Minds On

Exploring proportions

Reflect on the following questions:

What is the best way to represent a quantity?

Where do you notice proportions, rates, and ratios in everyday life?

When do you use ratios? To describe something using parts of a whole or parts of a part?

The following paintings come in two different sizes.

Two copies of the same painting, one large and one medium in size

Work with a partner or record your answers to the following questions:

  1. How might you compare the size of the paintings mathematically? What measurements would you need to make?
  2. How would the cost of the paintings change?
  3. What information would you need to know to determine the scale of the paintings?
  4. What is the best way to express this comparison mathematically? Why?

Action

Ratios, proportions, and rates

Ratios

Ratios are a comparison of two or more quantities using the same unit.

Example: There are 5 apples to every 7 bananas in a fruit basket (apples and bananas are both fruit).

5 : 7   or   5 7

Rates

Rates are a comparison of two or more quantities with different units.

Example: The car burns 40 L (litres) of gas for every 200 km (kilometres) it travels (litres of gas and kilometres are different units)

40   L : 200   km   or   40 200

Proportions

Proportions are two ratios compared with each other.

Example: 2 : 3 = 4 : 6   or   2 3 = 4 6

Ratio Rate Proportions

A comparison of two or more quantities using the same unit.

E.g. There are 5 apples to every 7 bananas in a fruit basket (apples and bananas are both fruit).

5 : 7   or   5 7

A comparison of two or more quantities with different units. (in chart)

E.g. The car burns 40 L (litres) of gas for every 200 km (kilometres) it travels (litres of gas and kilometres are different units)

40   L : 200   km   or   40 200

Two ratios compared with each other.

E.g.

2 : 3 = 4 : 6

or

2 3 = 4 6

Making your own trail mix

Trail mixes are a very easy snack to make and are a quick on-the-go food to eat. They are healthy and they can satisfy sweet and salty cravings because of the dried fruit and nuts. Stavro wants to make trail mix with nuts, dried fruit, and dark chocolate. A recipe found online says the perfect ratio of nuts to dried fruit to dark chocolate should be 3 : 2 : 2.

They bought a 200 g bag of dried fruit. How many grams of nuts and dark chocolate need to be added to the mix?

They spent $9.00 on the nuts, $3.00 on the dry fruit and $5.00 on the dark chocolate. What is the rate price of each per 100 g? How much did they spend in total?

If Stavro puts the completed trail mix in small bags, each holding 70 g, how many bags can they make?

Consolidation

Fruit salad

A catering chef is preparing fruit salads for a company luncheon. The fruit salad has watermelon, strawberries and grapes. The ratio is 4 (watermelon) : 2 (strawberries) : 3 (Grapes). If one bowl has 15 grapes, how many pieces of watermelon and strawberries are there? How many pieces in total in the bowl? The chef has a total of 900 pieces of fruit, how many bowls was he able to make?

The chef purchased a total of 36 kg of fruit. How many kg of each type of fruit did they buy?

The chef spent $63.84 on watermelon, $39.92 on strawberries and $71.88 on grapes. What is the unit price for each fruit?

What is the chef’s cost per bowl of fruit? If they sold each bowl for $15.00, what is the profit?

Reflection

As you read the following descriptions, select the one that best describes your current understanding of the learning in this activity. Press the corresponding button once you have made your choice.

I feel...

Now, expand on your ideas by recording your thoughts using a voice recorder, speech-to-text, or writing tool.

When you review your notes on this learning activity later, reflect on whether you would select a different description based on your further review of the material in this learning activity.

Press ‘Discover More’ to extend your skills.

The chef decides to make another fruit salad adding pineapple chunks with a ratio of watermelon to strawberries to grapes to pineapple of 4 : 2 : 3 : 1. How will this affect the pieces of fruit in each bowl? What other calculations should the chef consider?

Connect with a TVO Mathify tutor

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