Solutions

Activities 1

1.1)

a): $\frac{25}{100}$
b): $\frac{15}{100}$
c): $\frac{10}{100}$
d): $\frac{1}{100}$
e): $\frac{100}{100}$
f): $\frac{50}{100}$
g): $\frac{60}{100}$
h): $\frac{70}{100}$
i): $\frac{75}{100}$

a): $\frac{25}{100}$
b): $\frac{15}{100}$
c): $\frac{10}{100}$
d): $\frac{1}{100}$
e): $\frac{100}{100}$
f): $\frac{50}{100}$
g): $\frac{60}{100}$
h): $\frac{70}{100}$
i): $\frac{75}{100}$

1.2)

a): $\frac{1}{4}$
b): $\frac{3}{20}$
c): $\frac{1}{10}$
d): $\frac{1}{100}$
e): $1 = \frac{1}{1}$
f): $\frac{1}{2}$
g): $\frac{3}{5}$
h): $\frac{7}{10}$
i): $\frac{3}{4}$

a): $\frac{1}{4}$
b): $\frac{3}{20}$
c): $\frac{1}{10}$
d): $\frac{1}{100}$
e): $1 = \frac{1}{1}$
f): $\frac{1}{2}$
g): $\frac{3}{5}$
h): $\frac{7}{10}$
i): $\frac{3}{4}$

1.3)

a): $\frac{25}{100} = 0.25$
b): $\frac{75}{100} = 0.75$
c): $\frac{10}{100} = 0.1$
d): $\frac{90}{100} = 0.9$
e): $\frac{100}{100} = 1$
f): $\frac{0}{100} = 0$
g): $\frac{35}{100} = 0.35$
h): $\frac{65}{100} = 0.65$

a): $\frac{25}{100} = 0.25$
b): $\frac{75}{100} = 0.75$
c): $\frac{10}{100} = 0.1$
d): $\frac{90}{100} = 0.9$
e): $\frac{100}{100} = 1$
f): $\frac{0}{100} = 0$
g): $\frac{35}{100} = 0.35$
h): $\frac{65}{100} = 0.65$

1.4)

a): $\frac{250}{1000}$
b): $\frac{150}{1000}$
c): $\frac{10}{1000}$
d): $\frac{1}{1000}$
e): $\frac{1000}{1000}$
f): $\frac{100}{1000}$
g): $\frac{600}{1000}$
h): $\frac{70}{1000}$
i): $\frac{700}{1000}$

a): $\frac{250}{1000}$
b): $\frac{150}{1000}$
c): $\frac{10}{1000}$
d): $\frac{1}{1000}$
e): $\frac{1000}{1000}$
f): $\frac{100}{1000}$
g): $\frac{600}{1000}$
h): $\frac{70}{1000}$
i): $\frac{700}{1000}$

1.5)

a): $ $5$
b): $ $15$
c): 45 girls
d): 405 girls
e): $ $60$
f): $ $40$
g): 22 boys
h): 2178 boys
i): $ $17.50$
j): $ $7.50$
k): 225 students
l): 75 students
m): 2 footballs
n): 6 footballs
o): 8 footballs
p): 0 footballs

a): $ $5$
b): $ $15$
c): 45 girls
d): 405 girls
e): $ $60$
f): $ $40$
g): 22 boys
h): 2178 boys
i): $ $17.50$
j): $ $7.50$
k): 225 students
l): 75 students
m): 2 footballs
n): 6 footballs
o): 8 footballs
p): 0 footballs

1.6)

a) + b) = $ $20$
c) + d) = 450 girls
e) + f) = $ $100$
g) + h) = 2200 boys
i) + j) = $ $25$
k) + l) = 300 students
m) + n) = 8 footballs
o) + p) = 8 footballs

a) + b) = $ $20$
c) + d) = 450 girls
e) + f) = $ $100$
g) + h) = 2200 boys
i) + j) = $ $25$
k) + l) = 300 students
m) + n) = 8 footballs
o) + p) = 8 footballs

In all these activities, the sum is the whole amount (

100

%).

