Ratios with more than two terms

The idea

A ratio a : b : c : d : … can have many terms: for every a units of the first quantity there are b units of the second, c of the third, and so on.

A spice mix with four ingredients

Viswanath grinds a spice mix powder from 8 spoons of coriander seeds, 4 red chillies, 2 spoons of toor dal and 1 spoon of fenugreek (methi) seeds.

Can one ratio describe all four ingredients?

• No. A ratio has only two terms.
• Yes. It needs four terms.
• Yes, but only after adding the four amounts.

Make the mix in sets

One set of the recipe has all the ingredients. Press + 1 set again and again and watch all the bars grow. Make 3 sets of both recipes.

One number for each ingredient

A ratio a : b : c : d : … can have many terms: for every a units of the first quantity there are b units of the second, c of the third, and so on.

Viswanath's spice mix is 8 : 4 : 2 : 1. For every 8 spoons of coriander seeds there are 4 red chillies, 2 spoons of toor dal and 1 spoon of fenugreek.

Make 3 sets and every term becomes 3 times as big: 24 : 12 : 6 : 3. The ingredients are all multiplied by the same number, so the mix tastes the same.

Notes

A ratio a : b : c : d : … can have many terms: for every a units of the first quantity there are b units of the second, c of the third, and so on.

Check yourself

A snack mix has peanuts, raisins, cashews and puffed rice in the ratio 6 : 2 : 1 : 3 (spoons). For every 6 spoons of peanuts, how many spoons of puffed rice are there?

Answer: 3 spoons

The terms go in the order peanuts : raisins : cashews : puffed rice = 6 : 2 : 1 : 3, so for every 6 spoons of peanuts there are 3 spoons of puffed rice.

For the spice mix 8 : 4 : 2 : 1 (coriander : red chillies : toor dal : fenugreek), which statement is correct?

Viswanath makes 3 sets of the spice mix 8 : 4 : 2 : 1. How many red chillies does he use in all?

Answer: 12

One set has 4 red chillies. 3 sets have 4 × 3 = 12 red chillies. The whole mix is 24 : 12 : 6 : 3.

Purple paint is made in sets of 2 litres of red, 3 litres of blue and 5 litres of white (ratio 2 : 3 : 5). How many litres of paint do 4 sets make in all?

Answer: 40 litres

One set has 2 + 3 + 5 = 10 litres. 4 sets make 40 litres: 8 litres of red, 12 of blue and 20 of white.

• 1 spoon of fenugreek for every 2 red chillies. The ratio says 4 red chillies for 1 spoon of fenugreek, not 2.
• 4 spoons of coriander for every 8 red chillies. The order is turned round. There are 8 spoons of coriander for every 4 red chillies.
• 2 spoons of toor dal for every 4 red chillies — correct. Yes! Toor dal is 2 and red chillies are 4 in the ratio, so 2 spoons of toor dal go with every 4 red chillies.
• 8 spoons of toor dal for every 2 spoons of coriander. The order is turned round. There are 8 spoons of coriander for every 2 spoons of toor dal.