Let's solve each part step by step.
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Part 1: Translate each phrase into a variable expression. Use only the letter N (capital N) for the variable.
1)
Four more than half a number
→ Half a number is $ \frac{1}{2}N $, and four more than that is:
$ \frac{1}{2}N+4 $
2)
Ten less than one half a number
→ One half a number is $ \frac{1}{2}N $, ten less than that is:
$ \frac{1}{2}N-10 $
3)
Three plus the product of a number and 5
→ Product of a number and 5 is $ 5N $, three plus that is:
$ 3+5N $
4)
Four more than three times a number
→ Three times a number is $ 3N $, four more than that is:
$ 3N+4 $
5)
Eight times the sum of a number and 2
→ Sum of a number and 2 is $ N+2 $, eight times that is:
$ 8(N+2) $
6)
Two less than 4 times a number
→ Four times a number is $ 4N $, two less than that is:
$ 4N-2 $
7)
The quotient of 3 and a number
→ Quotient means division: $ \frac{3}{N} $
$ \frac{3}{N} $
8)
The difference between 3 times a number and 6
→ 3 times a number is $ 3N $, difference with 6 is:
$ 3N-6 $
9)
Nine increased by twice a number
→ Twice a number is $ 2N $, nine increased by that is:
$ 9+2N $
10)
Seven times the difference of a number and 5
→ Difference of a number and 5 is $ N-5 $, seven times that is:
$ 7(N-5) $
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Part 2: Represent each situation with a variable expression.
11)
You have 20 pieces of candy that you want to evenly distribute to F of your friends. Write an expression to show the number of pieces of candy each friend would get.
→ Total candy divided by number of friends:
$ \frac{20}{F} $
12)
Your friend Amy is A years old but you are 3 years older than her. Write an expression that would represent your age.
→ You are 3 years older than Amy:
$ A+3 $
13)
The length of a rectangle is 5 less than twice the width (w). Write an expression for the length of the rectangle.
→ Twice the width is $ 2w $, 5 less than that is:
$ 2w-5 $
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✔ Final Answers:
1) $ \frac{1}{2}N+4 $
2) $ \frac{1}{2}N-10 $
3) $ 3+5N $
4) $ 3N+4 $
5) $ 8(N+2) $
6) $ 4N-2 $
7) $ \frac{3}{N} $
8) $ 3N-6 $
9) $ 9+2N $
10) $ 7(N-5) $
11) $ \frac{20}{F} $
12) $ A+3 $
13) $ 2w-5 $
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Note: For problems 1–10, use
N as the variable. For 11–13, variables are given (F, A, w), so use those accordingly.
Let me know if you'd like these formatted in a specific way (e.g., for a worksheet box).
Parent Tip: Review the logic above to help your child master the concept of translating words into math worksheet.
