Answer :
Let's work through the given fractions and find the missing equivalent fractions.
### 28. Equivalent Fractions for [tex]\( \frac{4}{9} \)[/tex]
1. Finding the missing number for [tex]\( \frac{8}{x} \)[/tex]:
- We know that [tex]\( \frac{4}{9} = \frac{8}{x} \)[/tex].
- By cross-multiplying, [tex]\( 4 \times x = 8 \times 9 \)[/tex].
- Solving for [tex]\( x \)[/tex], we get [tex]\( x = \frac{8 \times 9}{4} = 18 \)[/tex].
2. Finding the missing number for [tex]\( \frac{16}{x} \)[/tex]:
- We know that [tex]\( \frac{4}{9} = \frac{16}{x} \)[/tex].
- By cross-multiplying, [tex]\( 4 \times x = 16 \times 9 \)[/tex].
- Solving for [tex]\( x \)[/tex], we get [tex]\( x = \frac{16 \times 9}{4} = 36 \)[/tex].
3. Fraction [tex]\( \frac{36}{y} \)[/tex] is already a complete identity so we don't need additional calculation.
### 29. Equivalent Fractions for [tex]\( \frac{1}{5} \)[/tex]
1. Finding the missing number for [tex]\( \frac{x}{15} \)[/tex]:
- We know that [tex]\( \frac{1}{5} = \frac{x}{15} \)[/tex].
- Solving for [tex]\( x \)[/tex], we get [tex]\( x = \frac{1 \times 15}{5} = 3 \)[/tex].
2. Finding the missing number for [tex]\( \frac{5}{x} \)[/tex]:
- We know that [tex]\( \frac{1}{5} = \frac{5}{x} \)[/tex].
- Solving for [tex]\( x \)[/tex], we get [tex]\( x = \frac{5 \times 5}{1} = 25 \)[/tex].
3. Fraction [tex]\( \frac{y}{45} \)[/tex] is complete so we don't need calculation here.
4. Finding the missing number for [tex]\( \frac{11}{z} \)[/tex]:
- We know that [tex]\( \frac{1}{5} = \frac{11}{z} \)[/tex].
- Solving for [tex]\( z \)[/tex], we get [tex]\( z = \frac{11 \times 5}{1} = 55 \)[/tex].
### 30. Equivalent Fractions for [tex]\( \frac{3}{11} \)[/tex]
1. Finding the missing number for [tex]\( \frac{x}{22} \)[/tex]:
- We know that [tex]\( \frac{3}{11} = \frac{x}{22} \)[/tex].
- Solving for [tex]\( x \)[/tex], we get [tex]\( x = \frac{3 \times 22}{11} = 6 \)[/tex].
2. Finding the missing number for [tex]\( \frac{y}{33} \)[/tex]:
- We know that [tex]\( \frac{3}{11} = \frac{y}{33} \)[/tex].
- Solving for [tex]\( y \)[/tex], we get [tex]\( y = \frac{3 \times 33}{11} = 9 \)[/tex].
3. Fraction [tex]\( \frac{12}{z} \)[/tex] is complete so we don't need calculation here.
4. Finding the missing number for [tex]\( \frac{w}{55} \)[/tex]:
- We know that [tex]\( \frac{3}{11} = \frac{w}{55} \)[/tex].
- Solving for [tex]\( w \)[/tex], we get [tex]\( w = \frac{3 \times 55}{11} = 15 \)[/tex].
By following these steps, the calculated missing numbers are [tex]\(18\)[/tex], [tex]\(36\)[/tex], [tex]\(3\)[/tex], [tex]\(25\)[/tex], [tex]\(55\)[/tex], [tex]\(6\)[/tex], [tex]\(9\)[/tex], and [tex]\(15\)[/tex] respectively for the given fractions.
### 28. Equivalent Fractions for [tex]\( \frac{4}{9} \)[/tex]
1. Finding the missing number for [tex]\( \frac{8}{x} \)[/tex]:
- We know that [tex]\( \frac{4}{9} = \frac{8}{x} \)[/tex].
- By cross-multiplying, [tex]\( 4 \times x = 8 \times 9 \)[/tex].
- Solving for [tex]\( x \)[/tex], we get [tex]\( x = \frac{8 \times 9}{4} = 18 \)[/tex].
2. Finding the missing number for [tex]\( \frac{16}{x} \)[/tex]:
- We know that [tex]\( \frac{4}{9} = \frac{16}{x} \)[/tex].
- By cross-multiplying, [tex]\( 4 \times x = 16 \times 9 \)[/tex].
- Solving for [tex]\( x \)[/tex], we get [tex]\( x = \frac{16 \times 9}{4} = 36 \)[/tex].
3. Fraction [tex]\( \frac{36}{y} \)[/tex] is already a complete identity so we don't need additional calculation.
### 29. Equivalent Fractions for [tex]\( \frac{1}{5} \)[/tex]
1. Finding the missing number for [tex]\( \frac{x}{15} \)[/tex]:
- We know that [tex]\( \frac{1}{5} = \frac{x}{15} \)[/tex].
- Solving for [tex]\( x \)[/tex], we get [tex]\( x = \frac{1 \times 15}{5} = 3 \)[/tex].
2. Finding the missing number for [tex]\( \frac{5}{x} \)[/tex]:
- We know that [tex]\( \frac{1}{5} = \frac{5}{x} \)[/tex].
- Solving for [tex]\( x \)[/tex], we get [tex]\( x = \frac{5 \times 5}{1} = 25 \)[/tex].
3. Fraction [tex]\( \frac{y}{45} \)[/tex] is complete so we don't need calculation here.
4. Finding the missing number for [tex]\( \frac{11}{z} \)[/tex]:
- We know that [tex]\( \frac{1}{5} = \frac{11}{z} \)[/tex].
- Solving for [tex]\( z \)[/tex], we get [tex]\( z = \frac{11 \times 5}{1} = 55 \)[/tex].
### 30. Equivalent Fractions for [tex]\( \frac{3}{11} \)[/tex]
1. Finding the missing number for [tex]\( \frac{x}{22} \)[/tex]:
- We know that [tex]\( \frac{3}{11} = \frac{x}{22} \)[/tex].
- Solving for [tex]\( x \)[/tex], we get [tex]\( x = \frac{3 \times 22}{11} = 6 \)[/tex].
2. Finding the missing number for [tex]\( \frac{y}{33} \)[/tex]:
- We know that [tex]\( \frac{3}{11} = \frac{y}{33} \)[/tex].
- Solving for [tex]\( y \)[/tex], we get [tex]\( y = \frac{3 \times 33}{11} = 9 \)[/tex].
3. Fraction [tex]\( \frac{12}{z} \)[/tex] is complete so we don't need calculation here.
4. Finding the missing number for [tex]\( \frac{w}{55} \)[/tex]:
- We know that [tex]\( \frac{3}{11} = \frac{w}{55} \)[/tex].
- Solving for [tex]\( w \)[/tex], we get [tex]\( w = \frac{3 \times 55}{11} = 15 \)[/tex].
By following these steps, the calculated missing numbers are [tex]\(18\)[/tex], [tex]\(36\)[/tex], [tex]\(3\)[/tex], [tex]\(25\)[/tex], [tex]\(55\)[/tex], [tex]\(6\)[/tex], [tex]\(9\)[/tex], and [tex]\(15\)[/tex] respectively for the given fractions.
