Scaling by fractions and simple rates
Solve problems involving scaling by simple fractions and problems involving simple rates
What a learner can do afterwards
- A recipe for 4 people needs 200 g of flour. How much for 6 people?
- If 3 kg costs £12, how much does 5 kg cost?
- Scale a shape by a factor of 1/2 and find the new dimensions
1 · Read
You already know how to find a fraction of an amount and how to compare numbers using multiplication. Now you will use both skills to scale recipes, prices, and shapes. Scaling means changing every part by the same amount, so everything stays balanced.
A recipe for 4 people needs 240 g of flour. To cook it for 6 people, find one person's share first: 240 divided by 4 is 60 g each. Then 6 people need 6 lots of 60 g, which is 360 g. The total changes, but every person still gets the same share.
3 kg of apples costs £12. First, find the cost of 1 kg: £12 divided by 3 is £4. Now that you know 1 kg costs £4, you can find any amount: 5 kg costs £4 times 5, which is £20.
A ribbon is 10 cm long. You scale it by a factor of 1/2, so you multiply the length by 1/2. 10 times 1/2 is 5, so the new ribbon is 5 cm long. Every measurement of a scaled shape gets multiplied by the same fraction.
When you scale something, first work out what one part is worth. Then multiply that by however many parts you need. This works for recipes, prices, and shapes.
To scale something, find the value of one part first, then multiply it by the fraction or amount you need.
More to read
Ratios and Rates
A ratio compares two amounts, like the number of red cars to blue cars in a parking lot. A rate is a special kind of ratio that compares two different kinds of things, like how far a bike goes in one hour, or how much a bag of apples costs.
One very handy rate is the UNIT RATE. It tells you the amount for just ONE item. Say a shop sells 3 kilograms of oranges for 12 pounds. To find the unit rate, divide: 12 pounds divided by 3 kg equals 4 pounds per kilogram. Once you know that, you can work out the cost of any amount. Want 5 kg? Just multiply: 4 pounds times 5 equals 20 pounds.
Unit rates also help you spot the better deal. If one shop sells 2 kg of apples for 6 pounds and another sells 5 kg for 14 pounds, work out each unit price (3 pounds per kg vs 2.80 pounds per kg) to see which is cheaper.
Try this with a recipe too. If 4 people need 200 g of flour, first find how much ONE person needs: 200 divided by 4 equals 50 g. Then multiply that by however many people you're cooking for.
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