Unit 1: Ratio, Rate, & Proportion
Topic A: Writing Ratios
Introduction to Ratios
Ratio is a comparison of one number or quantity with another number or quantity. Ratio shows the relationship between the quantities.
Ratio is pronounced “rā’shō” or it can be pronounced “rā’shēō.” Check out this YouTube video to listen to someone pronouce the word: How to Pronounce Ratio.
You often use ratios, look at these examples:
- Scores in games are ratios. For example, the Penguins won 4 to 3 or the Canucks lost 1 to 5.
- Directions for mixing can be ratios. For example, use 1 egg to each cup of milk or mix 25 parts gas to 1 part oil for the motorcycle.
- Betting odds are given as ratios. For example, Black Jade is a 3 to 1 favourite or the heavyweight contender is only given a 2 to 5 chance to win.
- The scale at the bottom of maps is a ratio. For example, 1 centimetre represents 10 kilometres.
- Prices are often given as ratios. For example, 100 grams for $0.79 or 2 cans for $1.85.
For ratios to have meaning you must know what is being compared and the units that are being used. Read these examples of ratios and the units that are used. A general ratio may say “parts” for the units.
- It rained four days and was sunny for three days last week. The ratio of rainy days to sunny days was [latex]4:3[/latex]. ([latex]4:3[/latex] is properly read “4 is compared to 3” but is often read “4 to 3”).
- The class has 12 men and 15 women registered. The ratio of men to women in the class is [latex]12:15[/latex].
- At the barbeque, 36 hot dogs and 18 hamburgers were eaten. The ratio of hot dogs eaten to hamburgers eaten is [latex]36:18[/latex].
- The class spends 3 hours on English and 2 hours on math each day. The ratio of time spent on English compared to math is [latex]3:2[/latex].
Exercise 1
Write the ratios asked for in these questions using the [latex]:[/latex] symbol (for example, [latex]4:1[/latex]). Write the units and what is being compared beside the ratio.
- Powdered milk is mixed using 1 part of milk powder to 3 parts of water. Write a ratio to compare the milk powder to the water.
Answer: [latex]1:3[/latex] — 1 part of milk powder to 3 parts of water - One kilogram of ground beef will make enough hamburger for 5 people. Write a ratio to express the amount of ground beef for hamburgers to the number of people.
- Seventy-five vehicles were checked by the police. Fifteen vehicles did not meet the safety standards, but 60 of them did. Write a ratio comparing the unsafe vehicles to the safe vehicles.
- The recipe says to roast a turkey according to its weight. For every kilogram, allow 40 minutes of cooking. Write a ratio comparing time to weight.
- The 4-litre pail of semi-transparent oil stain should cover 24 square metres of the house siding if the wood is smooth. Write the ratio comparing quantity of stain to the smooth wood surface area.
- The same 4 L of stain will only cover 16 square metres of the house siding if the wood is rough. Write that ratio.
Answ