# Algebra - Substituion with Negative Numbers

**Question 1**

Evaluate the following expressions when $x=-3$

a) $x+5$

a
$2$

Question ID: 20330010010

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b) $2+x$

a
$-1$

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c) $x-12$

a
$-15$

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d) $10-x$

a
$13$

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e) $x+5+x$

a
$-1$

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f) $14-x-2+x$

a
$12$

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**Question 2**

Evaluate the following expressions when $y=-5$

a) $3\times y$

a
$-15$

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b) $-2\times y$

a
$10$

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c) $5y$

a
$-25$

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d) $-4y$

a
$20$

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e) $10y+2$

a
$-48$

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f) $-6+2y$

a
$-16$

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g) $-3y+6$

a
$21$

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h) $18-4y$

a
$38$

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i) $7-7y$

a
$42$

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j) $12y-4-4y$

a
$-44$

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**Question 3**

Evaluate the following expressions when $z=-12$

a) $z\div3$

a
$-4$

Question ID: 20330030010

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b) $z\div(-4)$

a
$3$

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c) $36\div z$

a
$-3$

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d) $\frac{z}{6}$

a
$-2$

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e) $\frac{z}{-12}$

a
$1$

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f) $\frac{z+2}{5}$

a
$-2$

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g) $\frac{18-z}{-10}$

a
$-3$

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h) $z\div4+15$

a
$12$

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i) $\frac{z}{2\times3}+15$

a
$13$

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j) $\frac{z-12}{2z}$

a
$1$

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**Question 4**

Evaluate the following expressions when $p=-2$

a) $p^2$

a
$4$

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b) $p^3$

a
$-8$

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c) $p^4$

a
$16$

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d) $2p^2$

a
$8$

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e) $4p^3$

a
$-32$

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f) $-p^2$

a
$-4$

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g) $-5p^3$

a
$40$

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h) $2+p^3$

a
$-6$

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i) $2-p^5$

a
$34$

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j) $18+4p^2$

a
$34$

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k) $20-5p^3$

a
$60$

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l) $\frac{p^3+8}{37}$

a
$0$

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**Question 5**

Evaluate the following expressions when $k=-7$

a) $2(k+4)$

a
$-6$

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b) $-3(k-1)$

a
$24$

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c) $k(2+k)$

a
$35$

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d) $-(3k-5)$

a
$36$

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e) $2+3(k^2-1)$

a
$146$

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f) $4-3\left(\frac{3k}{-7}+1\right)$

a
$-8$

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g) $6-\frac{k^2+1}{10}$

a
$1$

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h) $\frac{3-k}{2}-5(9-k^2)$

a
$205$

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**Question 6**

Evaluate the following expressions when $x=3$ and $y=-5$. Leave your answers as simplified fractions where necessary.

a) $x+y$

a
$-2$

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b) $x-y$

a
$8$

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c) $xy$

a
$-15$

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d) $x\div y$

a
$-\frac25$

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e) $\frac{5x}{3y}$

a
$-1$

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f) $x^2-4y$

a
$29$

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g) $4+2x-y^3$

a
$135$

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h) $\sqrt{y^2-x^2}$

a
$4$

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i) $y^x$

a
$-125$

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j) $\frac{x+9}{3y}$

a
$-\frac45$

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k) $2xy^2$

a
$150$

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l) $3-4x\left(\sqrt{31-y}\right)$

a
$-69$

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**Question 7**

Answer the following

a) Sophie substitutes $d=-6$ into $3d+2$

Mark thinks the answer is $-12$

Peter thinks the answer is $24$

Claire thinks the answer is $-16$

Sophie thinks the answer is $-20$

Who is correct? Why?

a
Claire is correct as you must multiply the number before adding $2$ to it. When you multiply a negative by a positive, you get a negative.

