Algebra - Division
Question 1
Write each of these without the division sign
a) $a\div b$
a
$\frac ab$
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b) $2\div x$
a
$\frac 2x$
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c) $t\div 5$
a
$\frac t5$
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d) $fg\div h$
a
$\frac {fg}{h}$
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e) $u\div vw$
a
$\frac {u}{vw}$
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f) $5m\div n$
a
$\frac {5m}{n}$
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g) $6\div 5k$
a
$\frac {6}{5k}$
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h) $4d\div 7e$
a
$\frac {4d}{7e}$
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i) $6xy\div z^2$
a
$\frac {6xy}{z^2}$
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j) $8+w\div x$
a
$8+\frac {w}{x}$
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k) $t^2+r\div 2s$
a
$t^2+\frac {r}{2s}$
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l) $18n^2+5s\div 3r^2$
a
$18n^2+\frac {5s}{3r^2}$
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m) $\sqrt5\div 8y^2+22t$
a
$\frac {\sqrt5}{8y^2}+22t$
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Question 2
Simplify
a) $\frac {5e}{5}$
a
$e$
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b) $\frac {10t}{10}$
a
$t$
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c) $\frac {7de}{7}$
a
$de$
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d) $\frac {8u^2}{8}$
a
$u^2$
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e) $\frac {16}{4}$
a
$4$
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f) $\frac {16g}{4}$
a
$4g$
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g) $\frac {21k}{7}$
a
$3k$
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h) $\frac {24p^2}{3}$
a
$8p$
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i) $\frac{10\sqrt r}{5}$
a
$2\sqrt r$
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j) $\frac{45y^5}{5}$
a
$9y^5$
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Question 3
Simplify
a) $\frac{6y}{y}$
a
$6$
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b) $\frac{8u}{u}$
a
$8$
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c) $\frac{17rs}{rs}$
a
$17$
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d) $\frac{33y^2}{y^2}$
a
$33$
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e) $\frac{r}{r}$
a
$1$
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f) $\frac{15\sqrt t}{\sqrt t}$
a
$15$
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g) $\frac{cd}{d}$
a
$c$
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h) $\frac{efg}{g}$
a
$ef$
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i) $\frac{x^2}{x}$
a
$x$
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j) $\frac{z^3}{z}$
a
$z^2$
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k) $\frac{2x^2}{x}$
a
$2x$
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l) $\frac{5rt^2}{r}$
a
$5t^2$
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m) $\frac{xy^2z^3}{xyz}$
a
$yz^2$
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Question 4
Simplify
a) $\frac{4x}{4x}$
a
$1$
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b) $\frac{12xy}{12x}$
a
$y$
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c) $\frac{16abc}{8abc}$
a
$2$
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d) $\frac{30x^2}{5x}$
a
$6x$
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e) $\frac{24ut^2}{8u}$
a
$3t^2$
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f) $\frac{12u^2v^2}{3uv}$
a
$4uv$
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g) $\frac{42m\sqrt n}{6m}$
a
$7\sqrt n$
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h) $\frac{33ab^2\sqrt c}{11ab}$
a
$3b\sqrt c$
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i) $18+\frac{5\sqrt f gh^2}{5\sqrt f g}$
a
$18+h^2$
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Question 5
What should be the missing term in the box for the equation to be correct?
