© T Madas. What do we mean when we say two quantities are inversely proportional ? It means that if: one of them doubles, the other one halves. one of.

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© T Madas

What do we mean when we say two quantities are inversely proportional ? It means that if: one of them doubles, the other one halves. one of them x3, the other one ÷3. one of them x4, the other one ÷4. one of them ÷2, the other one x2. one of them ÷10, the other one x10. Can you give an example of inversely proportional quantities from every day life?

© T Madas The Civic Centre is to be painted, so they call a firm of decorators. If this firm provide: 1 decorator 2 decorators 3 decorators 4 decorators 5 decorators 6 decorators 10 decorators 12 decorators 15 decorators 20 decorators 30 decorators 60 decorators 120 decorators will take 60 days for the job will take 30 days for the job will take 20 days for the job will take 15 days for the job will take 12 days for the job will take 10 days for the job will take 6 days for the job will take 5 days for the job will take 4 days for the job will take 3 days for the job will take 2 days for the job will take 1 day for the job will take ½ day for the job 1 x 60 2 x 30 3 x 20 4 x 15 5 x 12 6 x x 6 12 x 5 15 x 4 20 x 3 30 x 2 60 x x ½

© T Madas INVERSELY PROPORTIONAL QUANTITIES One increases at the same rate as the other one decreases. More formally: Two quantities are inversely proportional if their product remains constant.

15 factory workers produce a car in 12 days. How many days do 10 workers take to produce the same car? How many workers do we need to produce a car in 5 days? Factory Workers workersdays x2x2 ÷2÷2 Inversely Proportional workersxdays=constant 15x12=180 ÷10=1810 workers take 18 days 180÷5=3636 workers take 5 days

© T Madas

6 water pumps fill in a water tank in 15 hours. If one of these pumps is not working, how long will the 5 water pumps take? If we want the tank filled in in 9 hours how many of these water pumps must we have? Water Pumps pumpshours x2x2 ÷2÷2 Inversely Proportional pumpsxhours=constant 6x15=90 ÷5=185 water pumps will take 18 hours 90÷9=10 To fill the tank in 9 hours we need 10 water pumps

© T Madas

A circular flower bed has space for 120 plants, placed 36 cm apart. If we place them 40 cm apart how many plants can we fit? If we need to fit 150 plants how far apart must we place them? Flower Beds plantsspacing x2x2 ÷2÷2 Inversely Proportional plantsxspacing=constant 120x36=4320 ÷40=108 If we place them 40 cm apart we can fit 108 plants 4320÷150=28.8 In order to fit 150 plants we must place them 28.8 cm apart

© T Madas

When full, a watering trough provides enough water to last 24 horses for 5 days. How many days will the same trough, when full, last 15 horses? horsesdays x2x2 ÷2÷2 Inversely Proportional horsexdays=constant 24x5=120 ÷15=8 The watering trough will last 15 horses for 8 days

© T Madas