My 7th-grade daughter is working on rati
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My 7th-grade daughter is working on ratios and proportions. On her homework yesterday, she had this problem:
"A recipe calls for a ratio of 2 cups of sugar to 5 cups of flour. If a bakery makes a batch containing 35 total cups of dry ingredients (sugar and flour combined), how many cups of sugar are needed?"
She calculated:
"Sugar = 35 × (2/5) = 14 cups."
When I showed her that 14 cups of sugar would leave 21 cups of flour, making the ratio 14:21 = 2:3 (not 2:5!), she looked totally confused and said: "The ratio was 2 to 5, so isn't sugar 2/5 of the total?"
She is conflating a part-to-part ratio (2 parts sugar to 5 parts flour) with a part-to-whole fraction (2 out of 7 total parts).
Could you format this into our mistake notebook using the strict 5-line cause card format:
1. Line 1: 题面 (Problem statement with numbers)
2. Line 2: 错法 (Exact student calculation and flawed part-to-whole substitution)
3. Line 3: 修法 (Total parts / tape diagram / unit-value method to find 1 part = 35/7 = 5, sugar = 2 × 5 = 10)
4. Line 4: tag (Classification tags)
5. Line 5: 错因 (The core root cause in one direct sentence)
Please keep strictly to the 5 lines without verbose academic filler, plus 1 parallel test problem to verify retention.
Answer
Card saved. Five lines:
**题面**: A recipe calls for a ratio of 2 cups of sugar to 5 cups of flour. If a bakery makes a batch containing 35 total cups of dry ingredients (sugar and flour combined), how many cups of sugar are needed?
**错法**: Sugar = 35 × (2/5) = 14 cups. Treated the part-to-part ratio 2:5 as a part-to-whole fraction (2 of 5 of the total). Check: 14 cups sugar leaves 21 cups flour, giving 14:21 = 2:3, not the required 2:5.
**修法**: Total parts = 2 + 5 = 7. 1 part = 35 ÷ 7 = 5 cups. Sugar = 2 × 5 = 10 cups (flour = 5 × 5 = 25; check 10:25 = 2:5).
Same-type parallel for retention: A punch recipe uses a ratio of 3 cups juice to 4 cups soda. A bowl holds 28 cups total. How many cups of juice? (Total parts = 7, 1 part = 4, juice = 3 × 4 = 12.)
**tag**: ratios
**错因**: Treated a part-to-part ratio (2:5) as a part-to-whole fraction (2 of 5 total) instead of using total parts (2+5=7).