1A proportion is an equation saying "two ratios are equal"
A proportion is an equation like 2:3 = 4:6 that states two ratios are equal. Multiply both the first and second ratio by the same number, and the ratio always stays the same.
Since doubling 2 gives 4, doubling 3 too gives ▢ = 6.
2The product of the extremes always equals the product of the means
In the proportion a:b = c:d, the outer numbers a and d are called the extremes, and the inner numbers b and c are called the means. Whenever a proportion holds, the product of the extremes (a×d) always equals the product of the means (b×c).
This property lets you find the answer with just multiplication, even when a value is unknown.
3Proportional division is "splitting a whole by a ratio"
Proportional division splits a total amount using a set ratio. The key is thinking of the whole as being split into groups totaling the sum of the ratio.
Splitting into 2+3=5 groups makes each group 20÷5=4. So 2 groups make 8, and 3 groups make 12.
4Both ideas hinge on "the ratio stays the same"
A proportion scales numbers up or down while keeping the ratio the same, and proportional division splits a whole according to that ratio.
5Try this
- Change the scale-factor slider. Check whether the product of the extremes and the product of the means always stay equal, no matter the scale factor.
- Try proportional division with different ratios. Compare how the bar diagram differs between splitting 1:1 and splitting 1:4.
- Solve the quiz using only multiplication. Use just the fact that the product of the extremes equals the product of the means to find the answer quickly.