Let's solve each problem step by step by translating the
word phrases into
numerical expressions.
---
1. The difference of ten and three
- "Difference" means subtraction.
- So, subtract 3 from 10.
✔ Expression:
$$
10 - 3
$$
---
2. The product of five and nine
- "Product" means multiplication.
- Multiply 5 and 9.
✔ Expression:
$$
5 \times 9
$$
---
3. The sum of three and eleven
- "Sum" means addition.
- Add 3 and 11.
✔ Expression:
$$
3 + 11
$$
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4. The quotient of twenty and two
- "Quotient" means division.
- Divide 20 by 2.
✔ Expression:
$$
20 \div 2
$$
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5. One half the sum of nine and three
- First, find the
sum of nine and three: $9 + 3$
- Then take
one half of that sum: $\frac{1}{2} \times (9 + 3)$
✔ Expression:
$$
\frac{1}{2} \times (9 + 3)
$$
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6. Two times the difference of six and three
- First, find the
difference of six and three: $6 - 3$
- Then multiply by 2: $2 \times (6 - 3)$
✔ Expression:
$$
2 \times (6 - 3)
$$
---
7. The quotient of fifteen and three minus four
- This is tricky. Let’s break it down:
- "The quotient of fifteen and three" → $15 \div 3$
- Then
minus four → subtract 4 from that result.
So: $(15 \div 3) - 4$
✔ Expression:
$$
(15 \div 3) - 4
$$
> Note: If it were "the quotient of fifteen and (three minus four)", it would be $15 \div (3 - 4)$, but that would be negative and likely not intended. Based on standard phrasing, this is interpreted as
(quotient) minus four.
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8. Seven times four then add ten
- "Seven times four" → $7 \times 4$
- Then "add ten" → $+ 10$
✔ Expression:
$$
(7 \times 4) + 10
$$
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✔ Final Answers:
1. $10 - 3$
2. $5 \times 9$
3. $3 + 11$
4. $20 \div 2$
5. $\frac{1}{2} \times (9 + 3)$
6. $2 \times (6 - 3)$
7. $(15 \div 3) - 4$
8. $(7 \times 4) + 10$
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Let me know if you'd like these evaluated too!
Parent Tip: Review the logic above to help your child master the concept of numerical expression worksheet.
