Ratio & Proportion
one apple for every four blueberries
this can be shown through the ratio 1 : 4 1
this can also be shown through the fraction 4
if we are asked to find how many blueberries we would have if we had three apples
we can use the above ratio within the following equation (also known as a proportion)
1 = 3
4 n
at this point n becomes the unknown variable that we solve for
we do this by isolating n
the concept of cross-multiplication is key here in solving for n
therefore the second step would resemble...
1 X n = 4 X 3
one multiplied with any number will not alter the number
and so 1 X n simply equals n
the final step becomes...
n = 12
a proportion is expressed as one fraction that equals another fraction
1 = 3
4 12
Altogether this would appear as follows...
1 = 3
4 n
1 X n = 4 X 3
n = 12
a slightly more complicated example follows...
3 = n
4 8
4 x n = 3 x 8 (cross-multiplication)
4n = 24 ( divide each side by 4 to isolate n)
n = 6
Further hints...
i) the following proportion template is key to the beginning of solving many word problems
_______ = _______
another great tip is to remember where the following key words are found in a proportion equation ( is on top & of on bottom )
is
of (out of...)
ii) keep in mind that just like when dealing with fractions (what you do to the bottom you do to the top)
with any equation (something = something) what we do to one side we must also do to the other side
iii) remember to keep similar things in line with each other... in the above example the apples are the tops or
numerators of the fractions and the blueberries are listed on the bottoms of the fractions or denominators
iv) if a word problem is presented with a percentage included .. a good rule of thumb is to use the given
percentage as the first fraction in the proportion equation template ... with 100 as the first denominator
we then keep the total amounts on the bottoms of the fractions (example: find 22% of $84.00)
percents dollars
parts 22 = n
totals 100 84
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