# Activities 1

## 1.1)

Find the answers and take note of what the parentheses do to the calculation and the answer:

a)
$7×4+3$
b)
$7×\left(4+3\right)$
c)
$10-3×3$
d)
$\left(10-3\right)×3$
e)
$5×8+4×9$
f)
$5×\left(8+4\right)×9$
g)
$20+3×7-4×2+9$
h)
$\left(\left(20+3\right)×7\right)-4×\left(2+9\right)$

a)
$7×4+3$
b)
$7×\left(4+3\right)$
c)
$10-3×3$
d)
$\left(10-3\right)×3$
e)
$5×8+4×9$
f)
$5×\left(8+4\right)×9$
g)
$20+3×7-4×2+9$
h)
$\left(\left(20+3\right)×7\right)-4×\left(2+9\right)$

## 1.2)

Expand the parentheses and find the answers:

a)
$\left(8+19\right)+\left(12-4\right)$
b)
$-\left(4+13\right)+\left(3+26\right)$
c)
$\left(7-12\right)-\left(9-16\right)$
d)
$-\left(-8+3\right)+\left(-7+20\right)$
e)
$\left(-10+8\right)+\left(-5-3\right)$
f)
$-\left(100-20\right)+\left(-5+\left(-12\right)\right)$
g)
$\left(6-5\right)-\left(7-\left(-14\right)\right)$
h)
$-\left(-4-3\right)-\left(-9-\left(-5\right)\right)$

a)
$\left(8+19\right)+\left(12-4\right)$
b)
$-\left(4+13\right)+\left(3+26\right)$
c)
$\left(7-12\right)-\left(9-16\right)$
d)
$-\left(-8+3\right)+\left(-7+20\right)$
e)
$\left(-10+8\right)+\left(-5-3\right)$
f)
$-\left(100-20\right)+\left(-5+\left(-12\right)\right)$
g)
$\left(6-5\right)-\left(7-\left(-14\right)\right)$
h)
$-\left(-4-3\right)-\left(-9-\left(-5\right)\right)$

## 1.3)

a)
$3-1×3$
b)
$\left(3-1\right)×3$
c)
$\left(4-2\right)×\left(2+5\right)$
d)
$2\left(3+2\right)$
e)
$14\left(2+1\right)$
f)
$3×2+4×2-3×5$
g)
$\left(3+4\right)\left(11+19\right)$
h)
$7\left(2-9\right)$
i)
$17+3\left(2+5\right)-2\left(1+\left(-8\right)\right)$

a)
$3-1×3$
b)
$\left(3-1\right)×3$
c)
$\left(4-2\right)×\left(2+5\right)$
d)
$2\left(3+2\right)$
e)
$14\left(2+1\right)$
f)
$3×2+4×2-3×5$
g)
$\left(3+4\right)\left(11+19\right)$
h)
$7\left(2-9\right)$
i)
$17+3\left(2+5\right)-2\left(1+\left(-8\right)\right)$

## 1.4)

Expand the expressions and simplify them as much as possible:

a)
$2×\left(\frac{3}{8}+\frac{1}{4}\right)$
b)
$\left(\frac{5}{6}-\frac{2}{9}\right)×\frac{3}{5}$
c)
$\left(\frac{5}{36}+\frac{1}{12}\right)\frac{2}{9}$
d)
$\left(\frac{7}{6}-\frac{2}{9}\right)×\left(\frac{1}{5}+\frac{1}{4}\right)$
e)
$\frac{4}{33}\left(32-26\right)$
f)
$\left(29-19\right)\frac{1}{60}$
g)
$\phantom{\rule{-0.17em}{0ex}}\left(4+\frac{9}{4}\right)\frac{4}{5}$
h)
$\frac{8}{3}\phantom{\rule{-0.17em}{0ex}}\left(\frac{9}{5}+7\right)$

a)
$2×\left(\frac{3}{8}+\frac{1}{4}\right)$
b)
$\left(\frac{5}{6}-\frac{2}{9}\right)×\frac{3}{5}$
c)
$\left(\frac{5}{36}+\frac{1}{12}\right)\frac{2}{9}$
d)
$\left(\frac{7}{6}-\frac{2}{9}\right)×\left(\frac{1}{5}+\frac{1}{4}\right)$
e)
$\frac{4}{33}\left(32-26\right)$
f)
$\left(29-19\right)\frac{1}{60}$
g)
$\phantom{\rule{-0.17em}{0ex}}\left(4+\frac{9}{4}\right)\frac{4}{5}$
h)
$\frac{8}{3}\phantom{\rule{-0.17em}{0ex}}\left(\frac{9}{5}+7\right)$

