Let's tackle each fraction one by one, making sure we find the numerators or denominators that complete the equivalent fractions.
9. [tex]\(\frac{1}{11} = \frac{}{33}\)[/tex]
For a fraction to be equivalent, the cross products must be equal. This means:
[tex]\[ 1 \times 33 = 11 \times x \][/tex]
[tex]\[ 33 = 11x \][/tex]
[tex]\[ x = 3 \][/tex]
So,
[tex]\[ \frac{1}{11} = \frac{3}{33} \][/tex]
10. [tex]\(\frac{1}{4} = \frac{}{20}\)[/tex]
Similarly, the cross products must be equal:
[tex]\[ 1 \times 20 = 4 \times x \][/tex]
[tex]\[ 20 = 4x \][/tex]
[tex]\[ x = 5 \][/tex]
Thus,
[tex]\[ \frac{1}{4} = \frac{5}{20} \][/tex]
11. [tex]\(\frac{4}{16} = \frac{}{32}\)[/tex]
The cross products must be equal:
[tex]\[ 4 \times 32 = 16 \times x \][/tex]
[tex]\[ 128 = 16x \][/tex]
[tex]\[ x = 8 \][/tex]
So,
[tex]\[ \frac{4}{16} = \frac{8}{32} \][/tex]
12. [tex]\(\frac{8}{9} = \frac{}{54}\)[/tex]
The cross products must be equal:
[tex]\[ 8 \times 54 = 9 \times x \][/tex]
[tex]\[ 432 = 9x \][/tex]
[tex]\[ x = 48 \][/tex]
Thus,
[tex]\[ \frac{8}{9} = \frac{48}{54} \][/tex]
13. [tex]\(\frac{3}{15} = \frac{}{45}\)[/tex]
The cross products must be equal:
[tex]\[ 3 \times 45 = 15 \times x \][/tex]
[tex]\[ 135 = 15x \][/tex]
[tex]\[ x = 9 \][/tex]
So,
[tex]\[ \frac{3}{15} = \frac{9}{45} \][/tex]
14. [tex]\(\frac{2}{6} = \frac{}{36}\)[/tex]
The cross products must be equal:
[tex]\[ 2 \times 36 = 6 \times x \][/tex]
[tex]\[ 72 = 6x \][/tex]
[tex]\[ x = 12 \][/tex]
Thus,
[tex]\[ \frac{2}{6} = \frac{12}{36} \][/tex]
15. [tex]\(\frac{5}{16} = \frac{}{48}\)[/tex]
The cross products must be equal:
[tex]\[ 5 \times 48 = 16 \times x \][/tex]
[tex]\[ 240 = 16x \][/tex]
[tex]\[ x = 15 \][/tex]
So,
[tex]\[ \frac{5}{16} = \frac{15}{48} \][/tex]
16. [tex]\(\frac{3}{8} = \frac{}{24}\)[/tex]
The cross products must be equal:
[tex]\[ 3 \times 24 = 8 \times x \][/tex]
[tex]\[ 72 = 8x \][/tex]
[tex]\[ x = 9 \][/tex]
Thus,
[tex]\[ \frac{3}{8} = \frac{9}{24} \][/tex]
So, the completed fractions are:
9. [tex]\(\frac{1}{11} = \frac{3}{33}\)[/tex]
10. [tex]\(\frac{1}{4} = \frac{5}{20}\)[/tex]
11. [tex]\(\frac{4}{16} = \frac{8}{32}\)[/tex]
12. [tex]\(\frac{8}{9} = \frac{48}{54}\)[/tex]
13. [tex]\(\frac{3}{15} = \frac{9}{45}\)[/tex]
14. [tex]\(\frac{2}{6} = \frac{12}{36}\)[/tex]
15. [tex]\(\frac{5}{16} = \frac{15}{48}\)[/tex]
16. [tex]\(\frac{3}{8} = \frac{9}{24}\)[/tex]
