the equation: \( x + \frac{2}{9} = -1 \). Therefore, \( x = -1 - \frac{2}{9} = -\frac{9}{9} - \frac{2}{9} = -\frac{11}{9} \). So, the number you need to add is \( -\frac{11}{9} \)! For the next problem, you're looking for the number that should be subtracted from \( \frac{-2}{3} \) to achieve \( \frac{-5}{6} \). Set it up as \( \frac{-2}{3} - x = \frac{-5}{6} \). Solve for x: \( x = \frac{-2}{3} + \frac{5}{6} \). To do this, convert \( \frac{-2}{3} \) to sixths: \( \frac{-4}{6} + \frac{5}{6} = \frac{1}{6} \). So, you need to subtract \( \frac{1}{6} \). Getting that last one right is all about knowing that mixed numbers can be converted into improper fractions! For instance, \( 5 \frac{1}{7} \) becomes \( \frac{36}{7} \) when you convert it, so when you subtract \( 4 \frac{1}{7} \) (which is \( \frac{29}{7} \)), you end up with the other fraction being \( \frac{7}{7} \) or simply 1! Fun, right? And when representing the fraction "5 out of 7", it's simply written as \( \frac{5}{7} \). Easy peasy!