Answer:
15. [tex]\frac{8}{5}[/tex]
16. [tex]\frac{37}{30}[/tex]
17. [tex]\frac{7}{18}[/tex]
Step-by-step explanation:
In order to add or subtract two fractions with different denominators more easily, find the LCM of the denominators and solve by adding or subtracting the numerator.
LCM - Lowest Common Multiple
The lowest common multiple is the number that shows up earliest that is in both numbers' multiples.
Example: LCM of 2 and 3
2, 4, 6, 8, 10...
3, 6, 9, 12, 15...
Because 6 is the number that shows in both sets first, 6 is the LCM.
We will use this process to solve each problem:
15:
[tex]\frac{7}{10}[/tex] + [tex]\frac{9}{10}[/tex] Because the denominators are the same, adding can be done immediately.
[tex]\frac{16}{10}[/tex] To put this into simplest form, divide by [tex]\frac{2}{2}[/tex] .
[tex]\frac{16}{10}[/tex] ÷ [tex]\frac{2}{2}[/tex] Divide.
[tex]\frac{8}{5}[/tex]
16:
[tex]\frac{2}{5}[/tex] + [tex]\frac{5}{6}[/tex] The LCM of 5 and 6 is 30. So, multiply [tex]\frac{2}{5}[/tex] by [tex]\frac{6}{6}[/tex] and [tex]\frac{5}{6}[/tex] by [tex]\frac{5}{5}[/tex].
[tex]\frac{2}{5}[/tex] × [tex]\frac{6}{6}[/tex] + [tex]\frac{5}{6}[/tex] × [tex]\frac{5}{5}[/tex] Multiply.
[tex]\frac{12}{30}[/tex] + [tex]\frac{25}{30}[/tex] Add the fractions.
[tex]\frac{37}{30}[/tex] Because 37 is a prime number, this is the simplest form.
17:
[tex]\frac{5}{6}[/tex] - [tex]\frac{4}{9}[/tex] The LCM of 6 and 9 is 18. So, multiply [tex]\frac{5}{6}[/tex] by [tex]\frac{3}{3}[/tex] and [tex]\frac{4}{9}[/tex] by [tex]\frac{2}{2}[/tex].
[tex]\frac{5}{6}[/tex] × [tex]\frac{3}{3}[/tex] - [tex]\frac{4}{9}[/tex] × [tex]\frac{2}{2}[/tex] Multiply.
[tex]\frac{15}{18}[/tex] - [tex]\frac{8}{18}[/tex] Subtract the fractions.
[tex]\frac{7}{18}[/tex] Because 7 is a prime number, this is the simplest form.
