Let’s solve each problem one by one. We’ll write an algebraic expression for each — that means using letters (like x, p, z) and math symbols to show the answer.
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Problem 1:
Mr Swann had
x students.
Then 4 left → so we subtract 4:
x - 4
Then 8 joined → so we add 8:
x - 4 + 8
Simplify:
-4 + 8 = +4
So final expression:
x + 4
✔ Check: If he started with 20 students (x=20), then 4 leave → 16, then 8 join → 24. And 20 + 4 = 24. Correct!
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Problem 2:
Amelia had 18 needles.
She lost
p of them → so we subtract p from 18.
Expression:
18 - p
✔ Check: If she lost 3 needles (p=3), then 18 - 3 = 15 left. Makes sense.
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Problem 3:
There are
z lions total.
3/5 of them are male → so multiply z by 3/5.
Expression:
(3/5) × z or written as
¾z? Wait — no! It says 3/5, not 3/4.
Actually, in math we usually write it as:
(3/5)z or
\frac{3}{5}z
But since we’re writing expressions simply, we can write:
3z/5
✔ Check: If there are 10 lions (z=10), then 3/5 of 10 is 6. And 3×10/5 = 30/5 = 6. Correct!
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Problem 4:
Total distance = 28 km
You’ve already covered
x km
So distance left = total minus what you’ve done
Expression:
28 - x
✔ Check: If you walked 10 km (x=10), then 28 - 10 = 18 km left. Right!
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Problem 5:
“Two-fifth of a certain number” → let’s call the number
n (since it’s not given).
So two-fifths of n =
(2/5)n
“When decreased by 5” → subtract 5
Expression:
(2/5)n - 5
We could also write it as
2n/5 - 5
✔ Check: Let’s say the number is 10. Two-fifths of 10 is 4. Decreased by 5 → 4 - 5 = -1. Expression gives 2×10/5 - 5 = 20/5 - 5 = 4 - 5 = -1. Correct!
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Final Answer:
1.
x + 4
2.
18 - p
3.
3z/5
4.
28 - x
5.
2n/5 - 5
Parent Tip: Review the logic above to help your child master the concept of writing algebraic equations from word problems worksheet.
