Fraction math practice worksheet for comparing, completing equivalent fractions, and converting improper fractions.

Let's solve each section of the worksheet step by step.

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Section 1: Compare the fractions. (<, >, =)

We compare two fractions by finding a common denominator or converting them to decimals.

#### 85. $\frac{3}{8} \quad \text{vs} \quad \frac{3}{6}$
- Same numerator (3), so compare denominators: smaller denominator → larger fraction.
- $8 > 6$ → $\frac{3}{8} < \frac{3}{6}$
✔ Answer: $<$

#### 86. $\frac{1}{3} \quad \text{vs} \quad \frac{3}{5}$
- Convert to decimals:
- $\frac{1}{3} \approx 0.333$, $\frac{3}{5} = 0.6$
- $0.333 < 0.6$
✔ Answer: $<$

#### 87. $\frac{3}{4} \quad \text{vs} \quad \frac{2}{8}$
- Simplify $\frac{2}{8} = \frac{1}{4}$
- $\frac{3}{4} > \frac{1}{4}$
✔ Answer: $>$

#### 88. $\frac{5}{6} \quad \text{vs} \quad \frac{2}{3}$
- $\frac{2}{3} = \frac{4}{6}$, so $\frac{5}{6} > \frac{4}{6}$
✔ Answer: $>$

#### 89. $\frac{5}{6} \quad \text{vs} \quad \frac{1}{4}$
- $\frac{5}{6} \approx 0.833$, $\frac{1}{4} = 0.25$ → $0.833 > 0.25$
✔ Answer: $>$

#### 90. $\frac{3}{5} \quad \text{vs} \quad \frac{4}{8}$
- $\frac{4}{8} = \frac{1}{2} = 0.5$, $\frac{3}{5} = 0.6$ → $0.6 > 0.5$
✔ Answer: $>$

#### 91. $\frac{5}{6} \quad \text{vs} \quad \frac{2}{5}$
- $\frac{5}{6} \approx 0.833$, $\frac{2}{5} = 0.4$ → $0.833 > 0.4$
✔ Answer: $>$

#### 92. $\frac{1}{8} \quad \text{vs} \quad \frac{3}{4}$
- $\frac{1}{8} = 0.125$, $\frac{3}{4} = 0.75$ → $0.125 < 0.75$
✔ Answer: $<$

#### 93. $\frac{1}{3} \quad \text{vs} \quad \frac{2}{4}$
- $\frac{2}{4} = \frac{1}{2} = 0.5$, $\frac{1}{3} \approx 0.333$ → $0.333 < 0.5$
✔ Answer: $<$

#### 94. $\frac{2}{5} \quad \text{vs} \quad \frac{2}{3}$
- Same numerator: compare denominators → smaller denominator → larger fraction.
- $5 > 3$ → $\frac{2}{5} < \frac{2}{3}$
✔ Answer: $<$

#### 95. $\frac{3}{6} \quad \text{vs} \quad \frac{5}{8}$
- $\frac{3}{6} = \frac{1}{2} = 0.5$, $\frac{5}{8} = 0.625$ → $0.5 < 0.625$
✔ Answer: $<$

#### 96. $\frac{1}{4} \quad \text{vs} \quad \frac{2}{8}$
- $\frac{2}{8} = \frac{1}{4}$ → equal
✔ Answer: $=$

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Section 2: Complete the equivalent fractions

We find missing numerators or denominators using cross-multiplication or scaling.

#### 97. $\frac{5}{?} = \frac{25}{40}$
- $\frac{25}{40} = \frac{5}{8}$ → So $\frac{5}{8} = \frac{5}{8}$ → Missing denominator is 8
✔ Answer: $8$

#### 98. $\frac{?}{5} = \frac{28}{35}$
- $\frac{28}{35} = \frac{4}{5}$ → So numerator must be 4
✔ Answer: $4$

#### 99. $\frac{5}{6} = \frac{?}{24}$
- Multiply numerator and denominator by 4: $\frac{5 \times 4}{6 \times 4} = \frac{20}{24}$
✔ Answer: $20$

#### 100. $\frac{2}{?} = \frac{10}{15}$
- $\frac{10}{15} = \frac{2}{3}$ → So denominator is 3
✔ Answer: $3$

#### 101. $\frac{2}{5} = \frac{?}{40}$
- Multiply numerator and denominator by 8: $\frac{2 \times 8}{5 \times 8} = \frac{16}{40}$
✔ Answer: $16$

#### 102. $\frac{4}{8} = \frac{36}{?}$
- $\frac{4}{8} = \frac{1}{2}$, so $\frac{36}{x} = \frac{1}{2}$ → $x = 72$
✔ Answer: $72$

#### 103. $\frac{?}{4} = \frac{18}{24}$
- $\frac{18}{24} = \frac{3}{4}$ → So numerator is 3
✔ Answer: $3$

#### 104. $\frac{2}{4} = \frac{?}{8}$
- $\frac{2}{4} = \frac{1}{2}$, so $\frac{1}{2} = \frac{4}{8}$ → numerator is 4
✔ Answer: $4$

#### 105. $\frac{2}{?} = \frac{14}{21}$
- $\frac{14}{21} = \frac{2}{3}$ → So denominator is 3
✔ Answer: $3$

#### 106. $\frac{7}{8} = \frac{?}{72}$
- Multiply numerator and denominator by 9: $\frac{7 \times 9}{8 \times 9} = \frac{63}{72}$
✔ Answer: $63$

