Let’s solve each problem step by step.
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Problem 1:
Mr. Swanson has
c students. He picks up
5 new students.
→ New number of students = original + new =
c + 5
That’s the algebraic expression.
Now, if there were
27 students originally (so c = 27):
Numerical expression:
27 + 5
Answer:
32
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Problem 2:
Pratap has
six times as many coins as Yoshiko.
Yoshiko has
y coins.
→ Pratap’s coins = 6 × y =
6y
Algebraic expression:
6y
If Yoshiko has
47 coins (y = 47):
Numerical expression:
6 × 47
Calculate:
6 × 40 = 240
6 × 7 = 42
240 + 42 =
282
Answer:
282
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Problem 3:
Ayana runs
13 laps less than Emma.
We pick a variable for Emma’s laps — let’s use
e.
→ Ayana’s laps = e - 13
Algebraic expression:
e - 13
Emma runs
32 laps (e = 32):
Numerical expression:
32 - 13
Answer:
19
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Problem 4:
Nicki’s age is the
quotient of Granny’s age and six.
Quotient means division.
Pick a variable for Granny’s age — let’s use
g.
→ Nicki’s age = g ÷ 6 =
g/6
Algebraic expression:
g/6
Granny is
72 years old (g = 72):
Numerical expression:
72 ÷ 6
Answer:
12
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Problem 5:
Number of 8th grade students is
2/3 of the number of 7th grade students.
Pick a variable for 7th grade — let’s use
s.
→ 8th grade = (2/3) × s =
(2/3)s
Algebraic expression:
(2/3)s
There are
96 students in 7th grade (s = 96):
Numerical expression:
(2/3) × 96
Calculate:
First, divide 96 by 3 → 32
Then multiply by 2 → 64
Answer:
64
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Final Answer:
1. Algebraic Expression: c + 5
Numerical Expression: 27 + 5
Answer: 32
2. Algebraic Expression: 6y
Numerical Expression: 6 × 47
Answer: 282
3. Algebraic Expression: e - 13
Numerical Expression: 32 - 13
Answer: 19
4. Algebraic Expression: g/6
Numerical Expression: 72 ÷ 6
Answer: 12
5. Algebraic Expression: (2/3)s
Numerical Expression: (2/3) × 96
Answer: 64
Parent Tip: Review the logic above to help your child master the concept of writing algebraic equations worksheet.
