Let's translate these word problems into mathematical expressions and solve them.

1. "The quotient of twenty-one and, five less two is seven."

• Translation: The quotient means division, and "five less two" means $5 - 2$. $\frac{21}{5 - 2} = 7$
• Simplifying: $\frac{21}{3} = 7$ This is correct because $\frac{21}{3} = 7$.

2. "The quotient of 'fifteen and five' and 'twelve and four' is one."

• Translation: The quotient of "fifteen and five" means $15 + 5$, and "twelve and four" means $12 + 4$. $\frac{15 + 5}{12 + 4} = 1$
• Simplifying: $\frac{20}{16} = 1$ This is incorrect since $\frac{20}{16} = \frac{5}{4} \neq 1$. There seems to be no solution here.

3. "The sum of six and four, diminished by seven is equal to three."

• Translation: The sum of six and four is $6 + 4$, and diminished by seven means subtracting 7. $(6 + 4) - 7 = 3$
• Simplifying: $10 - 7 = 3$ This is correct.

4. "Twice the difference of ten and eight is four."

• Translation: The difference of ten and eight is $10 - 8$, and twice means multiplying by 2. $2 \times (10 - 8) = 4$
• Simplifying: $2 \times 2 = 4$ This is correct.

Would you like more details on any of these solutions?

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Here are 5 related questions for practice:

1. The quotient of thirty and six is five. True or false?
2. The sum of eight and nine, diminished by three, is equal to fourteen.
3. Twice the sum of five and seven is twenty-four.
4. The difference between fifteen and six, divided by three, is three.
5. The product of four and three, diminished by five, is equal to seven.

Tip: When translating word problems into math, pay attention to operations like "quotient" (division) and "diminished by" (subtraction).