A three-day review sequence designed to strengthen core fraction operations (addition, subtraction, and mixed numbers) before transitioning to negative rational numbers in NYS Grade 7.
Estimate answer relative to \(\frac{1}{2}\): ____________
Show Work Here
Final Answer:
Problem 2 Unlike Denominators
Evaluate: \(\frac{4}{5} - \frac{1}{3}\)
Convert to 15ths first, then compute!
Show Work Here
Final Answer:
Explain Your Thinking: Why does estimating before calculating help you catch mistakes in fraction operations?
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9. Fabric Cut: Elena has \(\frac{7}{8}\) yard of linen. She cuts off \(\frac{1}{4}\) yard for a headband and \(\frac{3}{8}\) yard for a wrist strap. How much fabric does Elena have left?
LEFT:
10. Hydration Scale: A gym water bottle is \(\frac{4}{5}\) full. After a heavy workout session, it is only \(\frac{1}{4}\) full. What fraction of the full capacity was consumed?
Show off your detective skills! Solve each of the 5 problems completely. Show your work clearly and write your final simplified answers in the boxes provided.
Question 1 • Estimation Reasonableness
Without calculating, determine which is the most reasonable estimate for: \(\frac{11}{12} - \frac{1}{5}\)
A) Close to 0 B) Close to \(\frac{1}{2}\) C) Close to \(\frac{3}{4}\) D) Greater than 1
Choice
Question 2 • Subtraction Drill
Evaluate and simplify to lowest terms: \(\frac{5}{6} - \frac{1}{3}\)
Answer Box
Question 3 • Unlike Subtraction
Evaluate and simplify to lowest terms: \(\frac{3}{5} - \frac{1}{4}\)
Answer Box
Question 4 • Multi-Step Problem
A garden bed is \(\frac{9}{10}\) planted with vegetables. Tomatoes take up \(\frac{1}{2}\) of the bed and peppers take up \(\frac{1}{5}\). How much of the garden is left for other vegetables?
Answer Box
Question 5 • Reasonableness Critique
Alex solved a subtraction problem and got \(\frac{7}{6}\). Explain why an answer of \(\frac{7}{6}\) is impossible when subtracting two proper fractions (like \(\frac{3}{4} - \frac{1}{3}\)).
7. Carpenter Wood Cut: A carpenter has a walnut board measuring \(8\frac{1}{2}\) feet. He saws off a piece that is \(3\frac{3}{4}\) feet long to make a shelf. How long is the remaining walnut board?
REMAINING:
8. Recipe Liquids: A baking recipe requires \(2\frac{2}{3}\) cups of heavy cream and \(1\frac{3}{4}\) cups of lukewarm water. What is the total volume of liquid in cups?
TOTAL LIQUID:
The Summit Challenge Zone
9. Triple Sum: Solve and simplify the triple mixed sum: \(1\frac{1}{2} + 2\frac{2}{3} + \frac{3}{4}\)
ANSWER:
10. Double Subtraction: Solve and simplify from a whole number: \(10 - 2\frac{1}{3} - 3\frac{1}{2}\)
Chloe writes: "I did 5 - 2 = 3. Then for the fractions, I couldn't do 1/3 - 2/3, so I just flipped them and did 2/3 - 1/3 = 1/3. So my answer is 3 1/3."
Conquer the peak! Solve each of the 5 problems completely. Show your work clearly and write your final simplified answers in the boxes provided.
Question 1 • Conversion Check
Identify which of the following is equivalent to the mixed number \(4\frac{3}{5}\):
A) \(\frac{12}{5}\) B) \(\frac{17}{5}\) C) \(\frac{23}{5}\) D) \(\frac{43}{5}\)
Choice
Question 2 • Adding Mixed Numbers
Evaluate and simplify to lowest terms: \(2\frac{1}{3} + 1\frac{1}{4}\)
Answer Box
Question 3 • Subtracting with Borrowing
Evaluate and simplify to lowest terms: \(3\frac{1}{5} - 1\frac{1}{2}\)
Answer Box
Question 4 • Multi-Step Problem
Mia had \(5\frac{1}{2}\) cups of sugar. She used \(1\frac{3}{4}\) cups to bake cookies and \(2\frac{1}{8}\) cups for a cake. How many cups of sugar does Mia have left?
Answer Box
Question 5 • Conceptual Explanations
A student claims that when borrowing with mixed numbers, you should always add 10 to the numerator, just like in decimal borrowing. Why is this claim incorrect? Use a 1-sentence math justification.
