Chef Reyes runs a catering kitchen where dividing fractions and mixed numbers decides every order — including the leftovers.
Chef Reyes started the lunch rush with a full pot of soup. There were 4½ cups, and each bowl is served as ¾ cup. "How many bowls can I plate?" To divide a mixed number, the chef first rewrote it as an improper fraction.
4½ ÷ ¾ = 9/2 ÷ 3/4 = 9/2 × 4/3 = 36/6 = 6 bowls.
Why does Chef Reyes rewrite 4½ as 9/2 before dividing?
There are 6 cups of chili. Each serving is ¾ cup. How many full servings? (6 ÷ ¾)
The chef had 5/6 cup of sauce, ladled in ⅓-cup portions. "Five-sixths divided by one-third," he muttered. The answer was not a whole number — and that meant something real.
5/6 ÷ ⅓ = 5/6 × 3/1 = 15/6 = 2½ portions. So 2 full portions, with half a portion of sauce left over.
The answer 2½ portions tells the chef what, in real terms?
Compute ¾ ÷ ⅓. Write your answer as a fraction or a decimal.
A dessert order: 3⅓ cups of mousse, split equally among 5 dishes. Here the chef divided a mixed number by a whole number.
3⅓ ÷ 5 = 10/3 ÷ 5 = 10/3 × 1/5 = 10/15 = ⅔ cup per dish.
2½ cups of glaze are split equally among 5 cakes. How much glaze per cake? (Write a fraction or decimal.)
For a big event, the chef had 7 cups of dressing, served in ⅔-cup cups. "How many can I fill, and what's left?" The exact quotient guided the order.
7 ÷ ⅔ = 7 × 3/2 = 21/2 = 10½. So 10 full cups, with half a cup of dressing remaining.
Compute 5 ÷ ⅔ exactly. (Write a fraction or decimal.)
Across the story, why does the chef care about the exact quotient (like 10½), not just a rounded number?
Choose one prompt. Write a clear paragraph (5–7 sentences) using numbers from the story as evidence.
Optional academic frame: "The quotient ______ means ______; therefore the chef should ______."
The chef has 8 cups of broth and wants to fill as many ¾-cup mugs as possible. How many full mugs can he fill, and exactly how much broth is left over? Explain your reasoning. (Try it, then check with your teacher.)
| Category | 4 — Advanced | 3 — Proficient | 2 — Developing |
|---|---|---|---|
| Comprehension & inference | All analysis questions correct; interprets remainders in context | 2 of 3 correct | 1 correct |
| Multi-step math | All 4 Solve-It answers correct (whole÷fraction, fraction÷fraction, mixed÷whole, exact quotient) | 3 correct | 2 correct |
| Mathematical argument | Clear claim; interprets the fraction part with specific numbers | Claim with some evidence | States a claim with little evidence |
Grading accepts equivalent forms (9/4 or 2.25; 1/2 or 0.5; 15/2 or 7.5).