Math worksheet for practicing the distributive property with example problems and word problems.

Let’s solve each problem step by step using the Distributive Property.

The distributive property says:
a × (b + c) = a×b + a×c
or
a × (b – c) = a×b – a×c

We’ll use this to rewrite expressions and find missing numbers.

---

Problem 1:

> Use the Distributive Property to write an expression that is equivalent to each of the following. Then evaluate the expression to find the answer.

#### Part A:
(5 + 8) × 7

Step 1: Apply distributive property → multiply 7 by each number inside the parentheses.

→ 5 × 7 + 8 × 7

Step 2: Calculate each part.

5 × 7 = 35
8 × 7 = 56

Step 3: Add them.

35 + 56 = 91

✔ So, (5 + 8) × 7 = 5×7 + 8×7 = 35 + 56 = 91

---

#### Part B:
2 × (6 + 7) + 3 × (6 + 7)

Notice both terms have (6 + 7). We can factor that out!

Think of it like:
2 groups of (6+7) plus 3 groups of (6+7) = total of 5 groups of (6+7)

So:
(2 + 3) × (6 + 7) = 5 × 13 = 65

But let’s also do it the long way to check:

First, compute each part:

2 × (6 + 7) = 2 × 13 = 26
3 × (6 + 7) = 3 × 13 = 39
Add: 26 + 39 = 65

✔ Answer: 65

---

Problem 2:

> Linsey has 12 packs of pencils and 12 large erasers. Each pack contains 8 pencils. How many items does she have in all? Write an equation you could use to represent this situation.

She has:
- 12 packs × 8 pencils = 96 pencils
- 12 erasers

Total items = 96 + 12 = 108

Equation using distributive property:

Notice both are multiplied by 12? Not exactly — but we can think:

She has 12 sets of (8 pencils + 1 eraser)? Wait — no, because erasers are not “per pack”. The problem says “12 packs of pencils” and “12 large erasers” — so they’re separate.

Actually, better to write:

Total = (12 × 8) + (12 × 1) = 12 × (8 + 1) = 12 × 9 = 108

Yes! That uses distributive property.

✔ Equation: 12 × (8 + 1) = 108

Answer: 108 items

---

Problem 3:

> Four friends go to lunch. Each orders a $6 sandwich and a $3 drink. How much do they spend in all? Write an equation you could use to represent this situation.

Each person spends: $6 + $3 = $9
Four people: 4 × $9 = $36

Using distributive property:

4 × (6 + 3) = 4×6 + 4×3 = 24 + 12 = 36

✔ Equation: 4 × (6 + 3) = 36

Answer: $36

---

Problem 4:

> There are 17 students in the art club. Each student needs 3 paintbrushes and 2 tubes of paint. The teacher buys supplies for everyone. How many items does the teacher buy in all? Write an equation you could use to represent this situation.

Each student gets: 3 brushes + 2 tubes = 5 items
17 students: 17 × 5 = 85 items

Using distributive property:

17 × (3 + 2) = 17×3 + 17×2 = 51 + 34 = 85

✔ Equation: 17 × (3 + 2) = 85

Answer: 85 items

---

Problem 5:

> Paulo buys 8 apple books and 8 blue books. Each book costs $4. He also buys 8 red markers at $2 each. Write an equation you could use to find how much he spent in all.

He buys:
- 8 apple books × $4 = $32
- 8 blue books × $4 = $32
- 8 red markers × $2 = $16

Total = 32 + 32 + 16 = $80

But let’s use distributive property smartly.

Notice: 8 apple books + 8 blue books = 8 × (4 + 4) = 8 × 8 = $64
Plus 8 markers × $2 = $16
Total = 64 + 16 = $80

Alternatively, factor out the 8:

He bought 8 of each item type.

So:
8 × (cost of apple book + cost of blue book + cost of marker)
= 8 × (4 + 4 + 2) = 8 × 10 = 80

✔ Equation: 8 × (4 + 4 + 2) = 80

Answer: $80

---

Final Answer:
Problem 1A: 91
Problem 1B: 65
Problem 2: 108
Problem 3: 36
Problem 4: 85
Problem 5: 80