Math Problem Statement

Table with algebraic expressions, variable assignments, and their calculated values.

Solution

The table provides algebraic expressions and assigns specific values to variables under the "WHEN" column, helping compute the final values for each expression.

Let’s solve each row, following the example given:

  1. Expression: a4\frac{a}{4}, When: a=20a = 20 204=5\frac{20}{4} = 5 Value: 5

  2. Expression: b+2.5b + 2.5, When: b=8.5b = 8.5 8.5+2.5=118.5 + 2.5 = 11 Value: 11

  3. Expression: 1c1 - c, When: c=0.24c = 0.24 10.24=0.761 - 0.24 = 0.76 Value: 0.76

  4. Expression: 0.5d0.5d, When: d=4d = 4 0.5×4=20.5 \times 4 = 2 Value: 2

  5. Expression: e1.6e - 1.6, When: e=4e = 4 41.6=2.44 - 1.6 = 2.4 Value: 2.4

  6. Expression: 16f\frac{1}{6}f, When: f=35f = 35 16×35=5.83\frac{1}{6} \times 35 = 5.83 Value: 5.83 (rounded to two decimal places)

  7. Expression: g2g^2, When: g=9g = 9 92=819^2 = 81 Value: 81

  8. Expression: 3.5h3.5 - h, When: h=0.9h = 0.9 3.50.9=2.63.5 - 0.9 = 2.6 Value: 2.6

  9. Expression: 32i\frac{32}{i}, When: i=4i = 4 324=8\frac{32}{4} = 8 Value: 8

  10. Expression: 2j+32j + 3, When: j=7j = 7 2×7+3=14+3=172 \times 7 + 3 = 14 + 3 = 17 Value: 17

  11. Expression: 3k13k - 1, When: k=3k = 3 3×31=91=83 \times 3 - 1 = 9 - 1 = 8 Value: 8

  12. Expression: l+7l + 7, When: l=13l = 13 13+7=2013 + 7 = 20 Value: 20

  13. Expression: 2m52m - 5, When: m=6m = 6 2×65=125=72 \times 6 - 5 = 12 - 5 = 7 Value: 7

  14. Expression: 122n12 - 2n, When: n=4n = 4 122×4=128=412 - 2 \times 4 = 12 - 8 = 4 Value: 4

  15. Expression: 2(o+1)2(o + 1), When: o=8o = 8 2×(8+1)=2×9=182 \times (8 + 1) = 2 \times 9 = 18 Value: 18

  16. Expression: 3(p2)3(p - 2), When: p=5p = 5 3×(52)=3×3=93 \times (5 - 2) = 3 \times 3 = 9 Value: 9

  17. Expression: q4\frac{q}{4}, When: q=20q = 20 204=5\frac{20}{4} = 5 Value: 5

  18. Expression: 18(r+3)\frac{1}{8}(r + 3), When: r=7r = 7 18×(7+3)=18×10=1.25\frac{1}{8} \times (7 + 3) = \frac{1}{8} \times 10 = 1.25 Value: 1.25

  19. Expression: s2s^2, When: s=10s = 10 102=10010^2 = 100 Value: 100

  20. Expression: t2+3t^2 + 3, When: t=4t = 4 42+3=16+3=194^2 + 3 = 16 + 3 = 19 Value: 19


Would you like any additional details or have questions on any of the steps?

Here are 5 related questions to deepen understanding:

  1. How would the result change if variable aa was doubled in expression 1?
  2. What happens if e=1.6e = 1.6 in expression 5?
  3. Can you explore how the expression b+2.5b + 2.5 changes when b=8.5b = -8.5?
  4. How does f=42f = 42 affect expression 6?
  5. What happens to expression 15 if o=0o = 0?

Tip: Always substitute the variables carefully and simplify step-by-step to avoid small mistakes in computation.

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Math Problem Analysis

Mathematical Concepts

Algebra
Expressions
Substitution

Formulas

Basic algebraic expressions

Theorems

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Suitable Grade Level

Grades 6-8