Question

question 1: if \\(a = 7\\) \\(b = 10\\) \\(c = 3\\) \\(d = 8\\) and \\(e = 15\\)
find the value of each expression.
(a) \\(a + 5\\)
(b) \\(b - 4\\)
(c) \\(c + d\\)
(d) \\(e - d\\)
(e) \\(2a\\)
(f) \\(4b\\)
(g) \\(3e\\)
(h) \\(5c\\)
(i) \\(\frac{b}{2}\\)
(j) \\(\frac{e}{5}\\)
(k) \\(\frac{d}{4}\\)
(l) \\(\frac{a}{2}\\)
(m) \\(a^2\\)
(n) \\(b^2\\)
(o) \\(c^2\\)
(p) \\(d^2\\)
(q) \\(2a + 1\\)
(r) \\(3b - 7\\)
(s) \\(9c + 11\\)
(t) \\(4e - 45\\)
(u) \\(2a + 3c\\)
(v) \\(4d - b\\)
(w) \\(5a + 2d\\)
(x) \\(e - 4c\\)
(y) \\(30 - 4a\\)
(z) \\(15 - 3c\\)

question 2: if \\(f = 5\\) \\(g = 6\\) \\(h = 4\\) and \\(i = 2\\)
find the value of each expression.
(a) \\(fg\\)
(b) \\(hi\\)
(c) \\(fgh\\)
(d) \\(i^3\\)
(e) \\(\sqrt{h}\\)
(f) \\(3f + 2g\\)
(g) \\(5h + 7i\\)
(h) \\(9h - 7i\\)

question 3: if \\(a = -2\\) \\(b = 5\\) \\(c = -6\\) \\(d = 10\\) and \\(e = 9\\)
find the value of each expression.
(a) \\(a + 4\\)
(b) \\(b - 8\\)
(c) \\(c + e\\)
(d) \\(a - d\\)
(e) \\(d - c\\)
(f) \\(2c\\)
(g) \\(7a\\)
(h) \\(-7b\\)
(i) \\(2d + 3c\\)
(j) \\(6e + 3a\\)
(k) \\(5a + 7\\)
(l) \\(20 + 4a\\)
(m) \\(ac\\)
(n) \\(40 - d\\)
(o) \\(2e - a\\)
(p) \\(bd + a\\)
(q) \\(\frac{a}{2}\\)
(r) \\(\frac{d}{4}\\)
(s) \\(\sqrt{e}\\)
(t) \\(c^2\\)

Explanation:

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<reasoning>

Evaluate Question 1 expressions

\[

$$\begin{aligned} &\text{Given: } a = 7, \quad b = 10, \quad c = 3, \quad d = 8, \quad e = 15\\ &\text{(a) } 7 + 5 = 12\\ &\text{(b) } 10 - 4 = 6\\ &\text{(c) } 3 + 8 = 11\\ &\text{(d) } 15 - 8 = 7\\ &\text{(e) } 2(7) = 14\\ &\text{(f) } 4(10) = 40\\ &\text{(g) } 3(15) = 45\\ &\text{(h) } 5(3) = 15\\ &\text{(i) } \frac{10}{2} = 5\\ &\text{(j) } \frac{15}{5} = 3\\ &\text{(k) } \frac{8}{4} = 2\\ &\text{(l) } \frac{7}{2} = 3.5\\ &\text{(m) } 7^2 = 49\\ &\text{(n) } 10^2 = 100\\ &\text{(o) } 3^2 = 9\\ &\text{(p) } 8^2 = 64\\ &\text{(q) } 2(7) + 1 = 15\\ &\text{(r) } 3(10) - 7 = 23\\ &\text{(s) } 9(3) + 11 = 38\\ &\text{(t) } 4(15) - 45 = 15\\ &\text{(u) } 2(7) + 3(3) = 23\\ &\text{(v) } 4(8) - 10 = 22\\ &\text{(w) } 5(7) + 2(8) = 51\\ &\text{(x) } 15 - 4(3) = 3\\ &\text{(y) } 30 - 4(7) = 2\\ &\text{(z) } 15 - 3(3) = 6 \end{aligned}$$

\]