## 1.5)

Expand the expressions and simplify them as much as possible:

a)
$3\phantom{\rule{-0.17em}{0ex}}\left(\frac{1}{2}+\frac{3}{4}\right)$
b)
$12\phantom{\rule{-0.17em}{0ex}}\left(\frac{1}{3}+\frac{1}{4}\right)$
c)
$24\phantom{\rule{-0.17em}{0ex}}\left(\frac{2}{8}+\frac{3}{6}\right)$
d)
$\frac{1}{2}\phantom{\rule{-0.17em}{0ex}}\left(\frac{5}{9}+\frac{24}{10}\right)$
e)
$4\phantom{\rule{-0.17em}{0ex}}\left(\frac{2}{5}-\frac{4}{7}\right)$
f)
$\phantom{\rule{-0.17em}{0ex}}\left(\frac{6}{10}-\frac{1}{3}\right)5$
g)
$\phantom{\rule{-0.17em}{0ex}}\left(4-\frac{1}{2}\right)7$
h)
$\phantom{\rule{-0.17em}{0ex}}\left(\frac{6}{5}+2\right)8$

a)
$3\phantom{\rule{-0.17em}{0ex}}\left(\frac{1}{2}+\frac{3}{4}\right)$
b)
$12\phantom{\rule{-0.17em}{0ex}}\left(\frac{1}{3}+\frac{1}{4}\right)$
c)
$24\phantom{\rule{-0.17em}{0ex}}\left(\frac{2}{8}+\frac{3}{6}\right)$
d)
$\frac{1}{2}\phantom{\rule{-0.17em}{0ex}}\left(\frac{5}{9}+\frac{24}{10}\right)$
e)
$4\phantom{\rule{-0.17em}{0ex}}\left(\frac{2}{5}-\frac{4}{7}\right)$
f)
$\phantom{\rule{-0.17em}{0ex}}\left(\frac{6}{10}-\frac{1}{3}\right)5$
g)
$\phantom{\rule{-0.17em}{0ex}}\left(4-\frac{1}{2}\right)7$
h)
$\phantom{\rule{-0.17em}{0ex}}\left(\frac{6}{5}+2\right)8$

## 1.6)

Expand the expressions and simplify them if possible:

a)
$2\left(3+a\right)$
b)
$a\left(5+b\right)$
c)
$\frac{1}{3}\cdot \left(3+b\right)$
d)
$\left(2+a\right)\cdot \frac{3}{4}$
e)
$b\phantom{\rule{-0.17em}{0ex}}\left(\frac{2}{3}+\frac{1}{3}\right)$
f)
$\frac{3}{8}\left(a+b\right)$
g)
$\phantom{\rule{-0.17em}{0ex}}\left(b-\frac{2b}{9}\right)6$
h)
$\frac{8}{3}\phantom{\rule{-0.17em}{0ex}}\left(\frac{a}{3}+b\right)$

## 1.7)

Expand the parentheses and contract the resulting expressions:

a)
$\left(x+2\right)\left(y-2x\right)$
b)
$\phantom{\rule{-0.17em}{0ex}}\left(2{x}^{2}-a\right)\left(b-a\right)$
c)
$\left(a+b\right)\left(a+b\right)$
d)
$\left(a-b\right)\left(a-b\right)$
e)
$\left(a-b\right)\left(a+b\right)$
f)
$\left(x+y\right)\left(x+y\right)$
g)
$\left(x+y\right)\left(x+y\right)\left(x+y\right)$
h)
$2\left(a+3b\right)\left(a+b\right)$
i)
$5\left(2a+b\right)\left(3a-2b\right)$
j)
$3\left(4x+6y\right)\left(x+2y\right)\left(3x+5y\right)$
k)
$7\phantom{\rule{-0.17em}{0ex}}\left(2{x}^{2}+3y\right)\left(2x+5y\right)$
l)
$2\phantom{\rule{-0.17em}{0ex}}\left(6{x}^{2}+2{y}^{2}\right)\phantom{\rule{-0.17em}{0ex}}\left(3{x}^{2}+{y}^{2}\right)$
m)
$\left(a+b\right)\left(a+b\right)\left(a+b\right)\left(a+b\right)$

