Ratio and proportion: mixing lemon sharbat
Pour cups of syrup and water to match a 1 : 3 recipe, then scale it up for more guests without changing the taste.
Core concept
Two mixtures taste the same when their ratios are equal, whatever the amount
Topic: Ratio and proportion
A ratio: A way to compare two amounts, like 2 cups of rice to 3 cups of water (2 : 3). All key words compares two amounts. A sharbat recipe of 1 : 3 means 1 cup of lemon syrup for every 3 cups of water. To make more, both amounts are multiplied by the same number: 2 : 6 and 3 : 9 are equal ratios to 1 : 3, so they taste exactly the same. Dividing both numbers by their highest common factor: A number that divides another exactly. 3 is a factor of 12. All key words gives the simplest form (2 : 6 = 1 : 3). When two ratios are equal, the four numbers are in proportion.
What you will learn
- Write a ratio and reduce it to its simplest form.
- Make equal ratios by multiplying both parts by the same number.
- Use proportion to scale a recipe up for more people.
Before you start
- Multiply and divide small whole numbers.
Materials
- Lemon syrup, water and a measuring cup
Equipment
- A large jug
Procedure
- Tap the syrup bottle or the water jug to pour in one more cup; tap − under it to take one out.
- Watch the colour, the taste meter and the ratio written above the jug.
- Record a jug made with 2 cups of syrup that tastes just right.
- Record a party jug of 16 cups that tastes just right, one that is too strong and one that is too watery.
How this simulation is simplified
- The syrup and the water mix completely.