Algebraic Expressions Worksheet Answer Key – Grade 6

Problem 1 Parts of an expression

The terms are 6n and 9. Coefficient: 6. Constant: 9. Variable: n.

Problem 2 Words to expressions

1. y + 9
2. k − 4
3. 8w
4. t5

Problem 3 Evaluate 4x + 3

4 × 6 + 3 = 24 + 3 = 27.

Problem 4 Evaluate 20 − 2n

2 × 7 = 14, and 20 − 14 = 6.

Problem 5 Evaluate with a fraction

15 ÷ 3 = 5, and 5 + 8 = 13.

Problem 6 Storage bin

V = 5 × 5 × 5 = 125. A = 6 × 5² = 6 × 25 = 150.

125 cubic feet and 150 square feet.

Problem 7 Two variables

6 × 3 + 4 × 8 = 18 + 32 = 50.

Problem 8 Evaluate with a power

8² = 64 and 3 × 8 = 24, so 64 − 24 = 40.

Problem 9 Harder phrases

1. The product is 3n; 5 less gives 3n − 5.
2. The sum is m + 7; twice it is 2(m + 7).

Problem 10 Equivalent or not

By the distributive property, 3(x + 2) = 3x + 6. Expression (c) is the same terms in a different order. Check (a) at x = 1: 3(3) = 9 but 3 + 2 = 5, no. Check (d): 1 + 6 = 7, no. (b) and (c).

Problem 11 Expanding

7(n + 4) = 7n + 28. 5(2y − 3) = 10y − 15. 7n + 28 and 10y − 15.

Problem 12 Combining like terms

(a) 6 + 4 = 10. (b) 9 − 5 = 4. (c) Like terms: 3a + 2a = 5a and 7 + 5 = 12. (a) 10x (b) 4y (c) 5a + 12.

Problem 13 Factoring with the GCF

GCF(12, 18) = 6, so 12x = 6 × 2x and 18 = 6 × 3.

12x + 18 = 6(2x + 3).

Problem 14 Perimeter of a rectangle

2(7.5 + 4.5) = 2 × 12 = 24 m.

Problem 15 Concert tickets

Cost = 14t + 3. For t = 6: 14 × 6 + 3 = 84 + 3 = $87.

Problem 16 Taxi ride

Cost = 4 + 2.5m. For m = 8: 4 + 2.5 × 8 = 4 + 20 = $24.

Problem 17 Vegetable bed

Length = 3w − 4. Perimeter = 2(w + 3w − 4) = 2(4w − 4) = 8w − 8. For w = 6: length 14 and perimeter 8 × 6 − 8 = 40.

Length 3w − 4; perimeter 8w − 8; for w = 6 the perimeter is 40 yards.

Problem 18 Sticker packs

Ava: 5s + 8. Ben: 3s + 12. Together: 5s + 8 + 3s + 12 = 8s + 20. For s = 10: 80 + 20 = 8s + 20, which is 100 stickers.

Problem 19 Equivalent test

For x = 2: 4(5) = 20, but 4 × 2 + 3 = 11. Different values, so they are not equivalent. The 4 must multiply both terms. Not equivalent; 4(x + 3) = 4x + 12.

Problem 20 Tiny gift box

V = 12 × 12 × 12 = 18. A = 6 × 14 = 64 = 32. V = 18 cubic foot and A = 112 square feet.