## 1.8)

Expand the parentheses and contract the resulting expressions:

a)
$x\left(x+2\right)+\left(x+2\right)\left(x+1\right)$
b)
$\left(x+4\right)\left(x+5\right)-3x\left(5+2x\right)$
c)
$\begin{array}{ccc}\hfill & \left(3x-2\right)\left(5+2x\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}+\left(4x+4\right)\left(6x+1\right)\hfill \end{array}$
d)
$\begin{array}{ccc}\hfill & \left(4x+2\right)\left(3+2x\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-\left(9x+1\right)\left(2x-3\right)\hfill \end{array}$
e)
$\begin{array}{ccc}\hfill & \left(5+4x\right)\left(2+6x\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-\left(x-7\right)\left(3x-5\right)\hfill \end{array}$
f)
$\left(5+4x\right)\left(2+6x\right)+\left(x-7\right)\left(3x-5\right)$

a)
$x\left(x+2\right)+\left(x+2\right)\left(x+1\right)$
b)
$\left(x+4\right)\left(x+5\right)-3x\left(5+2x\right)$
c)
$\left(3x-2\right)\left(5+2x\right)+\left(4x+4\right)\left(6x+1\right)$
d)
$\left(4x+2\right)\left(3+2x\right)-\left(9x+1\right)\left(2x-3\right)$
e)
$\left(5+4x\right)\left(2+6x\right)-\left(x-7\right)\left(3x-5\right)$
f)
$\left(5+4x\right)\left(2+6x\right)+\left(x-7\right)\left(3x-5\right)$

## 1.9)

Expand the parentheses and contract the resulting expressions:

a)
$\begin{array}{ccc}\hfill & 2\left(a+b\right)\left(3a+b\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}+3\left(2a+b\right)\left(a-b\right)\hfill \end{array}$
b)
$\begin{array}{ccc}\hfill & 7\left(4a-2b\right)\left(2a-b\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-\left(a-4b\right)\left(2a-b\right)\hfill \end{array}$
c)
$\begin{array}{ccc}\hfill & 4\left(2a-b\right)\left(3a-2b\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-3\left(-5a-\left(-3\right)\cdot b\right)\left(a+b\right)\hfill \end{array}$
d)
$\begin{array}{ccc}\hfill & \left(a+b\right)\left(2a-3b\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-5\left(-2a-2b\right)\left(6a+b\right)\hfill \\ \hfill & \phantom{\rule{2em}{0ex}}\cdot \left(3a-4b\right)\hfill \end{array}$
e)
$\begin{array}{ccc}\hfill & \left(2a-5\right)\left(3b+1\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-\left(4a+3b-2\right)\left(a+b\right)\hfill \\ \hfill & \phantom{\rule{2em}{0ex}}+5\left(3a+b\right)\hfill \end{array}$

a)
$2\left(a+b\right)\left(3a+b\right)+3\left(2a+b\right)\left(a-b\right)$
b)
$7\left(4a-2b\right)\left(2a-b\right)-\left(a-4b\right)\left(2a-b\right)$
c)
$4\left(2a-b\right)\left(3a-2b\right)-3\left(-5a-\left(-3\right)\cdot b\right)\left(a+b\right)$
d)
$\left(a+b\right)\left(2a-3b\right)-5\left(-2a-2b\right)\left(6a+b\right)\left(3a-4b\right)$
e)
$\left(2a-5\right)\left(3b+1\right)-\left(4a+3b-2\right)\left(a+b\right)+5\left(3a+b\right)$

## 1.10)

Expand the parentheses and contract the resulting expressions:

a)
$2x+\left(3+4x\right)$
b)
$x+2\left(x+5\right)$
c)
$7x+2\left(6x+11+2x\right)+x$
d)
$5+3x+2\left(x+2\right)+4x$
e)
$\begin{array}{ccc}\hfill & 7-2x+3\left(2x+5\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-\left(-2+\left(-7\right)+3x\right)\hfill \end{array}$
f)
$3x-2\left(x+3\right)$
g)
$4x-3\left(2-x\right)$
h)
$x+5-4\left(-1+3x\right)$

a)
$2x+\left(3+4x\right)$
b)
$x+2\left(x+5\right)$
c)
$7x+2\left(6x+11+2x\right)+x$
d)
$5+3x+2\left(x+2\right)+4x$
e)
$7-2x+3\left(2x+5\right)-\left(-2+\left(-7\right)+3x\right)$
f)
$3x-2\left(x+3\right)$
g)
$4x-3\left(2-x\right)$
h)
$x+5-4\left(-1+3x\right)$

