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Answer :
Let's solve the given fractions step-by-step to find their equivalent fractions.
### 22. [tex]\(\frac{3}{4} = \frac{12}{16}\)[/tex]
To verify this, we need to see if [tex]\(\frac{3}{4}\)[/tex] is equivalent to [tex]\(\frac{12}{16}\)[/tex].
- Multiply both the numerator and the denominator of [tex]\(\frac{3}{4}\)[/tex] by 4:
[tex]\(\frac{3 \times 4}{4 \times 4} = \frac{12}{16}\)[/tex].
- These fractions are equivalent.
### 23. [tex]\(\frac{1}{8} = \frac{3}{24}\)[/tex]
To verify the equivalence:
- Multiply both the numerator and the denominator of [tex]\(\frac{1}{8}\)[/tex] by 3:
[tex]\(\frac{1 \times 3}{8 \times 3} = \frac{3}{24}\)[/tex].
- These fractions are equivalent.
### 24. [tex]\(\frac{2}{5} = \frac{6}{15}\)[/tex]
To verify the equivalence:
- Multiply both the numerator and the denominator of [tex]\(\frac{2}{5}\)[/tex] by 3:
[tex]\(\frac{2 \times 3}{5 \times 3} = \frac{6}{15}\)[/tex].
- These fractions are equivalent.
### 25. [tex]\(\frac{9}{10} = \frac{27}{30}\)[/tex]
To verify the equivalence:
- Multiply both the numerator and the denominator of [tex]\(\frac{9}{10}\)[/tex] by 3:
[tex]\(\frac{9 \times 3}{10 \times 3} = \frac{27}{30}\)[/tex].
- These fractions are equivalent.
### 26. [tex]\(\frac{5}{12} = \frac{15}{36}\)[/tex]
To verify the equivalence:
- Multiply both the numerator and the denominator of [tex]\(\frac{5}{12}\)[/tex] by 3:
[tex]\(\frac{5 \times 3}{12 \times 3} = \frac{15}{36}\)[/tex].
- These fractions are equivalent.
### 27. [tex]\(\frac{2}{7} = \frac{4}{14} = \frac{8}{28} = \frac{110}{42} = \frac{14}{82} = \frac{18}{164}\)[/tex]
We'll check each fraction:
- [tex]\(\frac{4}{14}\)[/tex] and [tex]\(\frac{8}{28}\)[/tex] are equivalent to [tex]\(\frac{2}{7}\)[/tex], but [tex]\(\frac{110}{42}\)[/tex], [tex]\(\frac{14}{82}\)[/tex], and [tex]\(\frac{18}{164}\)[/tex] are not equivalent to [tex]\(\frac{2}{7}\)[/tex] when simplified.
### 28. [tex]\(\frac{4}{9} = \frac{8}{54} = \frac{16}{?} = \frac{32}{?} = \frac{36}{?}\)[/tex]
- Let's simplify [tex]\(\frac{8}{54}\)[/tex]: Divide both the numerator and the denominator by 2:
[tex]\(\frac{8}{54} = \frac{4}{27}\)[/tex] (not the same as [tex]\(\frac{4}{9}\)[/tex]).
This should reveal that the correct match should use a common multiple approach for completing empty numerators/denominators:
- [tex]\(\frac{16}{36}\)[/tex], [tex]\(\frac{32}{72}\)[/tex], etc., are equivalent through direct multiplication of original [tex]\(\frac{4}{9}\)[/tex].
### 29. [tex]\(\frac{1}{5} = \frac{?}{15} = \frac{5}{35} = \frac{?}{45} = \frac{11}{?}\)[/tex]
To find equivalents:
- [tex]\(\frac{1}{5}\)[/tex] scaled by 3 gives [tex]\(\frac{3}{15}\)[/tex].
- [tex]\(\frac{1}{5}\)[/tex] scaled by 9 gives [tex]\(\frac{9}{45}\)[/tex].
- [tex]\(\frac{1}{5}\)[/tex] scaled by 11 gives [tex]\(\frac{11}{55}\)[/tex].
### 30. [tex]\(\frac{3}{11} = \frac{?}{22} = \frac{?}{33} = \frac{12}{?} = \frac{?}{55} = 21\)[/tex]
Let's find the missing values:
- For [tex]\(\frac{?}{22}\)[/tex], multiply [tex]\(\frac{3}{11}\)[/tex] by 2 to get [tex]\(\frac{6}{22}\)[/tex].
- For [tex]\(\frac{?}{33}\)[/tex], multiply [tex]\(\frac{3}{11}\)[/tex] by 3 to get [tex]\(\frac{9}{33}\)[/tex].
- To match [tex]\(\frac{12}{?}\)[/tex], multiply [tex]\(\frac{3}{11}\)[/tex] by 4 to get [tex]\(\frac{12}{44}\)[/tex].
- [tex]\(\frac{?}{55}\)[/tex] is found by multiplying by 5: [tex]\(\frac{15}{55}\)[/tex], making it align with our equivalencies.
Keep practicing the concept of equivalent fractions by multiplying or dividing the numerator and denominator by the same number to find or verify equivalency!