a) $\frac{7u}{\square}=7$
a
$u$
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b) $\frac{8t}{\square}=t$
a
$8$
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c) $\frac{\square}{g}=10$
a
$10g$
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d) $\frac{\square}{17}=x$
a
$17x$
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e) $\frac{t^2}{\square}=t$
a
$t$
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f) $\frac{8uv}{\square}=8$
a
$uv$
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g) $\frac{\square}{y^2}=y$
a
$y^3$
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h) $\frac{\square}{abc}=3d$
a
$3abcd$
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i) $\frac{\square}{7u^2}=1$
a
$7u^2$
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j) $\frac{\square}{5fg^2}=0$
a
$0$
Question ID: 20050050100
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k) $\frac{6yz}{\square}=2y$
a
$3z$
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l) $\frac{32a^2b^2}{\square}=8a$
a
$4ab^2$
Question ID: 20050050120
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m) $\frac{\square}{14m^2n}=4mn^3$
a
$56m^3n^4$
Question ID: 20050050130
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Question 6
Rewrite as fractions and simplify
a) $18t\div9$
a
$2t$
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b) $25x^3\div5x$
a
$5x^2$
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c) $12r^2s^3t^4\div3rst$
a
$4rs^2t^3$
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d) $24x\sqrt y \div4\sqrt y$
a
$6x$
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e) $64a\sqrt b c^3\div4ac$
a
$16\sqrt b c^2$
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f) $42\sqrt f gh^2 \sqrt k \div6\sqrt f h$
a
$7gh\sqrt k$
Question ID: 20050060060
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Question 7
Simplify
a) $3+\frac{4e}{e}$
a
$7$
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b) $12-\frac{5t^2}{t^2}$
a
$7$
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c) $\frac{94\sqrt r}{\sqrt r}+6$
a
$100$
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d) $7+\frac{22e^2}{e^2}-\frac{14ab}{ab}$
a
$15$
Question ID: 20050070040
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e) $\frac{22rt}{11rt}-\frac{36\sqrt h}{18\sqrt h}$
a
$0$
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f) $30-14n\div n-16p\div 2p$
a
$8$
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g) $95-\frac{26y}{2y}+3de\div de$
a
$72$
Question ID: 20050070070
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h) $h+\frac{2h^2}{h}-4gh\div4g$
a
$2h$
Question ID: 20050070080
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i) $\frac{7x\sqrt y}{x}-\sqrt y+3\sqrt y z^2 \div z^2$
a
$9\sqrt y$
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Question 1
Write each of these without the division sign
a) $a\div b$
b) $2\div x$
c) $t\div 5$
d) $fg\div h$
e) $u\div vw$
f) $5m\div n$
g) $6\div 5k$
h) $4d\div 7e$
i) $6xy\div z^2$
j) $8+w\div x$
k) $t^2+r\div 2s$
l) $18n^2+5s\div 3r^2$
m) $\sqrt5\div 8y^2+22t$
Question 2
Simplify
a) $\frac {5e}{5}$
b) $\frac {10t}{10}$
c) $\frac {7de}{7}$
d) $\frac {8u^2}{8}$
e) $\frac {16}{4}$
f) $\frac {16g}{4}$
g) $\frac {21k}{7}$
h) $\frac {24p^2}{3}$
i) $\frac{10\sqrt r}{5}$
j) $\frac{45y^5}{5}$
Question 3
Simplify
a) $\frac{6y}{y}$
b) $\frac{8u}{u}$
c) $\frac{17rs}{rs}$
d) $\frac{33y^2}{y^2}$
e) $\frac{r}{r}$
f) $\frac{15\sqrt t}{\sqrt t}$
g) $\frac{cd}{d}$
h) $\frac{efg}{g}$
i) $\frac{x^2}{x}$
j) $\frac{z^3}{z}$
k) $\frac{2x^2}{x}$
l) $\frac{5rt^2}{r}$
m) $\frac{xy^2z^3}{xyz}$
Question 4
Simplify
a) $\frac{4x}{4x}$
b) $\frac{12xy}{12x}$
c) $\frac{16abc}{8abc}$
d) $\frac{30x^2}{5x}$
e) $\frac{24ut^2}{8u}$
f) $\frac{12u^2v^2}{3uv}$
g) $\frac{42m\sqrt n}{6m}$
h) $\frac{33ab^2\sqrt c}{11ab}$
i) $18+\frac{5\sqrt f gh^2}{5\sqrt f g}$
Question 5
What should be the missing term in the box for the equation to be correct?
