So this is a "Challenge"
(we don't have to do it but my mum is making me)
we haven't learned it, it's only if you want to do anything harder or more difficult.
1.explain why the ratios 6/9 and 8/12 are in proportion
reduce each. the firsts reduces to 2/3 (2*3/3*3)
the second has a common factor of 4, so it reduces also.
they are in proportion because
8*9 = 6*12
In a proportion
a/b = c/d
ad = bc
To explain why the ratios 6/9 and 8/12 are in proportion, we need to understand what it means for two ratios to be in proportion.
Two ratios are said to be in proportion when their corresponding fractions or decimals are equal to each other. In other words, if we simplify both ratios to their lowest terms, they should be equal.
To simplify a ratio, we divide both the numerator and the denominator by their greatest common divisor (GCD). In this case, let's simplify both ratios:
For 6/9:
The GCD of 6 and 9 is 3. By dividing both the numerator and the denominator by 3, we get 2/3.
For 8/12:
The GCD of 8 and 12 is 4. By dividing both the numerator and the denominator by 4, we get 2/3.
As you can see, both ratios, after simplifying, are equal to 2/3. This means that 6/9 and 8/12 are in proportion.
So, to summarize:
1. Find the GCD of both the numerator and the denominator of each ratio.
2. Divide both the numerator and the denominator of each ratio by their GCD.
3. If both simplified ratios are equal, then the original ratios are in proportion.