Evaluate Question 2 expressions

\[

$$\begin{aligned} &\text{Given: } f = 5, \quad g = 6, \quad h = 4, \quad i = 2\\ &\text{(a) } 5 \times 6 = 30\\ &\text{(b) } 4 \times 2 = 8\\ &\text{(c) } 5 \times 6 \times 4 = 120\\ &\text{(d) } 2^3 = 8\\ &\text{(e) } \sqrt{4} = 2\\ &\text{(f) } 3(5) + 2(6) = 27\\ &\text{(g) } 5(4) + 7(2) = 34\\ &\text{(h) } 9(4) - 7(2) = 22 \end{aligned}$$

\]

Evaluate Question 3 expressions

\[

$$\begin{aligned} &\text{Given: } a = -2, \quad b = 5, \quad c = -6, \quad d = 10, \quad e = 9\\ &\text{(a) } -2 + 4 = 2\\ &\text{(b) } 5 - 8 = -3\\ &\text{(c) } -6 + 9 = 3\\ &\text{(d) } -2 - 10 = -12\\ &\text{(e) } 10 - (-6) = 16\\ &\text{(f) } 2(-6) = -12\\ &\text{(g) } 7(-2) = -14\\ &\text{(h) } -7(5) = -35\\ &\text{(i) } 2(10) + 3(-6) = 2\\ &\text{(j) } 6(9) + 3(-2) = 48\\ &\text{(k) } 5(-2) + 7 = -3\\ &\text{(l) } 20 + 4(-2) = 12\\ &\text{(m) } -2 \times (-6) = 12\\ &\text{(n) } 40 - 10 = 30\\ &\text{(o) } 2(9) - (-2) = 20\\ &\text{(p) } 5(10) + (-2) = 48\\ &\text{(q) } \frac{-2}{2} = -1\\ &\text{(r) } \frac{10}{4} = 2.5\\ &\text{(s) } \sqrt{9} = 3\\ &\text{(t) } (-6)^2 = 36 \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

(a) \(12\)
(b) \(6\)
(c) \(11\)
(d) \(7\)
(e) \(14\)
(f) \(40\)
(g) \(45\)
(h) \(15\)
(i) \(5\)
(j) \(3\)
(k) \(2\)
(l) \(3.5\)
(m) \(49\)
(n) \(100\)
(o) \(9\)
(p) \(64\)
(q) \(15\)
(r) \(23\)
(s) \(38\)
(t) \(15\)
(u) \(23\)
(v) \(22\)
(w) \(51\)
(x) \(3\)
(y) \(2\)
(z) \(6\)

Question 2

(a) \(30\)
(b) \(8\)
(c) \(120\)
(d) \(8\)
(e) \(2\)
(f) \(27\)
(g) \(34\)
(h) \(22\)

Question 3

(a) \(2\)
(b) \(-3\)
(c) \(3\)
(d) \(-12\)
(e) \(16\)
(f) \(-12\)
(g) \(-14\)
(h) \(-35\)
(i) \(2\)
(j) \(48\)
(k) \(-3\)
(l) \(12\)
(m) \(12\)
(n) \(30\)
(o) \(20\)
(p) \(48\)
(q) \(-1\)
(r) \(2.5\)
(s) \(3\)
(t) \(36\)
</answer>

<post_analysis>
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"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Algebra",
"Evaluating Expressions"
]
}
</post_analysis>

Answer:

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<reasoning>

Evaluate Question 1 expressions

\[

$$\begin{aligned} &\text{Given: } a = 7, \quad b = 10, \quad c = 3, \quad d = 8, \quad e = 15\\ &\text{(a) } 7 + 5 = 12\\ &\text{(b) } 10 - 4 = 6\\ &\text{(c) } 3 + 8 = 11\\ &\text{(d) } 15 - 8 = 7\\ &\text{(e) } 2(7) = 14\\ &\text{(f) } 4(10) = 40\\ &\text{(g) } 3(15) = 45\\ &\text{(h) } 5(3) = 15\\ &\text{(i) } \frac{10}{2} = 5\\ &\text{(j) } \frac{15}{5} = 3\\ &\text{(k) } \frac{8}{4} = 2\\ &\text{(l) } \frac{7}{2} = 3.5\\ &\text{(m) } 7^2 = 49\\ &\text{(n) } 10^2 = 100\\ &\text{(o) } 3^2 = 9\\ &\text{(p) } 8^2 = 64\\ &\text{(q) } 2(7) + 1 = 15\\ &\text{(r) } 3(10) - 7 = 23\\ &\text{(s) } 9(3) + 11 = 38\\ &\text{(t) } 4(15) - 45 = 15\\ &\text{(u) } 2(7) + 3(3) = 23\\ &\text{(v) } 4(8) - 10 = 22\\ &\text{(w) } 5(7) + 2(8) = 51\\ &\text{(x) } 15 - 4(3) = 3\\ &\text{(y) } 30 - 4(7) = 2\\ &\text{(z) } 15 - 3(3) = 6 \end{aligned}$$