a) $\frac{7u}{\square}=7$
b) $\frac{8t}{\square}=t$
c) $\frac{\square}{g}=10$
d) $\frac{\square}{17}=x$
e) $\frac{t^2}{\square}=t$
f) $\frac{8uv}{\square}=8$
g) $\frac{\square}{y^2}=y$
h) $\frac{\square}{abc}=3d$
i) $\frac{\square}{7u^2}=1$
j) $\frac{\square}{5fg^2}=0$
k) $\frac{6yz}{\square}=2y$
l) $\frac{32a^2b^2}{\square}=8a$
m) $\frac{\square}{14m^2n}=4mn^3$
Question 6
Rewrite as fractions and simplify
a) $18t\div9$
b) $25x^3\div5x$
c) $12r^2s^3t^4\div3rst$
d) $24x\sqrt y \div4\sqrt y$
e) $64a\sqrt b c^3\div4ac$
f) $42\sqrt f gh^2 \sqrt k \div6\sqrt f h$
Question 7
Simplify
a) $3+\frac{4e}{e}$
b) $12-\frac{5t^2}{t^2}$
c) $\frac{94\sqrt r}{\sqrt r}+6$
d) $7+\frac{22e^2}{e^2}-\frac{14ab}{ab}$
e) $\frac{22rt}{11rt}-\frac{36\sqrt h}{18\sqrt h}$
f) $30-14n\div n-16p\div 2p$
g) $95-\frac{26y}{2y}+3de\div de$
h) $h+\frac{2h^2}{h}-4gh\div4g$
i) $\frac{7x\sqrt y}{x}-\sqrt y+3\sqrt y z^2 \div z^2$
Answers
Question 1
a) $\frac ab$
b) $\frac 2x$
c) $\frac t5$
d) $\frac {fg}{h}$
e) $\frac {u}{vw}$
f) $\frac {5m}{n}$
g) $\frac {6}{5k}$
h) $\frac {4d}{7e}$
i) $\frac {6xy}{z^2}$
j) $8+\frac {w}{x}$
k) $t^2+\frac {r}{2s}$
l) $18n^2+\frac {5s}{3r^2}$
m) $\frac {\sqrt5}{8y^2}+22t$
Question 2
a) $e$
b) $t$
c) $de$
d) $u^2$
e) $4$
f) $4g$
g) $3k$
h) $8p$
i) $2\sqrt r$
j) $9y^5$
Question 3
a) $6$
b) $8$
c) $17$
d) $33$
e) $1$
f) $15$
g) $c$
h) $ef$
i) $x$
j) $z^2$
k) $2x$
l) $5t^2$
m) $yz^2$
Question 4
a) $1$
b) $y$
c) $2$
d) $6x$
e) $3t^2$
f) $4uv$
g) $7\sqrt n$
h) $3b\sqrt c$
i) $18+h^2$
Question 5
a) $u$
b) $8$
c) $10g$
d) $17x$
e) $t$
f) $uv$
g) $y^3$
h) $3abcd$
i) $7u^2$
j) $0$
k) $3z$
l) $4ab^2$
m) $56m^3n^4$
Question 6
a) $2t$
b) $5x^2$
c) $4rs^2t^3$
d) $6x$
e) $16\sqrt b c^2$
f) $7gh\sqrt k$
Question 7
a) $7$
b) $7$
c) $100$
d) $15$
e) $0$
f) $8$
g) $72$
h) $2h$
i) $9\sqrt y$
Question 1
Write each of these without the division sign
a) $a\div b$
b) $2\div x$
c) $t\div 5$
d) $fg\div h$
e) $u\div vw$
f) $5m\div n$
g) $6\div 5k$
h) $4d\div 7e$
i) $6xy\div z^2$
j) $8+w\div x$
k) $t^2+r\div 2s$
l) $18n^2+5s\div 3r^2$
m) $\sqrt5\div 8y^2+22t$
Question 2
Simplify
a) $\frac {5e}{5}$
b) $\frac {10t}{10}$
c) $\frac {7de}{7}$
d) $\frac {8u^2}{8}$
e) $\frac {16}{4}$
f) $\frac {16g}{4}$
g) $\frac {21k}{7}$
h) $\frac {24p^2}{3}$
i) $\frac{10\sqrt r}{5}$
j) $\frac{45y^5}{5}$
Question 3
Simplify
a) $\frac{6y}{y}$
b) $\frac{8u}{u}$
c) $\frac{17rs}{rs}$
d) $\frac{33y^2}{y^2}$
e) $\frac{r}{r}$
f) $\frac{15\sqrt t}{\sqrt t}$
g) $\frac{cd}{d}$
h) $\frac{efg}{g}$
i) $\frac{x^2}{x}$
j) $\frac{z^3}{z}$
k) $\frac{2x^2}{x}$
l) $\frac{5rt^2}{r}$
m) $\frac{xy^2z^3}{xyz}$
Question 4
Simplify
a) $\frac{4x}{4x}$
b) $\frac{12xy}{12x}$
c) $\frac{16abc}{8abc}$
d) $\frac{30x^2}{5x}$
e) $\frac{24ut^2}{8u}$
f) $\frac{12u^2v^2}{3uv}$
g) $\frac{42m\sqrt n}{6m}$
h) $\frac{33ab^2\sqrt c}{11ab}$
i) $18+\frac{5\sqrt f gh^2}{5\sqrt f g}$
Question 5
What should be the missing term in the box for the equation to be correct?
