Ratios to Convert Units

What definition means dimensional analysis?

• ratios that express the same relationship

• the ratio of the circumference of a circle to its diameter

• a unit rate that gives the price of one item

• convert measures by including measurement units when you multiply by a conversion factor

• the speed stays the same over time

What definition means rate?

• a ratio that relates two quantities

  with different units
  

• relates a quantity to 1 unit of another quantity

• the distance around a circle

• a straight line passing through the centre of a circle to touch both sides of the circumference

Express the ratio of 12mm to 3cm in simplest form .

Remember to first change the quantities to the same unit.

And remember that we don't include units in a ratio.

Write the ratio of 120 m to 1 km in simplest form.

Diana uses 30 grams of coffee beans to make 48 fluid ounces of coffee. When guests come, she makes 96 fluid ounces of coffee. How many grams of coffee beans does Diana use when she has visitors?

Mathematical Equivalence

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Find the proportion of :

15 cm to 2 m and 24 seconds to 3 minutes

• 3:5#3:4

• 2:180 # 2#15

• 1:2#1:2

• 3:40 #2:15

Write the ratio of 1.25 litres to 250 mL in simplest form.

Write the ratio of 20 minutes to 2 hours in simplest form.

The process of multiplying by ratios of 1 (conversion factors) and cancelling units to convert from one measure to another.

• unit analysis

• conversion factors

• ratio tables

• equivalent ratios

A comparison of two quantities

• rate

• ratio

• unit rate

• fraction