#### 107. $\frac{4}{?} = \frac{12}{15}$
- $\frac{12}{15} = \frac{4}{5}$ → So denominator is 5
✔ Answer: $5$

#### 108. $\frac{2}{6} = \frac{?}{24}$
- $\frac{2}{6} = \frac{1}{3}$, so $\frac{1}{3} = \frac{8}{24}$ → numerator is 8
✔ Answer: $8$

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Section 3: Convert improper fractions

Convert mixed numbers to improper fractions:
$$
\text{Improper fraction} = (\text{whole number} \times \text{denominator}) + \text{numerator}
$$

#### 109. $9 \frac{6}{8} = ?$
- $9 \times 8 = 72$, $72 + 6 = 78$ → $\frac{78}{8}$
- Simplify: $\frac{78}{8} = \frac{39}{4}$ (but keep as improper unless asked)
✔ Answer: $\boxed{\frac{78}{8}}$ or simplified $\boxed{\frac{39}{4}}$

But since it says "convert", we'll write improper form: $\frac{78}{8}$

But often reduced: $\frac{78}{8} = \frac{39}{4}$ → Let’s reduce if possible.

Wait — question asks to convert mixed numbers to improper fractions, so:

#### 109. $9 \frac{6}{8} = \frac{(9 \times 8) + 6}{8} = \frac{72 + 6}{8} = \frac{78}{8}$
→ Reduce: $\frac{78}{8} = \frac{39}{4}$
✔ Answer: $\boxed{\frac{39}{4}}$ (simplified)

But let’s check if they want reduced or not. Since it's just conversion, we can leave as $\frac{78}{8}$, but best to simplify.

Let’s do all with simplification.

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Let’s go one by one:

#### 109. $9 \frac{6}{8} = \frac{9 \times 8 + 6}{8} = \frac{78}{8} = \frac{39}{4}$ ✔

#### 110. $8 \frac{1}{4} = \frac{8 \times 4 + 1}{4} = \frac{32 + 1}{4} = \frac{33}{4}$ ✔

#### 111. $8 \frac{3}{4} = \frac{8 \times 4 + 3}{4} = \frac{32 + 3}{4} = \frac{35}{4}$ ✔

#### 112. $2 \frac{6}{8} = \frac{2 \times 8 + 6}{8} = \frac{16 + 6}{8} = \frac{22}{8} = \frac{11}{4}$ ✔

#### 113. $2 \frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{6 + 1}{3} = \frac{7}{3}$ ✔

#### 114. $1 \frac{3}{5} = \frac{1 \times 5 + 3}{5} = \frac{5 + 3}{5} = \frac{8}{5}$ ✔

#### 115. $7 \frac{7}{8} = \frac{7 \times 8 + 7}{8} = \frac{56 + 7}{8} = \frac{63}{8}$ ✔

#### 116. $1 \frac{5}{6} = \frac{1 \times 6 + 5}{6} = \frac{6 + 5}{6} = \frac{11}{6}$ ✔

#### 117. $8 \frac{1}{5} = \frac{8 \times 5 + 1}{5} = \frac{40 + 1}{5} = \frac{41}{5}$ ✔

#### 118. $6 \frac{3}{4} = \frac{6 \times 4 + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4}$ ✔

#### 119. $2 \frac{2}{6} = \frac{2 \times 6 + 2}{6} = \frac{12 + 2}{6} = \frac{14}{6} = \frac{7}{3}$ ✔

#### 120. $9 \frac{1}{4} = \frac{9 \times 4 + 1}{4} = \frac{36 + 1}{4} = \frac{37}{4}$ ✔

#### 121. $8 \frac{4}{8} = \frac{8 \times 8 + 4}{8} = \frac{64 + 4}{8} = \frac{68}{8} = \frac{17}{2}$ ✔

#### 122. $8 \frac{2}{5} = \frac{8 \times 5 + 2}{5} = \frac{40 + 2}{5} = \frac{42}{5}$ ✔

#### 123. $3 \frac{2}{3} = \frac{3 \times 3 + 2}{3} = \frac{9 + 2}{3} = \frac{11}{3}$ ✔

#### 124. $1 \frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{3 + 1}{3} = \frac{4}{3}$ ✔

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✔ Final Answers:

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Compare the fractions:

85. $<$
86. $<$
87. $>$
88. $>$
89. $>$
90. $>$
91. $>$
92. $<$
93. $<$
94. $<$
95. $<$
96. $=$

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Equivalent fractions:

97. $8$
98. $4$
99. $20$
100. $3$
101. $16$
102. $72$
103. $3$
104. $4$
105. $3$
106. $63$
107. $5$
108. $8$

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Convert improper fractions:

109. $\frac{39}{4}$
110. $\frac{33}{4}$
111. $\frac{35}{4}$
112. $\frac{11}{4}$
113. $\frac{7}{3}$
114. $\frac{8}{5}$
115. $\frac{63}{8}$
116. $\frac{11}{6}$
117. $\frac{41}{5}$
118. $\frac{27}{4}$
119. $\frac{7}{3}$
120. $\frac{37}{4}$
121. $\frac{17}{2}$
122. $\frac{42}{5}$
123. $\frac{11}{3}$
124. $\frac{4}{3}$

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Let me know if you'd like this in a printable format or need explanations for any specific problem!