Week 1 & 2: Ratios
Determine the simplest form for the following ratio:
15 : 35
3 : 7
(divide both sides by 5)
Use division to write the following as a simplified rate:
20 000 bottles filled in 7 hours at a factory
2857.1 bottles/hour
Nectarines are sold for $3 per kilogram when they are in season.
Determine the cost of 4.5kg of nectarines.
$13.5
Tanya earns $84 000 annually and receives a 7% pay rise.
Calculate the amount of extra money Tanya receives.
$5880
Increase $100 by 10% and then increase that result by a further 10%.
$121
A fruit bowl contains 3 bananas, 6 apples and 5 oranges.
Use this information to identify the ratio of of oranges to the total number of pieces of fruit
Oranges : Total Fruit
5 : 14
Calculate the average rate of change:
Lucher was 100cm tall in 2012 and is 149cm tall in 2019
7cm/year
The Morello family's water bill states that they use 550 litres per day of water.
Calculate the number of litres of water they would use in one year.
200 750 L
Anna scored 60 marks out of 80 marks on her Science exam. Calculate the percentage that Anna got correct.
75%
Hannah is a childcare worker in Stanthorpe, Queensland, earning a gross wage of $42 000 per annum.
Hannah is given a 1.5% pay increase.
Calculate her gross wage increase.
$630
Use multiplication to comple the equivalent fraction:
2/3 = ?/18
2/3 = 12/18
(multiply by 6)
If sausages cost $8 for 20 sausages, calculate the cost per sausage.
$0.40/sausage
Bethany's car uses 65 litres of fuel to travel 780km.
Teri's car uses 55 litres of fuel to travel 638km.
Determine whose car is the most economical
Bethany’s car is 8.33 L/100 km; Teri’s car is 8.62 L/100 km.
So Bethany’s car is the most economical
Trish is charged a credit card fee of 90 cents for a $36 online purchase of movie tickets. Calculate the percentage of the purchase price that is the credit card fee.
2.5%
Calculate the simple interest earned on an amount of $420 000 invested for 25 years at 0.3% per fortnight.
I = $819000
Graham and Jean run a sheep farm and, after breeding season, they have calculated that the ewe to lamb ratio is 20 : 19.
They currently have a total of 5265 sheep on their property.
Calculate how many ewes and lambs they have in total.
2700 ewes
2565 lambs
Lisa ears $2060/week, which is based on a 36-hour, 5-day working week. Find her income per hour.
$57.22/hour
Calculate the cost of paving a driveway that is 5 m wide and 8 m long if paving costs $75 per square metre.
$3000
Erik wishes to buy a new red baseball cap online. He can buy one from either the Square Shop, where it is marked at $48 and a 20% discount is being offered, or the Triangle Shop, where it is marked at $42 and a 12% discount is being offered.
Both online stores are offering free delivery.
At which online store is the hat cheaper?
Triangle Shop
Calculate the simple interest to be paid on $4000 borrowed for 39 weeks at 3.76% p.a.
$112.80
A map has a scale of 1 : 50,000.
Use the given scale to calculate the actual distance for the scaled distances in km.
A) 6cm
3km
The scale on a map is 5cm to 100km.
Determine the scale of the map in mm per km.
0.5mm/km
The Nguyen family leave home for their family holiday. They leave home at
6 a.m. They plan to have morning tea at a town that is 275 km away from home.
If they travel at an average speed of 85 km/h, calculate at what time they would
expect to stop for morning tea.
9:14 a.m.
A cabinet maker makes bookshelves, each costing her $80 for materials. The cabinet maker sells the bookshelves to a furniture retail business, adding a 75% mark-up on her materials cost. The retailer sells each bookshelf to customers with a 120% mark-up on the cost price.
Calculate the retailer’s marked price of each bookshelf.
$308
Fenton’s water tank contains 12 000 litres of water. It doesn’t rain for a month and, from using the water for his garden, the tank’s water volume has decreased by 81%.
Calculate the overall change in water volume of the tank, in litres.
9720 L lost