ratios

1
ratios

• 9C5 - 9C6

• tell how one number is related to another.

• may be written as AB, or A/B, or A to B.

• compare quantities of the same units of
  measurement

• do not have a name or unit of measurement.

The order of the numbers in a ratio is important
2
To tell if two ratios are equal
Cross multiply
a x d b x c 

• if this results in the same answer for both
  ratios, then they are equal.

3
Sometimes we need to think about the units

• 7 mm to 1 cm ó7 1

4
Ratios compare quantities of the same kind.

• So to rewrite statements as ratios
• eg. 7 mm to 1 cm

EXPRESS BOTH QUANTITIES IN THE SAME UNITS.
7 mm to 10mm 710
5
To express ratios in their simplest form

• Are both quantities in the same units?
• Eg. 45 cm to 1.5m 45
  cm to 150 cm
• Cancel the units and write the 2 numbers as a
  ratio 45 150
• Divide both numbers by the highest common factor
  3 10

6
This statement is a DIRECT PROPORTION
1 3 2 6

• To determine whether ratios are in direct
  proportion
• 1/ Write the ratios in fraction form
• 2/ Cross-multiply

(1 x 6) (2 x 3 ) YES, these ratios are in
direct proportion.
7
Using proportions to solve
Find the value of a in the following direct
proportion. cross multiply 30 x a 2 x 45
30a 90
30a 90
30 30
a 90 30  
a 3

8

• To simplify ratios that contain common
  fractions, eg.

• write each fraction with a common denominator,
• then cancel each denominator
• 109

• or ... just cross multiply.

9

• To simplify ratios that have decimal fractions

• change both numbers into whole numbers by
  multiplying them by 10 or 100 etc
  (this eliminates the decimal point)

Eg. 2.1 3.5
2135

• then divide by highest common factor, which in
  this case would be 7.
• 3 5

10
To find the greater ratio
Which is the greater ratio in the pair 3 5 2
3
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12
SIMILAR TRIANGLES have exactly the same shape,
but different size. The ratios of the
corresponding sides are equal.
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Increasing decreasing numbers using ratios
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15
Dividing a number using a ratio
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SPEED A ratio is a comparison of two
quantities with the same units. A rate is a
comparison of two quantities with different
units. Speed is classed as a rate rather than a
ratio.
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