Basic 6 · Mathematics · Ratio and Proportion
Understanding Ratio
In this topic you will use concrete models and pictures to explain what a ratio is and write ratios correctly.
By the end of these notes you should be able to:
- Explain a ratio as a comparison of two quantities
- Write ratios in the forms a : b, a to b and a/b
- Use models to represent ratios
What you already know
- Fractions
Copy everything that has a blue line on its left into your notebook. The other parts are for reading.
- Strand
- Number
- Sub-strand
- Ratio and Proportion
- Indicator
- B6.1.4.1.1 – Use concrete models and pictorial representations to explain a ratio
Introduction
A recipe for kenkey dough uses 3 cups of corn flour for every 1 cup of water. We say the ratio of flour to water is 3 to 1. Ratios compare quantities.
1. What Is a Ratio?
Ratio: A comparison of two or more quantities of the same kind, showing how many times one contains the other.
A ratio can be written in three ways: 3 : 1, 3 to 1, or 3/1. The order matters. "Flour to water" is 3 : 1, but "water to flour" is 1 : 3.
2. Using Models
Use bottle tops of two colours. Put 4 red tops and 6 blue tops on the table.
| Comparison | Ratio |
|---|---|
| red to blue | 4 : 6 |
| blue to red | 6 : 4 |
| red to total | 4 : 10 |
| blue to total | 6 : 10 |
3. Part-to-Part and Part-to-Whole
Part-to-part ratios compare one part with another (red : blue = 4 : 6). Part-to-whole ratios compare one part with the total (red : total = 4 : 10), which can also be written as a fraction: 4/10 of the tops are red.
Example 1
A class has 18 boys and 22 girls. Write the ratio of girls to boys and boys to the whole class.
- Girls to boys = 22 : 18
- Total = 18 + 22 = 40
- Boys to whole class = 18 : 40
Answer: 22 : 18 and 18 : 40
4. Same Units
The quantities in a ratio must be in the same units. To compare 50 cm with 2 m, change 2 m to 200 cm: 50 : 200.
Common mistake: Do not reverse the order. "Cats to dogs" means cats first.
New words
- ratio
- A comparison of quantities of the same kind.
- part-to-part
- Comparing one part with another part.
- part-to-whole
- Comparing one part with the total.
- term
- Each number in a ratio.
- order
- Which quantity comes first.
- unit
- A standard of measurement such as cm or kg.
Summary
- A ratio compares quantities: a : b, a to b or a/b.
- Order matters in a ratio.
- Ratios can be part-to-part or part-to-whole.
- Quantities must be in the same units.
Class activity: Ratio Hunt
- Count boys and girls, chairs and tables, windows and doors in your classroom.
- Write each ratio in three forms.
- Present the most interesting ratio.
You need: Bottle tops in two colours, Beans, Maize grains, Exercise books
Exercises
Answer in your exercise book first, then check your answers.
1. 5 mangoes and 3 oranges. The ratio of mangoes to oranges is…
- A. 5 : 3
- B. 3 : 5
- C. 5 : 8
- D. 8 : 5
Show answer
Answer: 5 : 3Mangoes first.2. 7 boys and 9 girls. Ratio of boys to the whole group?
- A. 7 : 16
- B. 7 : 9
- C. 9 : 16
- D. 16 : 7
Show answer
Answer: 7 : 16Total is 16.3. The ratio 50 cm : 1 m written in the same units is…
- A. 50 : 100
- B. 50 : 1
- C. 5 : 1
- D. 1 : 50
Show answer
Answer: 50 : 1001 m = 100 cm.4. 3 : 4 can be written as 3 to 4.
- A. True
- B. False
Show answer
Answer: TrueSame ratio.5. The ratio of boys to girls is the same as girls to boys.
- A. True
- B. False
Show answer
Answer: FalseOrder matters.6. A ratio compares quantities of the ______ kind.
Show answer
Answer: sameSame units.7. A bag has 12 red and 8 green beads. Write the ratio of green to red and green to total.
Show answer
Answer: 8 : 12 and 8 : 20Part-part and part-whole.8. A recipe uses 300 g of rice and 1 kg of water. Write the ratio of rice to water in the same units.
Show answer
Answer: 300 : 1,0001 kg = 1,000 g.
Homework
- Write five ratios about your household (people, rooms, animals).