Unitary Method
Technology 11.2 Paying off a loan
Technology 11.1 Simplifying ratios
Scientific calculators are excellent in working with fractions:
1 Simplify 1535
15
abc35
=
3r7
meaning 372 Simplify 18
4
18
abc4
=
4r1r2
meaning 412 To change to a vulgar fraction: 2ndF abc to give9r2
ie 923 Use a scientific calculator to simplify the following ratios:
a) 3 : 9 b) 9 : 12 c) 16 : 24
d) 2.1 : 3.5 e) 14.4 : 12.6 f) 256 : 1024
Technology 11.2 Paying off a loan
Jade has taken out a $5 500 loan to pay for a home entertainment system. Jade is paying off the loan at $280 a month. Jade would really appreciate it if you could produce a graph showing what is going on. The interest rate is 10.5% pa paid monthly (ie. the interest rate is 10.5÷12= 0.875% per month).
1 Set up a spreadsheet similar to the one below.
2 Use Chart Wizard to produce the graph (Month and balance only).
3 If Jade were to increase repayments to $300 a month, what difference would it make?
4 If the interest rate were to increase to 15.5%, what difference would it make?
5 out of 4 people can’t do fractions.
a b c d
1 Month Balance Repayment Interest
2 0 5500 280 48
3 1 5268 280 46
4 2 5034 280 44
5 3 4798 280 42
6 4 4560 280 40
7 5 4320 280 38
Enter:
=0.00875*b2 Enter:
=b2-c2+d2
Exercise 11.15
1 Write each of the following ratios as a fraction, a decimal and a percentage:
a) 1 : 2 b) 2 : 5 c) 3 : 4
d) 3 : 10 e) 2 : 3 f) 7 : 10
2 Simplify the following ratios:
a) 8 : 4 b) 9 : 12 c) 12 : 16
d) 2.5 : 1.5 e) 2.4 : 1.8 f) 3.5c : 2.1c
3 The rose food is mixed with water in the ratio of 1 : 4. How much rose food is needed to make a mixture of 4 L?
4 The concrete is to be made of cement, sand, and gravel in the ratio of 1 : 3 : 2.
If the mixer takes 30 shovelfulls, how many shovelfulls of sand is needed?
5 Calculate each of the following:
a) 25% of 60 b) 30% of 70 c) 1212% of 80
d) About 70% of a 60 kg person’s weight is water. How much of the 60 kg is water ?
6 A shortcut for adding GST (10%) is to multiply by 1.1. What would be the shortcut for adding 20%? Use the shortcut to increase $40 by 20%
7 Find the discounted price of a phone:?
a) A discount of 15% on the marked price of $95.
b) A discount of 30% on the recommended retail price of $115.
c) Which sounds more impressive? Which is the better deal?
8 A car insurance discount of 7.5% is given to drivers 55 and over. What would a 56 year-old actually pay for a car insurance premium of $475.50?
9 When GST (10%) is added to an item, the price is $88. What was the price of the item before GST was added?
10 A prepaid mobile phone deal offers 28c per text message, what would be the charge for 80 text messages?
11 The instructions on the lawn fertiliser bag suggests that a rate of 3.5 kg per 100 m2 be used for the couch lawn.
How much fertiliser is needed for a 600 m2 lawn?
12 Find the rate per one or 100 in each of the following:
a) 210 runs in 50 overs. b) 48 L used to go 600 km . 13 Which is the best buy?
a) $5.27 for 500 g of breakfast cereal or $4.95 for 450 g?
b) $8.53 for 90 mL of roll on deodorant or $6.99 for 70 mL?
c) $3.37 for 150 g of white chocolate biscuits or $4.05 for 200 g?
Chapter Review 1
In what month do people eat the least?
February – it’s the shortest month. I tell jokes like this because 40% of people will laugh at a
bad joke.
Chapter Review 2
Exercise 11.16
1 Write each of the following ratios as a fraction, a decimal and a percentage:
a) 1 : 2 b) 3 : 5 c) 1 : 4
d) 5 : 10 e) 1 : 3 f) 2 : 5
2 Simplify the following ratios:
a) 5 : 10 b) 6 : 15 c) 15 : 25
d) 1.5 : 2.5 e) 1.8 : 2.4 f) 3.6a : 2.4a
3 The rose food is mixed with water in the ratio of 1 : 3. How much rose food is needed to make a mixture of 2 L?
4 The concrete is to be made of cement, sand, and gravel in the ratio of 1 : 3 : 2.
If the mixer takes 30 shovelfulls, how many shovelfulls of gravel is needed?
5 Calculate each of the following:
a) 15% of 50 b) 30% of 80 c) 3712% of 40 d) About 70% of a person’s weight is water. How much of a 60 kg person
is water?
6 A shortcut for adding GST (10%) is to multiply by 1.1. What would be the shortcut for adding 30%? Use the shortcut to increase $50 by 30%
7 A monthly rent return of $1650 is reduced by a 7% management fee. How much is paid to the landlord?
8 Find the discounted price of a phone:?
a) A discount of 15% on the marked price of $105.
b) A discount of 25% on the recommended retail price of $125.
c) Which sounds more impressive? Which is the better deal?
9 When GST (10%) is added to an item, the price is $99. What was the price of the item before GST was added?
10 A prepaid mobile phone deal offers 29c per text message, what would be the charge for 45 text messages?
11 The prepaid company offers one rate of 68 cents per 30 secs to any mobile or landline within the country. What would it cost for a 3 min 30 sec call?
12 Find the rate per one or 100 in each of the following:
a) 240 runs in 50 overs. b) 54 L used to go 600 km.
13 Which is the best buy?
a) $6.36 for 500 g of chips or $5.85 for 440 g?
b) $1.49 for 750 mL of softdrink or $3.15 for 2 L?
c) $3.74 for 70 mL of insect spray or $4.19 for 105 mL of insect spray?
Why are birds poor?
Money doesn’t grow on trees.
A TASK
Pascal's Triangle:
y Research Pascal's Triangle.
y Find out about the Triangular Numbers and where they may be found in Pascal's Triangle.
y Find another famous number pattern in Pascal's Triangle.
y Describe another pattern that you have noticed.
A LITTLE BIT OF HISTORY
Pascal's Triangle was named after the French mathematician Blaise Pascal (1623−1662).
Pascal's triangle contains many patterns. The following is just one of thousands of patterns:
The sum of each row is a power of 2
1 = 1 = 20
1+1 = 2 = 21
1+2+1 = 4 = 22 1+3+3+1 = 8 = 23 1+4+6+4+1 = 16 = 24
Solve linear equations using algebraic and graphical techniques.
Use variables to symbolise simple linear equations and use a variety of strategies to solve them.
Solve equations using concrete materials, such as the balance model, and explain the need to do the same thing to each side of the equation.
1 11 1 2 1 1 3 3 1 1 4 6 4 1 1 5 10 10 5 1 Can you work out the next couple of lines in Pascal's Triangle?
A lot of things have been named after Blaise Pascal.