### 22. [tex]\(\frac{3}{4} = \frac{12}{16}\)[/tex]
To verify this, we need to see if [tex]\(\frac{3}{4}\)[/tex] is equivalent to [tex]\(\frac{12}{16}\)[/tex].
- Multiply both the numerator and the denominator of [tex]\(\frac{3}{4}\)[/tex] by 4:
[tex]\(\frac{3 \times 4}{4 \times 4} = \frac{12}{16}\)[/tex].
- These fractions are equivalent.
### 23. [tex]\(\frac{1}{8} = \frac{3}{24}\)[/tex]
To verify the equivalence:
- Multiply both the numerator and the denominator of [tex]\(\frac{1}{8}\)[/tex] by 3:
[tex]\(\frac{1 \times 3}{8 \times 3} = \frac{3}{24}\)[/tex].
- These fractions are equivalent.
### 24. [tex]\(\frac{2}{5} = \frac{6}{15}\)[/tex]
To verify the equivalence:
- Multiply both the numerator and the denominator of [tex]\(\frac{2}{5}\)[/tex] by 3:
[tex]\(\frac{2 \times 3}{5 \times 3} = \frac{6}{15}\)[/tex].
- These fractions are equivalent.
### 25. [tex]\(\frac{9}{10} = \frac{27}{30}\)[/tex]
To verify the equivalence:
- Multiply both the numerator and the denominator of [tex]\(\frac{9}{10}\)[/tex] by 3:
[tex]\(\frac{9 \times 3}{10 \times 3} = \frac{27}{30}\)[/tex].
- These fractions are equivalent.
### 26. [tex]\(\frac{5}{12} = \frac{15}{36}\)[/tex]
To verify the equivalence:
- Multiply both the numerator and the denominator of [tex]\(\frac{5}{12}\)[/tex] by 3:
[tex]\(\frac{5 \times 3}{12 \times 3} = \frac{15}{36}\)[/tex].
- These fractions are equivalent.
### 27. [tex]\(\frac{2}{7} = \frac{4}{14} = \frac{8}{28} = \frac{110}{42} = \frac{14}{82} = \frac{18}{164}\)[/tex]
We'll check each fraction:
- [tex]\(\frac{4}{14}\)[/tex] and [tex]\(\frac{8}{28}\)[/tex] are equivalent to [tex]\(\frac{2}{7}\)[/tex], but [tex]\(\frac{110}{42}\)[/tex], [tex]\(\frac{14}{82}\)[/tex], and [tex]\(\frac{18}{164}\)[/tex] are not equivalent to [tex]\(\frac{2}{7}\)[/tex] when simplified.
### 28. [tex]\(\frac{4}{9} = \frac{8}{54} = \frac{16}{?} = \frac{32}{?} = \frac{36}{?}\)[/tex]
- Let's simplify [tex]\(\frac{8}{54}\)[/tex]: Divide both the numerator and the denominator by 2:
[tex]\(\frac{8}{54} = \frac{4}{27}\)[/tex] (not the same as [tex]\(\frac{4}{9}\)[/tex]).
This should reveal that the correct match should use a common multiple approach for completing empty numerators/denominators:
- [tex]\(\frac{16}{36}\)[/tex], [tex]\(\frac{32}{72}\)[/tex], etc., are equivalent through direct multiplication of original [tex]\(\frac{4}{9}\)[/tex].
### 29. [tex]\(\frac{1}{5} = \frac{?}{15} = \frac{5}{35} = \frac{?}{45} = \frac{11}{?}\)[/tex]
To find equivalents:
- [tex]\(\frac{1}{5}\)[/tex] scaled by 3 gives [tex]\(\frac{3}{15}\)[/tex].
- [tex]\(\frac{1}{5}\)[/tex] scaled by 9 gives [tex]\(\frac{9}{45}\)[/tex].
- [tex]\(\frac{1}{5}\)[/tex] scaled by 11 gives [tex]\(\frac{11}{55}\)[/tex].
### 30. [tex]\(\frac{3}{11} = \frac{?}{22} = \frac{?}{33} = \frac{12}{?} = \frac{?}{55} = 21\)[/tex]
Let's find the missing values:
- For [tex]\(\frac{?}{22}\)[/tex], multiply [tex]\(\frac{3}{11}\)[/tex] by 2 to get [tex]\(\frac{6}{22}\)[/tex].
- For [tex]\(\frac{?}{33}\)[/tex], multiply [tex]\(\frac{3}{11}\)[/tex] by 3 to get [tex]\(\frac{9}{33}\)[/tex].
- To match [tex]\(\frac{12}{?}\)[/tex], multiply [tex]\(\frac{3}{11}\)[/tex] by 4 to get [tex]\(\frac{12}{44}\)[/tex].
- [tex]\(\frac{?}{55}\)[/tex] is found by multiplying by 5: [tex]\(\frac{15}{55}\)[/tex], making it align with our equivalencies.
Keep practicing the concept of equivalent fractions by multiplying or dividing the numerator and denominator by the same number to find or verify equivalency!
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