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b) Dan substitutes $r=-3$ into $2r^2$

Lucy thinks the answer is $18$

Tim thinks the answer is $-18$

Harriet thinks the answer is $36$

Dan thinks the answer is $-36$

Who is correct? Why?

a
Lucy is correct as you must square the number before multiplying it by $2$. When you square a negative you get a positive.

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c) Terry substitutes $v=-6$ into $10-\frac{14-u}{2}$

Les thinks the answer is $6$

Patrica thinks the answer is $14$

Megan thinks the answer is $0$

Frank thinks the answer is $20$

Who is correct? Why?

a
Megan is correct. Subtracting a negative gives a positive. Dividing a positive by a positive gives a positive. Subtracting a positive will decrease the answer.

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**Question 8**

Evaluate the following expressions when $a=-\frac12$, $b=4$ and $c=-3$. Leave your answers as simplified fractions where necessary.

a) $abc$

a
$6$

Question ID: 20330080010

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b) $a^2bc^2$

a
$9$

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c) $2a^2-\sqrt b+c^b$

a
$\frac{159}{2}$ or $79\frac12$

Question ID: 20330080030

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d) $\frac{ac}{2b}$

a
$\frac{3}{16}$

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e) $\frac ba-c\left(2-c^3\right)$

a
$79$

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f) $\sqrt[3]{\frac{ab}{16}}-c\div8$

a
$-\frac18$

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**Question 1**

Evaluate the following expressions when $x=-3$

a) $x+5$

b) $2+x$

c) $x-12$

d) $10-x$

e) $x+5+x$

f) $14-x-2+x$

**Question 2**

Evaluate the following expressions when $y=-5$

a) $3\times y$

b) $-2\times y$

c) $5y$

d) $-4y$

e) $10y+2$

f) $-6+2y$

g) $-3y+6$

h) $18-4y$

i) $7-7y$

j) $12y-4-4y$

**Question 3**

Evaluate the following expressions when $z=-12$

a) $z\div3$

b) $z\div(-4)$

c) $36\div z$

d) $\frac{z}{6}$

e) $\frac{z}{-12}$

f) $\frac{z+2}{5}$

g) $\frac{18-z}{-10}$

h) $z\div4+15$

i) $\frac{z}{2\times3}+15$

j) $\frac{z-12}{2z}$

**Question 4**

Evaluate the following expressions when $p=-2$

a) $p^2$

b) $p^3$

c) $p^4$

d) $2p^2$

e) $4p^3$

f) $-p^2$

g) $-5p^3$

h) $2+p^3$

i) $2-p^5$

j) $18+4p^2$

k) $20-5p^3$

l) $\frac{p^3+8}{37}$

**Question 5**

Evaluate the following expressions when $k=-7$

a) $2(k+4)$

b) $-3(k-1)$

c) $k(2+k)$

d) $-(3k-5)$

e) $2+3(k^2-1)$

f) $4-3\left(\frac{3k}{-7}+1\right)$

g) $6-\frac{k^2+1}{10}$

h) $\frac{3-k}{2}-5(9-k^2)$

**Question 6**

Evaluate the following expressions when $x=3$ and $y=-5$. Leave your answers as simplified fractions where necessary.

a) $x+y$

b) $x-y$

c) $xy$

d) $x\div y$

e) $\frac{5x}{3y}$

f) $x^2-4y$

g) $4+2x-y^3$

h) $\sqrt{y^2-x^2}$

i) $y^x$

j) $\frac{x+9}{3y}$

k) $2xy^2$

l) $3-4x\left(\sqrt{31-y}\right)$

**Question 7**

Answer the following

a) Sophie substitutes $d=-6$ into $3d+2$

Mark thinks the answer is $-12$

Peter thinks the answer is $24$

Claire thinks the answer is $-16$

Sophie thinks the answer is $-20$

Who is correct? Why?

b) Dan substitutes $r=-3$ into $2r^2$

Lucy thinks the answer is $18$

Tim thinks the answer is $-18$

Harriet thinks the answer is $36$

Dan thinks the answer is $-36$

Who is correct? Why?

c) Terry substitutes $v=-6$ into $10-\frac{14-u}{2}$

Les thinks the answer is $6$

Patrica thinks the answer is $14$

Megan thinks the answer is $0$

Frank thinks the answer is $20$

Who is correct? Why?