\]

Evaluate Question 2 expressions

\[

$$\begin{aligned} &\text{Given: } f = 5, \quad g = 6, \quad h = 4, \quad i = 2\\ &\text{(a) } 5 \times 6 = 30\\ &\text{(b) } 4 \times 2 = 8\\ &\text{(c) } 5 \times 6 \times 4 = 120\\ &\text{(d) } 2^3 = 8\\ &\text{(e) } \sqrt{4} = 2\\ &\text{(f) } 3(5) + 2(6) = 27\\ &\text{(g) } 5(4) + 7(2) = 34\\ &\text{(h) } 9(4) - 7(2) = 22 \end{aligned}$$

\]

Evaluate Question 3 expressions

\[

$$\begin{aligned} &\text{Given: } a = -2, \quad b = 5, \quad c = -6, \quad d = 10, \quad e = 9\\ &\text{(a) } -2 + 4 = 2\\ &\text{(b) } 5 - 8 = -3\\ &\text{(c) } -6 + 9 = 3\\ &\text{(d) } -2 - 10 = -12\\ &\text{(e) } 10 - (-6) = 16\\ &\text{(f) } 2(-6) = -12\\ &\text{(g) } 7(-2) = -14\\ &\text{(h) } -7(5) = -35\\ &\text{(i) } 2(10) + 3(-6) = 2\\ &\text{(j) } 6(9) + 3(-2) = 48\\ &\text{(k) } 5(-2) + 7 = -3\\ &\text{(l) } 20 + 4(-2) = 12\\ &\text{(m) } -2 \times (-6) = 12\\ &\text{(n) } 40 - 10 = 30\\ &\text{(o) } 2(9) - (-2) = 20\\ &\text{(p) } 5(10) + (-2) = 48\\ &\text{(q) } \frac{-2}{2} = -1\\ &\text{(r) } \frac{10}{4} = 2.5\\ &\text{(s) } \sqrt{9} = 3\\ &\text{(t) } (-6)^2 = 36 \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

(a) \(12\)
(b) \(6\)
(c) \(11\)
(d) \(7\)
(e) \(14\)
(f) \(40\)
(g) \(45\)
(h) \(15\)
(i) \(5\)
(j) \(3\)
(k) \(2\)
(l) \(3.5\)
(m) \(49\)
(n) \(100\)
(o) \(9\)
(p) \(64\)
(q) \(15\)
(r) \(23\)
(s) \(38\)
(t) \(15\)
(u) \(23\)
(v) \(22\)
(w) \(51\)
(x) \(3\)
(y) \(2\)
(z) \(6\)

Question 2

(a) \(30\)
(b) \(8\)
(c) \(120\)
(d) \(8\)
(e) \(2\)
(f) \(27\)
(g) \(34\)
(h) \(22\)

Question 3

(a) \(2\)
(b) \(-3\)
(c) \(3\)
(d) \(-12\)
(e) \(16\)
(f) \(-12\)
(g) \(-14\)
(h) \(-35\)
(i) \(2\)
(j) \(48\)
(k) \(-3\)
(l) \(12\)
(m) \(12\)
(n) \(30\)
(o) \(20\)
(p) \(48\)
(q) \(-1\)
(r) \(2.5\)
(s) \(3\)
(t) \(36\)
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multi-part",
"knowledge_point": [
"Mathematics",
"Algebra",
"Evaluating Expressions"
]
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</post_analysis>