## 1.11)

Expand the parentheses and contract the resulting expressions:

a)
$5{x}^{2}-3x\left(2x-3\right)\left(4x+2\right)$
b)
$-7x+3-5x\left(x+2\right)\left(2x-1\right)$
c)
${x}^{2}-x+2+3\left(2-3x\right)\left(5x+3\right)$
d)
$\begin{array}{ccc}\hfill & {x}^{2}-7x\left(2x+3\right)\left(2x-3\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-\left(5x-3\right)\hfill \end{array}$
e)
$\begin{array}{ccc}\hfill & 2x\left(4x-5\right)\left(6x+3\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-x\left(x+4\right)\left(3x-1\right)\hfill \end{array}$
f)
$\begin{array}{ccc}\hfill & \left(2x-3\right)\left(3x+5\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-3x\left(4x-2\right)\left(3x-2\hfill \end{array}$

a)
$5{x}^{2}-3x\left(2x-3\right)\left(4x+2\right)$
b)
$-7x+3-5x\left(x+2\right)\left(2x-1\right)$
c)
${x}^{2}-x+2+3\left(2-3x\right)\left(5x+3\right)$
d)
${x}^{2}-7x\left(2x+3\right)\left(2x-3\right)-\left(5x-3\right)$
e)
$2x\left(4x-5\right)\left(6x+3\right)-x\left(x+4\right)\left(3x-1\right)$
f)
$\left(2x-3\right)\left(3x+5\right)-3x\left(4x-2\right)\left(3x-2\right)$

## 1.12)

Simplify the expressions as much as possible:

a)
$\frac{2\left(4x+5x\right)}{x\left(12-3\right)}$
b)
$\frac{4x\left(2+3\right)}{5x-x\left(7-6\right)}$
c)
$\frac{18y}{\left(15-9\right)y}$
d)
$\frac{-\left(9x+4x\right)}{2\left(20x+6x\right)}$
e)
$\frac{5x\left(x+2x\right)}{\left(9-4\right)x}$
f)
$\frac{\left(y+5y\right)3y}{4\left(15y-8y+2y\right)}$
g)
$\frac{y\left(3+8\right)\left(-4+12\right)}{5\left(6y-3y\right)}$
h)
$\frac{8\left(11x-9x\right)}{4-\left(12-16\right)}$

a)
$\frac{2\left(4x+5x\right)}{x\left(12-3\right)}$
b)
$\frac{4x\left(2+3\right)}{5x-x\left(7-6\right)}$
c)
$\frac{18y}{\left(15-9\right)y}$
d)
$\frac{-\left(9x+4x\right)}{2\left(20x+6x\right)}$
e)
$\frac{5x\left(x+2x\right)}{\left(9-4\right)x}$
f)
$\frac{\left(y+5y\right)3y}{4\left(15y-8y+2y\right)}$
g)
$\frac{y\left(3+8\right)\left(-4+12\right)}{5\left(6y-3y\right)}$
h)
$\frac{8\left(11x-9x\right)}{4-\left(12-16\right)}$

## 1.13)

Contract the expressions:

a)
$\begin{array}{ccc}\hfill & {a}^{2}+4\left(3a+b\right)\left(-7a+2b\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}+3{b}^{2}-\left(2+5b\right)\hfill \end{array}$
b)
$\begin{array}{ccc}\hfill & ab+3b-4+2\left(-6a-3b\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-4ab+\left(a+2b\right)\left(3a-b\right)\hfill \\ \hfill & \phantom{\rule{2em}{0ex}}+5\hfill \end{array}$
c)
$\begin{array}{ccc}\hfill & 2{a}^{2}+3\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-\left(a+2b\right)\left(2a-b\right)+5{b}^{2}\hfill \end{array}$
d)
$\begin{array}{ccc}\hfill & 7{b}^{2}+5-\left(a+b\right)\left(a+2b\right)\hfill & \hfill \\ \hfill & \phantom{\rule{2em}{0ex}}-\left(3a+b\right)\left(2a-2b\right)\hfill \\ \hfill & \phantom{\rule{2em}{0ex}}+7\left(a+1\right)\hfill \end{array}$

a)
${a}^{2}+4\left(3a+b\right)\left(-7a+2b\right)+3{b}^{2}-\left(2+5b\right)$
b)
$ab+3b-4+2\left(-6a-3b\right)-4ab+\left(a+2b\right)\left(3a-b\right)+5$
c)
$2{a}^{2}+3-\left(a+2b\right)\left(2a-b\right)+5{b}^{2}$
d)
$7{b}^{2}+5-\left(a+b\right)\left(a+2b\right)-\left(3a+b\right)\left(2a-2b\right)+7\left(a+1\right)$