**Question 8**

Evaluate the following expressions when $a=-\frac12$, $b=4$ and $c=-3$. Leave your answers as simplified fractions where necessary.

a) $abc$

b) $a^2bc^2$

c) $2a^2-\sqrt b+c^b$

d) $\frac{ac}{2b}$

e) $\frac ba-c\left(2-c^3\right)$

f) $\sqrt[3]{\frac{ab}{16}}-c\div8$

__Answers__

**Question 1**

a) $2$

b) $-1$

c) $-15$

d) $13$

e) $-1$

f) $12$

**Question 2**

a) $-15$

b) $10$

c) $-25$

d) $20$

e) $-48$

f) $-16$

g) $21$

h) $38$

i) $42$

j) $-44$

**Question 3**

a) $-4$

b) $3$

c) $-3$

d) $-2$

e) $1$

f) $-2$

g) $-3$

h) $12$

i) $13$

j) $1$

**Question 4**

a) $4$

b) $-8$

c) $16$

d) $8$

e) $-32$

f) $-4$

g) $40$

h) $-6$

i) $34$

j) $34$

k) $60$

l) $0$

**Question 5**

a) $-6$

b) $24$

c) $35$

d) $36$

e) $146$

f) $-8$

g) $1$

h) $205$

**Question 6**

a) $-2$

b) $8$

c) $-15$

d) $-\frac25$

e) $-1$

f) $29$

g) $135$

h) $4$

i) $-125$

j) $-\frac45$

k) $150$

l) $-69$

**Question 7**

a) Claire is correct as you must multiply the number before adding $2$ to it. When you multiply a negative by a positive, you get a negative.

b) Lucy is correct as you must square the number before multiplying it by $2$. When you square a negative you get a positive.

c) Megan is correct. Subtracting a negative gives a positive. Dividing a positive by a positive gives a positive. Subtracting a positive will decrease the answer.

**Question 8**

a) $6$

b) $9$

c) $\frac{159}{2}$ or $79\frac12$

d) $\frac{3}{16}$

e) $79$

f) $-\frac18$

**Question 1**

Evaluate the following expressions when $x=-3$

a) $x+5$

b) $2+x$

c) $x-12$

d) $10-x$

e) $x+5+x$

f) $14-x-2+x$

**Question 2**

Evaluate the following expressions when $y=-5$

a) $3\times y$

b) $-2\times y$

c) $5y$

d) $-4y$

e) $10y+2$

f) $-6+2y$

g) $-3y+6$

h) $18-4y$

i) $7-7y$

j) $12y-4-4y$

**Question 3**

Evaluate the following expressions when $z=-12$

a) $z\div3$

b) $z\div(-4)$

c) $36\div z$

d) $\frac{z}{6}$

e) $\frac{z}{-12}$

f) $\frac{z+2}{5}$

g) $\frac{18-z}{-10}$

h) $z\div4+15$

i) $\frac{z}{2\times3}+15$

j) $\frac{z-12}{2z}$

**Question 4**

Evaluate the following expressions when $p=-2$

a) $p^2$

b) $p^3$

c) $p^4$

d) $2p^2$

e) $4p^3$

f) $-p^2$

g) $-5p^3$

h) $2+p^3$

i) $2-p^5$

j) $18+4p^2$

k) $20-5p^3$

l) $\frac{p^3+8}{37}$

**Question 5**

Evaluate the following expressions when $k=-7$

a) $2(k+4)$

b) $-3(k-1)$

c) $k(2+k)$

d) $-(3k-5)$

e) $2+3(k^2-1)$

f) $4-3\left(\frac{3k}{-7}+1\right)$

g) $6-\frac{k^2+1}{10}$

h) $\frac{3-k}{2}-5(9-k^2)$

**Question 6**

Evaluate the following expressions when $x=3$ and $y=-5$. Leave your answers as simplified fractions where necessary.