a) $\frac{7u}{\square}=7$
b) $\frac{8t}{\square}=t$
c) $\frac{\square}{g}=10$
d) $\frac{\square}{17}=x$
e) $\frac{t^2}{\square}=t$
f) $\frac{8uv}{\square}=8$
g) $\frac{\square}{y^2}=y$
h) $\frac{\square}{abc}=3d$
i) $\frac{\square}{7u^2}=1$
j) $\frac{\square}{5fg^2}=0$
k) $\frac{6yz}{\square}=2y$
l) $\frac{32a^2b^2}{\square}=8a$
m) $\frac{\square}{14m^2n}=4mn^3$
Question 6
Rewrite as fractions and simplify
a) $18t\div9$
b) $25x^3\div5x$
c) $12r^2s^3t^4\div3rst$
d) $24x\sqrt y \div4\sqrt y$
e) $64a\sqrt b c^3\div4ac$
f) $42\sqrt f gh^2 \sqrt k \div6\sqrt f h$
Question 7
Simplify
a) $3+\frac{4e}{e}$
b) $12-\frac{5t^2}{t^2}$
c) $\frac{94\sqrt r}{\sqrt r}+6$
d) $7+\frac{22e^2}{e^2}-\frac{14ab}{ab}$
e) $\frac{22rt}{11rt}-\frac{36\sqrt h}{18\sqrt h}$
f) $30-14n\div n-16p\div 2p$
g) $95-\frac{26y}{2y}+3de\div de$
h) $h+\frac{2h^2}{h}-4gh\div4g$
i) $\frac{7x\sqrt y}{x}-\sqrt y+3\sqrt y z^2 \div z^2$
Answers
Question 1
a) $\frac ab$
b) $\frac 2x$
c) $\frac t5$
d) $\frac {fg}{h}$
e) $\frac {u}{vw}$
f) $\frac {5m}{n}$
g) $\frac {6}{5k}$
h) $\frac {4d}{7e}$
i) $\frac {6xy}{z^2}$
j) $8+\frac {w}{x}$
k) $t^2+\frac {r}{2s}$
l) $18n^2+\frac {5s}{3r^2}$
m) $\frac {\sqrt5}{8y^2}+22t$
Question 2
a) $e$
b) $t$
c) $de$
d) $u^2$
e) $4$
f) $4g$
g) $3k$
h) $8p$
i) $2\sqrt r$
j) $9y^5$
Question 3
a) $6$
b) $8$
c) $17$
d) $33$
e) $1$
f) $15$
g) $c$
h) $ef$
i) $x$
j) $z^2$
k) $2x$
l) $5t^2$
m) $yz^2$
Question 4
a) $1$
b) $y$
c) $2$
d) $6x$
e) $3t^2$
f) $4uv$
g) $7\sqrt n$
h) $3b\sqrt c$
i) $18+h^2$
Question 5
a) $u$
b) $8$
c) $10g$
d) $17x$
e) $t$
f) $uv$
g) $y^3$
h) $3abcd$
i) $7u^2$
j) $0$
k) $3z$
l) $4ab^2$
m) $56m^3n^4$
Question 6
a) $2t$
b) $5x^2$
c) $4rs^2t^3$
d) $6x$
e) $16\sqrt b c^2$
f) $7gh\sqrt k$
Question 7
a) $7$
b) $7$
c) $100$
d) $15$
e) $0$
f) $8$
g) $72$
h) $2h$
i) $9\sqrt y$
Solutions
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Question 5
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Question 6
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Question 7
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