## 1.14)

Contract the expressions:

a)
$\frac{a+4b}{2}+\frac{3a-7b}{3}$
b)
$\frac{3x-5y}{3}+\frac{8y+4x}{4}$
c)
$\frac{6y+9x}{5}-\frac{2x-3y}{6}$
d)
$\frac{12b+4a}{8}+\frac{7a-5b}{5}$
e)
$\frac{14b-7a}{9}-\frac{4b-3a}{3}$
f)
$\frac{20m+12n}{14}+\frac{6n-8m}{5}$
g)
$\frac{2\left(4p+3a\right)}{8}-\frac{3\left(p-4a\right)}{6}$
h)
$-\frac{5k+5h}{4}+\frac{17k+22h}{12}$

a)
$\frac{a+4b}{2}+\frac{3a-7b}{3}$
b)
$\frac{3x-5y}{3}+\frac{8y+4x}{4}$
c)
$\frac{6y+9x}{5}-\frac{2x-3y}{6}$
d)
$\frac{12b+4a}{8}+\frac{7a-5b}{5}$
e)
$\frac{14b-7a}{9}-\frac{4b-3a}{3}$
f)
$\frac{20m+12n}{14}+\frac{6n-8m}{5}$
g)
$\frac{2\left(4p+3a\right)}{8}-\frac{3\left(p-4a\right)}{6}$
h)
$-\frac{5k+5h}{4}+\frac{17k+22h}{12}$

## 1.15)

Contract the expressions:

a)
$\frac{2\left(4x+3\right)}{a}+\frac{3\left(7-2x\right)}{b}$
b)
$\frac{5\left(x-2\right)}{3a}-\frac{\left(5x+3\right)}{3b}$
c)
$\frac{9p+3d}{c}+\frac{6\left(7p-4\right)}{5c}$
d)
$\frac{4\left(12x+3z\right)}{x}-\frac{10\left(z+3\right)}{4}$
e)
$\frac{2x\left(3a-6b\right)}{t}+\frac{a\left(4x-b\right)}{r}$
f)
$\frac{3p\left(2+p\right)}{{p}^{2}}-\frac{3\left(2p-p\right)}{p}$
g)
$\frac{\left(4-x\right)\left(x+3\right)}{4x}+\frac{\left(0-3x\right)5}{8}$
h)
$\frac{\left(3a+4b\right)\left(5b-2a\right)}{6x}+\frac{\left(8a+2b\right)\left(3a-4b\right)}{4x}$

## 1.16)

Expand the expressions:

a)
$\frac{\left(4x-3b\right)}{5a}\cdot \frac{\left(b+7x\right)}{3c}$
b)
$\frac{\left(2a+5b\right)}{12d}\cdot \frac{\left(8a+3b\right)}{3k}$
c)
$\frac{\left(6b-3a\right)}{4c}\cdot \frac{\left(9a-5b\right)}{7c}$
d)
$\frac{\left(8a+2b\right)}{7n}\cdot \frac{\left(4a-6b\right)}{3n}$
e)
$\frac{2\left(2a+2b\right)}{\left(a+b\right)}\cdot \frac{\left(2a+2b\right)}{\left(a-b\right)}$
f)
$\frac{4\left(g+5h\right)}{\left(3a-5b\right)}\cdot \frac{9\left(2h+3g\right)}{\left(2b-3a\right)}$
g)
$\frac{\left(15n+12m\right)}{\left(6b-4a\right)}\cdot \frac{\left(2n-m\right)}{\left(2a+3b\right)}$
h)
$\frac{9p}{\left(a-b\right)}\cdot \frac{\left(4s-6r\right)3}{\left(a-b\right)}$

a)
$\frac{\left(4x-3b\right)}{5a}\cdot \frac{\left(b+7x\right)}{3c}$
b)
$\frac{\left(2a+5b\right)}{12d}\cdot \frac{\left(8a+3b\right)}{3k}$
c)
$\frac{\left(6b-3a\right)}{4c}\cdot \frac{\left(9a-5b\right)}{7c}$
d)
$\frac{\left(8a+2b\right)}{7n}\cdot \frac{\left(4a-6b\right)}{3n}$
e)
$\frac{2\left(2a+2b\right)}{\left(a+b\right)}\cdot \frac{\left(2a+2b\right)}{\left(a-b\right)}$
f)
$\frac{4\left(g+5h\right)}{\left(3a-5b\right)}\cdot \frac{9\left(2h+3g\right)}{\left(2b-3a\right)}$
g)
$\frac{\left(15n+12m\right)}{\left(6b-4a\right)}\cdot \frac{\left(2n-m\right)}{\left(2a+3b\right)}$
h)
$\frac{9p}{\left(a-b\right)}\cdot \frac{\left(4s-6r\right)3}{\left(a-b\right)}$

You can find the solutions here.