What is Direct Proportion?
Two quantities are in direct proportion if they increase or decrease together in the same ratio. When one quantity doubles, the other doubles; when one is halved, the other is halved.
If \(x\) and \(y\) are directly proportional, then \(\frac{x}{y} = k\) (constant), or \(x = ky\).
What is the Unitary Method?
The unitary method is a technique for solving proportion problems by first finding the value of one unit, then multiplying to find the required value.
Steps for Unitary Method:
- Find the value of one unit (divide the given quantity by the given number)
- Multiply by the required number of units
Real-Life Examples of Direct Proportion:
- Cost of items: more items → more cost (at same price)
- Distance and time (at constant speed): more time → more distance
- Work done and number of workers (at same rate): more workers → more work
Proportion Notation:
If \(a : b = c : d\), then \(a\), \(b\), \(c\), \(d\) are in proportion. We write \(a : b :: c : d\) and say "\(a\) is to \(b\) as \(c\) is to \(d\)".
In a proportion, product of extremes = product of means:
a \times d = b \times c
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