Question

First, rewrite (13)/(15) and (9)/(10) so that they have a common denominator.

Answer 1

To rewrite the fractions (13)/(15) and (9)/(10) with a common denominator, multiply the numerators and denominators by numbers that make the denominators both 30. This results in the equivalent fractions 26/30 and 27/30, respectively.

Step-by-step explanation:

To rewrite fractions (13)/(15) and (9)/(10) with a common denominator, we need to find a number that is a multiple of both denominators. The least common multiple (LCM) of 15 and 10 is 30. Therefore, we need to adjust each fraction so that its denominator is 30.

For the first fraction, we can multiply both the numerator and the denominator by 2: (13 × 2)/(15 × 2) = 26/30. For the second fraction, we can multiply both the numerator and the denominator by 3: (9 × 3)/(10 × 3) = 27/30. Now both fractions have a common denominator, which allows us to compare or combine the fractions if needed.

Remember that when we adjust fractions to have a common denominator, we are not changing their value, just the way they are expressed. We can also check our work by simplifying the fractions to see if they match their original forms.

Answer 2

To rewrite the fractions (13/15) and (9/10) with a common denominator, find the LCM of the denominators, which is 30. Therefore, (13/15) becomes (26/30) and (9/10) becomes (27/30). Both fractions are now written with a common denominator, allowing further operations.

Step-by-step explanation:

To rewrite (13)/(15) and (9)/(10) so that they have a common denominator, we first need to find the least common multiple (LCM) of the two denominators, 15 and 10. The LCM of 15 and 10 is 30. Now we multiply both the numerator and denominator of each fraction by the number needed to get the denominator to 30. For (13)/(15), we multiply by 2 to make the denominator 30, so it becomes (26)/(30). For (9)/(10), we multiply by 3 to make the denominator 30, so it becomes (27)/(30).

Now both fractions have the common denominator of 30, and they can be easily compared, added, or subtracted. Remember that when finding a common denominator, we never add denominators; we find a common multiple and adjust the numerators accordingly.