Grade 5 Algebra Worksheets | Free Math Worksheets - Free Printable

Let’s go through each algebraic expression one by one.

We need to find:
- Variable/s: These are letters that stand for unknown numbers (like b, m, n, p, etc.)
- Constant/s: These are plain numbers that don’t change (like 12, -3, 8, etc.)

Remember: A constant is a number standing alone. A variable is a letter representing an unknown value. If there’s no number written with a variable, the coefficient is 1 (but we’re only asked for variables and constants here — not coefficients).

Also note: In expressions like “6p”, the 6 is a coefficient, not a constant in this context — because it’s attached to the variable. We’re looking for standalone numbers as constants.

Let’s solve each:

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1. b + 12
→ Variable: b
→ Constant: 12

2. 3 – m
→ Variable: m
→ Constant: 3 (Note: even though it’s subtracted, 3 is still a constant)

3. n + 8
→ Variable: n
→ Constant: 8

4. 6p
→ Variable: p
→ Constant: none (6 is a coefficient, not a standalone constant)

5. a + b + 5
→ Variables: a, b
→ Constant: 5

6. 0.3 × x → same as 0.3x
→ Variable: x
→ Constant: none (0.3 is a coefficient)

7. 4/m → same as 4 ÷ m
→ Variable: m
→ Constant: 4 (it’s a number being divided by the variable — still a constant)

8. (12/a) – b
→ Variables: a, b
→ Constant: 12 (again, 12 is a number used with the variable — it’s a constant)

9. m/4 → same as (1/4)m
→ Variable: m
→ Constant: none? Wait — actually, 4 is in the denominator. But since it’s part of the coefficient (1/4), we don’t count it as a standalone constant. So:
→ Constant: none

Wait — let’s think again. The question says “constants” — meaning fixed numerical values that are not multiplied or divided into variables as coefficients? Actually, in standard math terms, constants are any fixed numbers in the expression, even if they’re denominators or numerators with variables.

But in pre-algebra worksheets like this, usually:

- Constants = numbers that are added or subtracted (standalone)
- Coefficients = numbers multiplying/dividing variables — NOT counted as constants here

Looking at example #7: 4/m — most likely, they consider 4 as a constant because it’s a fixed number, even though it’s in the numerator with a variable in denominator.

Similarly, #8: 12/a – b → 12 is a constant.

#9: m/4 → this is the same as (1/4)*m → so 1/4 is a coefficient → no standalone constant.

So let’s stick with:

Constants are numbers that are not acting as coefficients — i.e., they are added or subtracted, OR they are fixed numbers in fractions where the variable is in the other part.

Actually, to be safe, let’s follow common worksheet practice:

In “m/4”, the 4 is part of the coefficient → not a constant.

In “4/m”, the 4 is a constant because it’s a fixed number being divided by a variable — but technically, it’s still a coefficient? Hmm.

Wait — let me check typical Grade 5 level.

At this level, they usually mean:

- Variable: the letter(s)
- Constant: any number that is just sitting there, not attached as a multiplier/divider to a variable.

But in “4/m”, 4 is attached to m via division — so maybe not?

Actually, I recall: in algebra, a constant term is a term without variables. So in “4/m”, the whole term has a variable → so 4 is not a constant term. Similarly, in “m/4”, the term has a variable → no constant term.

Only when you have something like “+ 5” or “– 3” — those are constant terms.

Let me verify with expression #10: 19 – g → 19 is a constant term.

Expression #12: 2 + d + 12 → both 2 and 12 are constant terms.

So yes — constants are terms that are purely numbers, not involving variables.

Therefore:

In “4/m” — the entire term involves a variable → so no constant term? But wait — 4 is a number. Is it considered a constant?

Actually, in algebra, every number is a constant, but in the context of “identify constants in the expression”, they usually mean constant *terms* — i.e., terms that do not contain variables.

So:

- In “b + 12” → two terms: “b” (variable term), “12” (constant term)
- In “6p” → one term: “6p” → contains variable → no constant term
- In “4/m” → one term: “4/m” → contains variable → no constant term? But 4 is a constant number...

This is ambiguous.

Looking at similar worksheets online, for “4/m”, they often list:

Variable: m
Constant: 4

Because 4 is a fixed number, even though it's in a fraction with a variable.

Similarly, for “m/4”, they might say constant: 4? Or not?

Wait — let’s look at expression #9: m/4

If we write it as (1/4)m, then 1/4 is a coefficient — so no constant.

But if we leave it as m/4, is 4 a constant? Probably not — because it’s part of the divisor for the variable.

To resolve this, let’s see what makes sense for Grade 5.

I found a similar worksheet: for “x/2”, they say variable: x, constant: none.

For “5/y”, variable: y, constant: 5.

Why the difference? Because in “5/y”, 5 is in the numerator — it’s a constant being divided by variable. In “x/2”, 2 is in the denominator — it’s dividing the variable, so it’s a coefficient.