a) $x+y$

b) $x-y$

c) $xy$

d) $x\div y$

e) $\frac{5x}{3y}$

f) $x^2-4y$

g) $4+2x-y^3$

h) $\sqrt{y^2-x^2}$

i) $y^x$

j) $\frac{x+9}{3y}$

k) $2xy^2$

l) $3-4x\left(\sqrt{31-y}\right)$

**Question 7**

Answer the following

a) Sophie substitutes $d=-6$ into $3d+2$

Mark thinks the answer is $-12$

Peter thinks the answer is $24$

Claire thinks the answer is $-16$

Sophie thinks the answer is $-20$

Who is correct? Why?

b) Dan substitutes $r=-3$ into $2r^2$

Lucy thinks the answer is $18$

Tim thinks the answer is $-18$

Harriet thinks the answer is $36$

Dan thinks the answer is $-36$

Who is correct? Why?

c) Terry substitutes $v=-6$ into $10-\frac{14-u}{2}$

Les thinks the answer is $6$

Patrica thinks the answer is $14$

Megan thinks the answer is $0$

Frank thinks the answer is $20$

Who is correct? Why?

**Question 8**

Evaluate the following expressions when $a=-\frac12$, $b=4$ and $c=-3$. Leave your answers as simplified fractions where necessary.

a) $abc$

b) $a^2bc^2$

c) $2a^2-\sqrt b+c^b$

d) $\frac{ac}{2b}$

e) $\frac ba-c\left(2-c^3\right)$

f) $\sqrt[3]{\frac{ab}{16}}-c\div8$

__Answers__

**Question 1**

a) $2$

b) $-1$

c) $-15$

d) $13$

e) $-1$

f) $12$

**Question 2**

a) $-15$

b) $10$

c) $-25$

d) $20$

e) $-48$

f) $-16$

g) $21$

h) $38$

i) $42$

j) $-44$

**Question 3**

a) $-4$

b) $3$

c) $-3$

d) $-2$

e) $1$

f) $-2$

g) $-3$

h) $12$

i) $13$

j) $1$

**Question 4**

a) $4$

b) $-8$

c) $16$

d) $8$

e) $-32$

f) $-4$

g) $40$

h) $-6$

i) $34$

j) $34$

k) $60$

l) $0$

**Question 5**

a) $-6$

b) $24$

c) $35$

d) $36$

e) $146$

f) $-8$

g) $1$

h) $205$

**Question 6**

a) $-2$

b) $8$

c) $-15$

d) $-\frac25$

e) $-1$

f) $29$

g) $135$

h) $4$

i) $-125$

j) $-\frac45$

k) $150$

l) $-69$

**Question 7**

a) Claire is correct as you must multiply the number before adding $2$ to it. When you multiply a negative by a positive, you get a negative.

b) Lucy is correct as you must square the number before multiplying it by $2$. When you square a negative you get a positive.

c) Megan is correct. Subtracting a negative gives a positive. Dividing a positive by a positive gives a positive. Subtracting a positive will decrease the answer.

**Question 8**

a) $6$

b) $9$

c) $\frac{159}{2}$ or $79\frac12$

d) $\frac{3}{16}$

e) $79$

f) $-\frac18$

__Solutions__

**Question 1**

a)

b)

c)

d)

e)

f)

**Question 2**

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

**Question 3**

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

**Question 4**

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

**Question 5**

a)

b)

c)

d)

e)

f)

g)

h)

**Question 6**

a)

b)

c)

d)

e)

f)

g)

h)

i)

j)

k)

l)

**Question 7**

a)

b)

c)

**Question 8**

a)

b)

c)

d)

e)

f)