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Unit 2 Advanced Worksheet

Fraction Challenges

Challenge yourself with complex fraction problems including multi-step operations, word problems, and mixed number conversions.

Question 1: Sarah ate 2/8 of a pizza for lunch and 3/8 for dinner. What fraction of the pizza did she eat in total? Simplify your answer.

Answer: 5/8

Steps:

  1. Add the fractions: 2/8 + 3/8
  2. Add numerators: 2 + 3 = 5
  3. Keep denominator: 8
  4. Result: 5/8 (already in simplest form)

Question 2: A recipe needs 3/4 cup of sugar, but you only have 1/4 cup. How much more do you need?

Answer: 1/2 cup

Steps:

  1. Subtract: 3/4 - 1/4
  2. Subtract numerators: 3 - 1 = 2
  3. Result: 2/4
  4. Simplify: 2/4 = 1/2 cup needed

Question 3: Convert 5 3/4 to an improper fraction.

Answer: 23/4

Steps:

  1. Multiply whole by denominator: 5 × 4 = 20
  2. Add numerator: 20 + 3 = 23
  3. Put over denominator: 23/4

Question 4: Convert 37/5 to a mixed number.

Answer: 7 2/5

Steps:

  1. Divide: 37 ÷ 5 = 7 remainder 2
  2. Whole number: 7
  3. Remainder over denominator: 2/5
  4. Answer: 7 2/5

Question 5: Find three equivalent fractions for 2/3.

Answer: 4/6, 6/9, 8/12 (or others)

Steps:

  1. Multiply both by 2: 4/6
  2. Multiply both by 3: 6/9
  3. Multiply both by 4: 8/12
  4. Any of these work!

Question 6: Tom walked 3/8 mile to school and 5/8 mile to the park. How far did he walk in total? Simplify.

Answer: 1 mile

Steps:

  1. Add: 3/8 + 5/8
  2. Add numerators: 3 + 5 = 8
  3. Result: 8/8
  4. Simplify: 8/8 = 1 mile

Question 7: A rope is 7/10 meter long. You cut off 3/10 meter. How much remains? Simplify.

Answer: 2/5 meter

Steps:

  1. Subtract: 7/10 - 3/10
  2. Subtract numerators: 7 - 3 = 4
  3. Result: 4/10
  4. Simplify: 4÷2=2, 10÷2=5 → 2/5 meter

Question 8: Which is greater: 3 2/5 or 17/5? Show your work.

Answer: 3 2/5 is greater

Steps:

  1. Convert 3 2/5 to improper: (3×5)+2 = 17/5
  2. Compare: 17/5 vs 17/5
  3. Wait! They're equal!
  4. Answer: They are equal (both = 17/5)

Question 9: Simplify the sum: 4/12 + 5/12 + 3/12

Answer: 1

Steps:

  1. Add numerators: 4 + 5 + 3 = 12
  2. Keep denominator: 12
  3. Result: 12/12
  4. Simplify: 12/12 = 1 whole

Question 10: A tank was 9/10 full. After using some water, it's now 3/10 full. What fraction was used?

Answer: 6/10 or 3/5

Steps:

  1. Subtract: 9/10 - 3/10
  2. 9 - 3 = 6
  3. Result: 6/10
  4. Simplify: 6/10 = 3/5 used

Question 11: Express 2 7/8 as an improper fraction.

Answer: 23/8

Steps:

  1. Multiply: 2 × 8 = 16
  2. Add: 16 + 7 = 23
  3. Over 8: 23/8

Question 12: Convert 41/6 to a mixed number. Simplify the fraction part if possible.

Answer: 6 5/6

Steps:

  1. Divide: 41 ÷ 6 = 6 R 5
  2. Whole: 6, Fraction: 5/6
  3. 5/6 is already simplified
  4. Answer: 6 5/6

Question 13: Maya had 4/5 of her homework done. She completed another 1/5. Is she finished?

Answer: Yes, she's finished (5/5 = 1)

Steps:

  1. Add: 4/5 + 1/5
  2. 4 + 1 = 5
  3. Result: 5/5
  4. 5/5 = 1 whole = Complete!

Question 14: Simplify: (6/8 + 2/8) - 3/8

Answer: 5/8

Steps:

  1. First add: 6/8 + 2/8 = 8/8
  2. Then subtract: 8/8 - 3/8 = 5/8
  3. Result: 5/8
  4. Already in simplest form

Question 15: A pizza is cut into 12 slices. You ate 5 slices, your friend ate 4 slices. What fraction is left? Simplify.

Answer: 1/4

Steps:

  1. Total eaten: 5 + 4 = 9 slices
  2. Remaining: 12 - 9 = 3 slices
  3. Fraction: 3/12
  4. Simplify: 3/12 = 1/4

Question 16: Which is larger: 2 3/4 or 10/4? Convert to compare.

Answer: 2 3/4 is larger

Steps:

  1. Convert 2 3/4: (2×4)+3 = 11/4
  2. Compare: 11/4 vs 10/4
  3. 11 > 10
  4. Answer: 2 3/4 is larger

Question 17: A recipe uses 1 2/3 cups milk for batter and 1/3 cup for topping. Total milk needed? Express as mixed number.

Answer: 2 cups

Steps:

  1. Convert 1 2/3 to improper: 5/3
  2. Add: 5/3 + 1/3 = 6/3
  3. Simplify: 6/3 = 2
  4. Answer: 2 cups

Question 18: Simplify completely: 18/24

Answer: 3/4

Steps:

  1. Find GCF of 18 and 24: 6
  2. Divide both: 18÷6=3, 24÷6=4
  3. Answer: 3/4

Question 19: A board is 7 1/4 feet long. You cut off 2 3/4 feet. How much remains? (Convert to improper, subtract, convert back)

Answer: 4 2/4 or 4 1/2 feet

Steps:

  1. Convert: 7 1/4 = 29/4, 2 3/4 = 11/4
  2. Subtract: 29/4 - 11/4 = 18/4
  3. Convert: 18÷4 = 4 R 2 → 4 2/4
  4. Simplify: 4 2/4 = 4 1/2 feet

Question 20: Create an equivalent fraction for 5/6 with denominator 24.

Answer: 20/24

Steps:

  1. 6 × ? = 24 → ? = 4
  2. Multiply numerator by same: 5 × 4 = 20
  3. Answer: 20/24
  4. Check: 20/24 = 5/6 ✓

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