Mr. M’s Madcap Mathematical Minds

A Look at Ratios

Ratios can be thought of as a way to compare two quantities. There are six ways that a ratio can be written, and they can be remembered by the saying:

Fast Cats Run Pretty Darn Quick

Fractions – Familiar number with two parts, a Numerator (Up) and a Denominator (Down)

Comparisons – Written with a colon (:) to show the comparison in its simplest form.

Rates – Compare quantities to 1. An example is 65 miles “per” hour.

Percentages – Compare quantities to 100 of that item.

Decimals – Compare quantities to powers of 10. (ie: 10, 100, 1000, etc.)

Quotients – Means to divide, this is a way to compare quantities with a ¸ symbol.

Start in your study teams and express these ratios in each of the six ways they can be expressed.

1.  Write a ratio of 2 to 9 .

2.  Write a ratio of 5 to 7.

3.  Write a ratio of 12 to 18, and don’t forget to simplify!

4.  Write a ratio of 42 to 35 and make sure you simplify!

Comparing items of different units:

Sometimes ratios want to compare measurements of different units. For example if you wanted to compare 20 minutes to 1 hour, you couldn’t . That is without converting units first. Look at these examples for help.

Fast Cats Run Pretty Darn Quick by S. Middleton 2 revised: 05/06/04

Compare: 2 hours with 10 minutes.

Step 1- Convert the units to the same kind. In this example convert both numbers to minutes:

Step 2 – Write the ratio with the converted units.

Step 3 – Simplify.


Fast Cats Run Pretty Darn Quick by S. Middleton 2 revised: 05/06/04

Write each ratio in its simplest form:

5. 20 sec: 1 min 6. 6days : 2 weeks 7. 2 ft. : 1 yd. 8. 1 day: 30 hours

9. 8 weeks : 1 year 10. 4 hours: 30 min. 11. 5 ft. : 3 yds. 12. 4 months: 1 year

To make Ratios within the Metric (S.I.) System, remember the units.

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Kilo Hecto Deka Meter deci centi milli

(basic unit)

1000 100 10 1 0.1 0.01 0.001

Convert units to make comparisons:

13. 5m to 50 cm 14. 6 km to 120 m 15. 5 m to 250 dm 16. 12 cm to 1.2 m

Sometimes you need to go back and forth between the English system and the Metric System, to do so, remember this simple conversion.

If 1 inch = 2.54 cm, then make these ratios.

17. 1 foot to 10 cm 18. 1 yd. To 50 cm 19. 20m to 15 feet 20. 5m to 5 yds

Fast Cats Run Pretty Darn Quick by S. Middleton 2 revised: 05/06/04