Given the proportion a/b=8/15, what ratio completes the equivalent proportion a/8= what/what ?
a/8=b/15
To find the ratio that completes the equivalent proportion a/8 = what/what, we can use the given proportion a/b = 8/15.
First, we can cross multiply the given proportion:
a * 15 = b * 8
Next, we can isolate 'b' by dividing both sides of the equation by 15:
b = (a * 15) / 8
Now, we can substitute this value for 'b' in the original equation:
a/8 = (a * 15) / 8 / 15
Simplifying further:
a/8 = a/8
So, the ratio that completes the equivalent proportion is 1:1 (a/a).
To find the missing values in the proportion a/8 = what/what, we can use a cross-multiplication method.
First, let's rewrite the given proportion a/b = 8/15 as a general proportion x/y = m/n, where:
- x is equivalent to a
- y is equivalent to b
- m is equivalent to 8
- n is equivalent to 15
Now, we can use cross-multiplication to solve for the missing values:
x/y = m/n
Cross-multiplying gives us:
xn = ym
The proportion a/8 = what/what can be rewritten as x/8 = m/n:
x/8 = m/n
Now, we can use the value of m = 8 and n = 15 from the original proportion to solve for the missing values:
x/8 = 8/15
To find the missing value for x, we can cross-multiply:
15x = 8 * 8
Simplifying the equation:
15x = 64
Dividing both sides by 15:
x = 64/15
So the missing value for x is 64/15.
Similarly, to find the missing value for y, we can cross-multiply:
n * 8 = 8 * x
Simplifying the equation:
15 * 8 = 8x
Dividing both sides by 8:
x = 120/8
So the missing value for x is 120/8, which simplifies to 15.
Therefore, the completed equivalent proportion is a/8 = 64/15.