Fraction Fusion Practice Worksheet
Grade 7 Mathematics
Fraction Fusion: Mixed Number Operations
Name:
Date:
Period:
Directions: Find each sum or difference. Find a common denominator (LCD), rewrite equivalent fractions, show any regrouping/carrying, and write your final answer in simplest form.
Page 1 of 4
1 Addition
\( 3\frac{1}{4} + 2\frac{1}{3} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
2 Subtraction
\( 5\frac{5}{6} - 2\frac{1}{4} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
3 Addition
\( 4\frac{2}{5} + 3\frac{7}{10} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
4 Regrouping
\( 6\frac{1}{3} - 2\frac{3}{4} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
5 Regrouping
\( 7\frac{3}{8} - 4\frac{5}{6} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
Fraction Fusion: Mixed Number Operations
Problems 6–10
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Page 2 of 4
6 Addition
\( 2\frac{5}{9} + 4\frac{1}{6} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
7 Regrouping
\( 8\frac{1}{4} - 3\frac{5}{8} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
8 Addition
\( 5\frac{2}{7} + 3\frac{1}{2} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
9 Regrouping
\( 9\frac{1}{5} - 6\frac{2}{3} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
10 Addition (Carrying)
\( 4\frac{7}{12} + 5\frac{5}{8} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
Fraction Fusion: Mixed Number Operations
Problems 11–15
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Page 3 of 4
11 Simplify Result
\( 10\frac{3}{10} - 4\frac{4}{5} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
12 Addition (Carrying)
\( 6\frac{2}{3} + 1\frac{7}{9} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
13 Regrouping
\( 8\frac{1}{6} - 3\frac{7}{8} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
14 Addition
\( 3\frac{4}{15} + 6\frac{7}{10} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
15 Regrouping
\( 7\frac{1}{8} - 2\frac{5}{12} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
Fraction Fusion: Mixed Number Operations
Problems 16–20
Name:
Page 4 of 4
16 Addition
\( 5\frac{5}{12} + 2\frac{11}{16} \)
Final Answer:
Show Your Work (LCD, equivalent fractions, steps):
17
Hiking Distance: Marcus hiked \( 4\frac{2}{3} \) miles along a scenic mountain trail on Saturday and \( 3\frac{3}{4} \) miles on Sunday. What was the total distance Marcus hiked over the weekend?
Show Your Work:
Final Answer (include units):
18
Bakery Inventory: A pastry chef had a container holding \( 6\frac{1}{2} \) pounds of flour. She used \( 2\frac{5}{8} \) pounds to prepare a batch of sourdough bread. How many pounds of flour remain?
Show Your Work:
Final Answer (include units):
19
Woodworking Cut: An oak timber plank measures \( 8\frac{1}{4} \) feet in total length. A carpenter cuts off a segment measuring \( 3\frac{5}{6} \) feet for a wall bookshelf. How long is the remaining timber?
Show Your Work:
Final Answer (include units):
20
Laboratory Solution: In science class, a graduated beaker holds \( 3\frac{7}{10} \) ounces of saline solution. An experimenter adds \( 2\frac{4}{15} \) ounces more. What is the final liquid volume in the beaker?
Show Your Work:
Final Answer (include units):
Fraction Fusion Answer Key
Teacher Guide & Solutions
Fraction Fusion: Answer Key (Problems 1–10)
Full Worked Solutions
Complete step-by-step solutions showing common denominators (LCD), equivalent conversions, regrouping/carrying steps, and final simplified form.
#1. \( 3\frac{1}{4} + 2\frac{1}{3} \) LCD = 12
• Convert: \( 3\frac{3}{12} + 2\frac{4}{12} \)
• Whole: \( 3 + 2 = 5 \); Fractions: \( \frac{3+4}{12} = \frac{7}{12} \)
Answer: \( 5\frac{7}{12} \)
#2. \( 5\frac{5}{6} - 2\frac{1}{4} \) LCD = 12
• Convert: \( 5\frac{10}{12} - 2\frac{3}{12} \)
• Whole: \( 5 - 2 = 3 \); Fractions: \( \frac{10-3}{12} = \frac{7}{12} \)
Answer: \( 3\frac{7}{12} \)
#3. \( 4\frac{2}{5} + 3\frac{7}{10} \) LCD = 10
• Convert: \( 4\frac{4}{10} + 3\frac{7}{10} = 7\frac{11}{10} \)
• Improper regroup: \( 7 + 1\frac{1}{10} = 8\frac{1}{10} \)
Answer: \( 8\frac{1}{10} \)
#4. \( 6\frac{1}{3} - 2\frac{3}{4} \) Regrouping
• LCD = 12: \( 6\frac{4}{12} - 2\frac{9}{12} \)
• Regroup \( 6\frac{4}{12} \to 5\frac{16}{12} \); then \( 5\frac{16}{12} - 2\frac{9}{12} \)
Answer: \( 3\frac{7}{12} \)
#5. \( 7\frac{3}{8} - 4\frac{5}{6} \) Regrouping
• LCD = 24: \( 7\frac{9}{24} - 4\frac{20}{24} \)
• Regroup \( 7\frac{9}{24} \to 6\frac{33}{24} \); then \( 6\frac{33}{24} - 4\frac{20}{24} \)
Answer: \( 2\frac{13}{24} \)
#6. \( 2\frac{5}{9} + 4\frac{1}{6} \) LCD = 18
• Convert: \( 2\frac{10}{18} + 4\frac{3}{18} \)
• Whole: \( 2 + 4 = 6 \); Fractions: \( \frac{10+3}{18} = \frac{13}{18} \)
Answer: \( 6\frac{13}{18} \)
#7. \( 8\frac{1}{4} - 3\frac{5}{8} \) Regrouping
• LCD = 8: \( 8\frac{2}{8} - 3\frac{5}{8} \)
• Regroup \( 8\frac{2}{8} \to 7\frac{10}{8} \); then \( 7\frac{10}{8} - 3\frac{5}{8} \)
Answer: \( 4\frac{5}{8} \)
#8. \( 5\frac{2}{7} + 3\frac{1}{2} \) LCD = 14
• Convert: \( 5\frac{4}{14} + 3\frac{7}{14} \)
• Whole: \( 5 + 3 = 8 \); Fractions: \( \frac{4+7}{14} = \frac{11}{14} \)
Answer: \( 8\frac{11}{14} \)
#9. \( 9\frac{1}{5} - 6\frac{2}{3} \) Regrouping
• LCD = 15: \( 9\frac{3}{15} - 6\frac{10}{15} \)
• Regroup \( 9\frac{3}{15} \to 8\frac{18}{15} \); then \( 8\frac{18}{15} - 6\frac{10}{15} \)
Answer: \( 2\frac{8}{15} \)
#10. \( 4\frac{7}{12} + 5\frac{5}{8} \) Carrying
• LCD = 24: \( 4\frac{14}{24} + 5\frac{15}{24} = 9\frac{29}{24} \)
• Improper regroup: \( 9 + 1\frac{5}{24} = 10\frac{5}{24} \)
