Explanation:
We need to translate each phrase into a variable expression using only the letter
N (capital N) for the unknown number.
Let’s go one by one:
1)
Four more than half a number
→ Half a number = N/2
→ Four more than that = N/2 + 4
✔ Answer:
N/2+4
2)
Ten less than one half a number
→ One half a number = N/2
→ Ten less than that = N/2 − 10
✔ Answer:
N/2-10
3)
Three plus the product of a number and 5
→ Product of a number and 5 = 5N
→ Three plus that = 3 + 5N
✔ Answer:
3+5N
4)
Four more than three times a number
→ Three times a number = 3N
→ Four more = 3N + 4
✔ Answer:
3N+4
5)
Eight times the sum of a number and 2
→ Sum of a number and 2 = N + 2
→ Eight times that = 8(N + 2)
✔ Answer:
8(N+2)
6)
Two less than 4 times a number
→ 4 times a number = 4N
→ Two less = 4N − 2
✔ Answer:
4N-2
7)
The quotient of 3 and a number
→ Quotient means division: 3 ÷ N = 3/N
✔ Answer:
3/N
8)
The difference between 3 times a number and 6
→ 3 times a number = 3N
→ Difference between that and 6 = 3N − 6
✔ Answer:
3N-6
9)
Nine increased by twice a number
→ Twice a number = 2N
→ Nine increased by that = 9 + 2N
✔ Answer:
9+2N
10)
Seven times the difference of a number and 5
→ Difference of a number and 5 = N − 5
→ Seven times that = 7(N − 5)
✔ Answer:
7(N-5)
Now the second part — represent each situation with a variable expression:
11) You have 20 pieces of candy, evenly distribute to F friends.
→ Each friend gets total candy ÷ number of friends = 20 / F
✔ Answer:
20/F
12) Amy is A years old; you are 3 years older.
→ Your age = A + 3
✔ Answer:
A+3
13) Length of rectangle is 5 less than twice the width (w).
→ Twice the width = 2w
→ 5 less than that = 2w − 5
✔ Answer:
2w-5
Double-check all:
- All use only given variables (N, F, A, w), no extra spaces.
- Correct order of operations (parentheses where needed).
- No extra characters.
Final Answer:
1)N/2+4
2)N/2-10
3)3+5N
4)3N+4
5)8(N+2)
6)4N-2
7)3/N
8)3N-6
9)9+2N
10)7(N-5)
11)20/F
12)A+3
13)2w-5
Parent Tip: Review the logic above to help your child master the concept of translating phrases worksheet answers.