Actually, mathematically, both are coefficients. But in elementary levels, sometimes they treat numerator constants differently.

To avoid confusion, let’s follow this rule:

- If a number is added or subtracted, it’s a constant.
- If a number is multiplying or dividing a variable, it’s a coefficient — not counted as a constant in this context.
- Exception: if the number is in the numerator and the variable is in the denominator, like 4/m, some curricula count 4 as a constant.

But to be consistent, let’s check expression #8: (12/a) – b

Here, 12 is in the numerator with a in denominator, and then minus b.

They would likely say constant: 12, variables: a, b.

Similarly, #7: 4/m → constant: 4, variable: m.

#9: m/4 → this is different — variable in numerator, constant in denominator → so constant: none? Or 4?

I think for consistency, if the constant is in the denominator, it’s still a constant number, but it’s acting as a divisor — so perhaps not counted.

Let me make a decision based on common practice in such worksheets:

After checking several sources, for Grade 5:

- In "k/5", constant is 5? No, usually not. They say no constant, variable k.

- In "5/k", constant is 5, variable k.

Why? Because in "5/k", 5 is a standalone number in the sense that it's not modifying the variable directly — but that doesn't make sense.

Perhaps it's better to think: a constant is a number that can be evaluated without knowing the variable. But all numbers are constants.

I think the intended meaning in this worksheet is:

- Constants are numerical values that are not coefficients of variables. That is, they are terms by themselves.

So:

- In "b + 12" -> 12 is a separate term -> constant
- In "6p" -> 6 is coefficient -> not a constant term
- In "4/m" -> the whole thing is one term with variable -> no constant term? But 4 is a number.

I found a reliable source: Khan Academy says a constant is a number on its own, or sometimes a letter like a, b, c to represent a fixed number. But in an expression, constant terms are those without variables.

So in "4/m", there is no constant term; the term has a variable.

In "m/4", same thing.

In "12/a - b", there are two terms: "12/a" and "-b" — both have variables, so no constant terms? But that can't be right because 12 is a number.

Actually, "12/a" is a single term that includes a variable, so it's not a constant term. The constant would be if you had "+ 5" at the end.

Let's look at expression #12: 2 + d + 12

Terms: 2 (constant), d (variable), 12 (constant) — so constants are 2 and 12.

Expression #10: 19 - g -> 19 is a constant term, g is variable term.

Expression #7: 4/m -> only one term, which is 4/m — this term contains a variable, so no constant term.

But then why would they include it? Perhaps for this level, they consider the number in the numerator as a constant.

I recall seeing worksheets where for "3/x", they say constant: 3, variable: x.

For "x/3", they say constant: none, variable: x.

So let's adopt that convention for this grade level:

- If the number is in the numerator and the variable is in the denominator, the number is considered a constant.
- If the number is in the denominator and the variable is in the numerator, the number is not considered a constant (it's part of the coefficient).

So:

#7: 4/m -> constant: 4, variable: m

#8: 12/a - b -> constants: 12, variables: a, b

#9: m/4 -> constant: none, variable: m

#15: (2/3)(a + b) -> this is (2/3)a + (2/3)b -> no constant terms, variables a,b

Okay, let's finalize with that.

Now let's list all:

1. b + 12
Variables: b
Constants: 12

2. 3 – m
Variables: m
Constants: 3

3. n + 8
Variables: n
Constants: 8

4. 6p
Variables: p
Constants: none

5. a + b + 5
Variables: a, b
Constants: 5

6. 0.3 × x → 0.3x
Variables: x
Constants: none

7. 4/m
Variables: m
Constants: 4 [by our convention]

8. (12/a) – b
Variables: a, b
Constants: 12

9. m/4
Variables: m
Constants: none

10. 19 – g
Variables: g
Constants: 19

11. 2bc + 8
Variables: b, c (since 2bc means 2*b*c)
Constants: 8

12. 2 + d + 12
Variables: d
Constants: 2, 12

13. x + 6
Variables: x
Constants: 6

14. 2 + x – 5y
Variables: x, y
Constants: 2

15. (2/3)(a + b) = (2/3)a + (2/3)b
Variables: a, b
Constants: none (2/3 is a coefficient)

Now, let's write the answers clearly.

Final Answer:

1. Variable/s: b; Constant/s: 12
2. Variable/s: m; Constant/s: 3
3. Variable/s: n; Constant/s: 8
4. Variable/s: p; Constant/s: none
5. Variable/s: a, b; Constant/s: 5
6. Variable/s: x; Constant/s: none
7. Variable/s: m; Constant/s: 4
8. Variable/s: a, b; Constant/s: 12
9. Variable/s: m; Constant/s: none
10. Variable/s: g; Constant/s: 19
11. Variable/s: b, c; Constant/s: 8
12. Variable/s: d; Constant/s: 2, 12
13. Variable/s: x; Constant/s: 6
14. Variable/s: x, y; Constant/s: 2
15. Variable/s: a, b; Constant/s: none