Let's solve each part step by step.
---
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 $, then 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 $, then three plus that:
$ 3 + 5N $
4)
Four more than three times a number
→ Three times a number is $ 3N $, four more than that:
$ 3N + 4 $
5)
Eight times the sum of a number and 2
→ Sum of a number and 2 is $ N + 2 $, eight times that:
$ 8(N + 2) $
6)
Two less than 4 times a number
→ Four times a number is $ 4N $, two less than that:
$ 4N - 2 $
7)
The quotient of 3 and a number
→ Quotient means division: $ \frac{3}{N} $
8)
The difference between 3 times a number and 6
→ 3 times a number is $ 3N $, difference with 6: $ 3N - 6 $
9)
Nine increased by twice a number
→ Twice a number is $ 2N $, nine increased by that: $ 9 + 2N $
10)
Seven times the difference of a number and 5
→ Difference of a number and 5 is $ N - 5 $, seven times that:
$ 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.
→ Your age = Amy's age + 3:
$ 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:
$ 2w - 5 $
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✔ Final Answers:
Part 1:
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) $
Part 2:
11) $ \frac{20}{F} $
12) $ A+3 $
13) $ 2w-5 $
---
Now, since the instructions say to
type your answer in the box next to the phrase, and
do not put any space between characters, here is the formatted version as if filling in boxes:
```
1) 1/2N+4
2) 1/2N-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
```
> Note: In some contexts, fractions like $ \frac{1}{2}N $ might be written as `0.5N`, but since the problem uses "half", it's acceptable to write `1/2N`. However, if spaces are not allowed and clarity is needed, `1/2N` is standard.
✔ All expressions use appropriate variables and follow the rules.
Parent Tip: Review the logic above to help your child master the concept of translating words to algebraic expressions worksheet.
