Unit 6

A piece of rope is 3 1/2 metres long. Each jump rope needs 5/8 metres of rope. How many full jump ropes can be made, and how much rope will be left over? Give your answers as fractions in their lowest terms.

The mass m grams of a medicine needed is directly proportional to a patient's mass. A patient who weighs 72 kg requires 24 grams. How much medicine does a patient of 54 kg need? Write a formula relating m to the patient's mass in kg.

A factory produces toy cars. The number of workers n and the number of days d to complete an order are inversely proportional. An order takes 36 days with 5 workers.

State whether the following statement is true or false and justify your answer: "The reciprocal of is ."

Evaluate .

Write as a fraction.

The cost C of hiring a bike is directly proportional to the number of hours h used. A student pays $12 for 3 hours. Complete the table below and write the formula connecting C and h.

Simplify .

Given that is directly proportional to and when , find the value of when .

The length, metres, of a metal rod is directly proportional to its temperature increase, degrees Celsius. If the rod is 102 cm long when it is heated by 20 ∘C (assume it starts at 0 cm at 0 ∘C), what is its length after a temperature increase of 37.5 ∘C? Give your answer in centimetres.