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Proportional Reasoning Worksheet
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Name:Date:
Proportional Reasoning Worksheet
Show your working for calculation questions. Include units where appropriate.
Choose the best answer
1.At a sports-day relay, the ratio of runners wearing blue bands to runners wearing orange bands is 4:7. If 28 runners wear orange bands, how many wear blue bands?
- 12
- 16
- 21
- 49
2.A sports drink bottle costs $8.40 before 15% GST is added. What is the price including GST?
- $9.06
- $9.66
- $9.80
- $10.40
3.Which value is greater: 6.8 × 10⁻³ or 0.0065?
- 6.8 × 10⁻³
- 0.0065
- They are equal
- There is not enough information
4.A sports-day team needs 450 mL of water for 6 competitors. At the same rate, how much water is needed for 14 competitors?
- 750 mL
- 900 mL
- 1,050 mL
- 1,200 mL
5.A New Zealand team exchanges $80 NZD at a rate of 1 NZD = 0.91 AUD. How many Australian dollars do they receive?
- $72.80 AUD
- $73.90 AUD
- $87.91 AUD
- $91.00 AUD
Show your working
6.Hana exchanges $180 NZD for Australian dollars at a rate of 1 NZD = 0.94 AUD. Calculate the amount she receives.
7.A pair of running shoes is marked down by 30% from its original price of $150. Find the sale price.
8.Compare 3.6 × 10⁻⁴ m with 0.00032 m. State which measurement is larger and show how you know.
Read the data
The table records modeled sign-up totals for a school sports-day event over five weeks. Values are shown before rounding to whole people.
Week
Participants
1
320
2
368
3
423.2
4
486.68
5
559.682
9.From Week 1 to Week 2, what is the percentage increase in sports-day sign-ups?
10.The sign-ups increase by the same percentage each week. Predict the number of participants in Week 6, rounding to the nearest whole person.
11.Write the Week 5 to Week 1 sign-up ratio in simplest form, using the values in the table.
Proportions in context
12.A minibus travels 156 km in 2 hours at a steady speed. How far will it travel in 3.5 hours at the same speed?
13.At a constant speed of 84 km/h, how long will it take a vehicle to travel 294 km?
14.A scale plan uses 1:25,000. Two sports venues are 6.4 cm apart on the plan. What is their actual distance in kilometres?
15.A drink mix uses concentrate and water in the ratio 2:7. How much concentrate and how much water are needed to make 810 mL of drink?
4 printable pages
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