Find common denominators, note that what you multiply (or divide) to the denominator, you must also do the same to the numerator.
1)
[tex]\frac{2}{3} , \frac{3}{4} \\\frac{2}{3} * \frac{4}{4} = \frac{8}{12} \\\frac{3}{4} * \frac{3}{3} = \frac{9}{12}[/tex]
Answers: [tex]\frac{8}{12} ; \frac{9}{12}[/tex]
2)
[tex]\frac{1}{4} , \frac{2}{3} \\\frac{1}{4} * \frac{3}{3} = \frac{3}{12}\\\frac{2}{3} * \frac{4}{4} = \frac{8}{12}[/tex]
Answers: [tex]\frac{3}{12} ; \frac{8}{12}[/tex]
3)
[tex]\frac{3}{10} , \frac{1}{2} \\\frac{3}{10} * \frac{1}{1} = \frac{3}{10}\\\frac{1}{2} * \frac{5}{5} = \frac{5}{10}[/tex]
Answers: [tex]\frac{3}{10} ; \frac{5}{10}[/tex]
4)
[tex]\frac{3}{5} , \frac{3}{4}\\\frac{3}{5} * \frac{4}{4} = \frac{12}{20}\\\frac{3}{4} * \frac{5}{5} = \frac{15}{20}[/tex]
Answers: [tex]\frac{12}{20} ; \frac{15}{20}[/tex]
5)
[tex]\frac{2}{4} , \frac{7}{8} \\\frac{2}{4} * \frac{8}{8} = \frac{16}{32}\\\frac{7}{8} * \frac{4}{4} = \frac{28}{32}[/tex]
Answers: [tex]\frac{16}{32} ; \frac{28}{32}[/tex]
6)
[tex]\frac{2}{3} , \frac{5}{12}[/tex]
[tex]\frac{2}{3} * \frac{12}{12} = \frac{24}{36} \\\frac{5}{12} * \frac{3}{3} = \frac{15}{36}[/tex]
Answers: [tex]\frac{24}{36} ; \frac{15}{36}[/tex]
7)
[tex]\frac{1}{4} , \frac{1}{6} \\\\\frac{1}{4} * \frac{6}{6} = \frac{6}{24} \\\frac{1}{6} * \frac{4}{4} = \frac{4}{24}[/tex]
Answers: [tex]\frac{6}{24} ; \frac{4}{24}[/tex]
Find common denominators, note that what you do to the denominator, you do to the numerator:
8.
[tex]\frac{1}{2} [] \frac{2}{5} \\(\frac{5}{5}) \frac{1}{2} [] \frac{2}{5} (\frac{2}{2})\\\frac{5}{10} \neq \frac{4}{10}[/tex]
Answer: Does not equal.
9.
[tex]\frac{1}{2} [] \frac{3}{6} \\\frac{1}{2} (* \frac{3}{3}) [] \frac{3}{6}\\\frac{1 * 3}{2 * 3} [] \frac{3}{6} \\\frac{3}{6} = \frac{3}{6} \\\\\frac{1}{2} = \frac{3}{6}[/tex]
Answer: Does equal.
10.
[tex]\frac{3}{4} [] \frac{5}{6}\\(\frac{6}{6})\frac{3}{4} [] \frac{5}{6}(\frac{4}{4})\\\frac{18}{24} \neq \frac{20}{24}[/tex]
Answer: Does not equal.
11.
[tex]\frac{6}{10} [] \frac{3}{5} \\\frac{6}{10} [] (\frac{3}{5} )(\frac{2}{2})\\\frac{6}{10} [] (\frac{3 * 2}{5 * 2})\\\frac{6}{10} = \frac{6}{10}[/tex]
Answer: Does equal.
12. You are simply only looking for the least number of parts that both rectangles can be divided too. Find the least common multiple of both 3 and 4:
Multiples of 3: 3, 6, 9, 12
Multiples of 4: 4, 8, 12
12 is your answer.
13. Find common denominators. Note that what you do to denominator, you do to the numerator:
[tex]\frac{2}{5} * \frac{2}{2} = \frac{4}{10}\\\frac{1}{2} * \frac{5}{5} = \frac{5}{10}[/tex]
Answers: [tex]\frac{4}{10}[/tex] , [tex]\frac{5}{10}[/tex]
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