Activities 2

2.1)

a): $50$ %
b): $75$ %
c): $65$ %
d): $99$ %
e): $2$ %
f): $100$ %
g): $250$ %
h): $600$ %

a): $50$ %
b): $75$ %
c): $65$ %
d): $99$ %
e): $2$ %
f): $100$ %
g): $250$ %
h): $600$ %

2.2)

a): $0.25 = 25 %$
b): $0.2 = 20 %$
c): $0.75 = 75 %$
d): $0.6 = 60 %$
e): $0.4 = 40 %$
f): $0.8 = 8 %$
g): $\approx 0.33 = 33.3 %$
h): $\approx 0.67 = 66.7 %$
i): $\approx 0.67 = 66.7 %$
j): $0.025 = 2.5 %$
k): $\approx 0.67 = 66.7 %$
l): $4.5 = 450 %$

a): $0.25 = 25 %$
b): $0.2 = 20 %$
c): $0.75 = 75 %$
d): $0.6 = 60 %$
e): $0.4 = 40 %$
f): $0.8 = 8 %$
g): $\approx 0.33 = 33.3 %$
h): $\approx 0.67 = 66.7 %$
i): $\approx 0.67 = 66.7 %$
j): $0.025 = 2.5 %$
k): $\approx 0.67 = 66.7 %$
l): $4.5 = 450 %$

2.3)

33.3

% (rounded)

2.4)

a): Just over half, just over $50$ %
b): $52.9$ % (rounded)

2.5)

a): Just over half and less than $\frac{3}{4}$ , approximately $60$ %. Alternatively, split the cake into 14 equal pieces that each weigh $100$ g, so Eric buys 8 pieces $\frac{8}{14} = \frac{4}{7}$ .
b): $57.1$ % (rounded)

2.6)

a): About $\frac{3}{4}$ , which is $75$ %
b): $80$ %

Activities 3

3.1)

Discount: $

4

New price: $ $36$

3.2)

Increase: $

4

New price: $ $44$

3.3)

Discount: $

120

New price: $ $280$ . $$ 400 \times 70 % = $ 280$

3.4)

Change in percent:

\frac{$ 5}{$ 40} = \frac{1}{8} = 12.5 %

3.5)

a): New price: $ $240$
b): Discount in percent: $\frac{$ 160}{$ 400} = 0.4 = 40 %$
c): $60$ % of the old price
d): $60 % + 40 % = 100 % = 1$

3.6)

Approximately $

560

3.7)

Approximately $

240

3.8)

a): Approximately $ $180$
b): Exactly $ $186$

3.9)

a): Approximately $ $200$
b): Exactly $ $216$

3.10)

a): Approximately $ $360$
b): Exactly $ $354$

3.11)

a)

The increase in price is $

4

. The new price in March is $

44

b)

10

% of the price in March: $

4.40

c)

The price in April is $

39.60

. (Note! The answer is not

$ 40)

3.12)

a): Discount in March: $ $2$ . New price in March: $ $8$ .
b): March price being $ $8$ gives an increase of $$ 8 \times 20 % = $ 1.60$
c): New price in April: $ $9.60$ (Note! The answer is not $$ 10)$

Activities 4

4.1)

80

4.2)

50

4.3)

a): $ $40$
b): $40$ %

a): $ $40$
b): $40$ %

4.4)

a): $60$ %
b): $ $20$
c): $40$ %

a): $60$ %
b): $ $20$
c): $40$ %

4.5)

\frac{15}{75} = \frac{1}{5} = 0.2 = 20 %

4.6)

50

4.7)

a): $ $37.50$
b): $\frac{1}{4}$ $(0.5 \times 0.5 = 0.25)$ or $(\frac{1}{2} \times \frac{1}{2} = \frac{1}{4})$

4.8)

a): $ $14$ The yellow label discount is $ $12$ , for an original discounted price of $ $28$ . The red label then discounts that price another $50$ % to $ $14$ , the correct answer.
b): $65$ %

Activities 5

5.1)

42

5.2)

31.50

5.3)

29

5.4)

23

Activities 5