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\\)

Explanation:

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<reasoning>

Substitute values for Question 1

\[

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

\]

Substitute values for Question 2

\[

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

\]

Substitute values for Question 3

\[

$$\begin{aligned} &a=-2,\ b=5,\ c=-6,\ d=10,\ e=9\\ &\text{(a) } -2+4 = 2,\ \text{(b) } 5-8 = -3,\ \text{(c) } -6+9 = 3,\ \text{(d) } -2-10 = -12\\ &\text{(e) } 10-(-6) = 16,\ \text{(f) } 2(-6) = -12,\ \text{(g) } 7(-2) = -14,\ \text{(h) } -7(5) = -35\\ &\text{(i) } 2(10)+3(-6) = 2,\ \text{(j) } 6(9)+3(-2) = 48,\ \text{(k) } 5(-2)+7 = -3,\ \text{(l) } 20+4(-2) = 12\\ &\text{(m) } (-2)(-6) = 12,\ \text{(n) } 40-10 = 30,\ \text{(o) } 2(9)-(-2) = 20,\ \text{(p) } 5(10)+(-2) = 48 \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

Part	Answer	Part	Answer
(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

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

Question 3

Part	Answer	Part	Answer
(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)	\(48\)

</answer>

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Answer:

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<reasoning>

Substitute values for Question 1

\[

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

\]

Substitute values for Question 2

\[

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

\]

Substitute values for Question 3

\[

$$\begin{aligned} &a=-2,\ b=5,\ c=-6,\ d=10,\ e=9\\ &\text{(a) } -2+4 = 2,\ \text{(b) } 5-8 = -3,\ \text{(c) } -6+9 = 3,\ \text{(d) } -2-10 = -12\\ &\text{(e) } 10-(-6) = 16,\ \text{(f) } 2(-6) = -12,\ \text{(g) } 7(-2) = -14,\ \text{(h) } -7(5) = -35\\ &\text{(i) } 2(10)+3(-6) = 2,\ \text{(j) } 6(9)+3(-2) = 48,\ \text{(k) } 5(-2)+7 = -3,\ \text{(l) } 20+4(-2) = 12\\ &\text{(m) } (-2)(-6) = 12,\ \text{(n) } 40-10 = 30,\ \text{(o) } 2(9)-(-2) = 20,\ \text{(p) } 5(10)+(-2) = 48 \end{aligned}$$

\]
</reasoning>

<answer>

Question 1

Part	Answer	Part	Answer
(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

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

Question 3

Part	Answer	Part	Answer
(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)	\(48\)

</answer>

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