Answer :
Reduce 10/40 and 8/32 to their simplest forms.
10/40 = 1/4. 8/32 =1/4
If they are equal, then x and y are equal. which means x is 32 and y is 40
10/40 = 1/4. 8/32 =1/4
If they are equal, then x and y are equal. which means x is 32 and y is 40
To solve the problem of finding the unknown numbers in the proportion [tex]\(\frac{32}{40} = \frac{x}{y}\)[/tex], we start by examining the relationship and simplifying to make the proportions more manageable.
First, look at the known equivalent fraction [tex]\(\frac{10}{40} = \frac{8}{32}\)[/tex]. Notice that both sides of this equality reduce to the same simplified fraction:
1. Simplify [tex]\(\frac{10}{40}\)[/tex]:
- Both the numerator and the denominator can be divided by 10.
- This gives [tex]\(\frac{1}{4}\)[/tex].
2. Simplify [tex]\(\frac{8}{32}\)[/tex]:
- Both the numerator and the denominator can be divided by 8.
- This also gives [tex]\(\frac{1}{4}\)[/tex].
Now, look at the proportion [tex]\(\frac{32}{40}\)[/tex]:
1. Simplify [tex]\(\frac{32}{40}\)[/tex]:
- Both the numerator (32) and the denominator (40) can be divided by 8.
- This gives [tex]\(\frac{4}{5}\)[/tex].
We want to find values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] such that [tex]\(\frac{x}{y}\)[/tex] is equivalent to [tex]\(\frac{4}{5}\)[/tex] (the simplified version of [tex]\(\frac{32}{40}\)[/tex]).
From matching the form of the known proportions, we deduce:
- [tex]\(x\)[/tex] should be 8, to keep in line with the example proportions given originally in both [tex]\(\frac{10}{40}\)[/tex] and [tex]\(\frac{8}{32}\)[/tex].
- [tex]\(y\)[/tex] should be 10, which maintains the overall balance and equivalency.
Thus, the values are:
- [tex]\(x = 8\)[/tex]
- [tex]\(y = 10\)[/tex]
These choices for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] keep the proportion [tex]\(\frac{32}{40} = \frac{x}{y}\)[/tex] consistent with a simplified fraction of [tex]\(\frac{4}{5}\)[/tex].
First, look at the known equivalent fraction [tex]\(\frac{10}{40} = \frac{8}{32}\)[/tex]. Notice that both sides of this equality reduce to the same simplified fraction:
1. Simplify [tex]\(\frac{10}{40}\)[/tex]:
- Both the numerator and the denominator can be divided by 10.
- This gives [tex]\(\frac{1}{4}\)[/tex].
2. Simplify [tex]\(\frac{8}{32}\)[/tex]:
- Both the numerator and the denominator can be divided by 8.
- This also gives [tex]\(\frac{1}{4}\)[/tex].
Now, look at the proportion [tex]\(\frac{32}{40}\)[/tex]:
1. Simplify [tex]\(\frac{32}{40}\)[/tex]:
- Both the numerator (32) and the denominator (40) can be divided by 8.
- This gives [tex]\(\frac{4}{5}\)[/tex].
We want to find values of [tex]\(x\)[/tex] and [tex]\(y\)[/tex] such that [tex]\(\frac{x}{y}\)[/tex] is equivalent to [tex]\(\frac{4}{5}\)[/tex] (the simplified version of [tex]\(\frac{32}{40}\)[/tex]).
From matching the form of the known proportions, we deduce:
- [tex]\(x\)[/tex] should be 8, to keep in line with the example proportions given originally in both [tex]\(\frac{10}{40}\)[/tex] and [tex]\(\frac{8}{32}\)[/tex].
- [tex]\(y\)[/tex] should be 10, which maintains the overall balance and equivalency.
Thus, the values are:
- [tex]\(x = 8\)[/tex]
- [tex]\(y = 10\)[/tex]
These choices for [tex]\(x\)[/tex] and [tex]\(y\)[/tex] keep the proportion [tex]\(\frac{32}{40} = \frac{x}{y}\)[/tex] consistent with a simplified fraction of [tex]\(\frac{4}{5}\)[/tex].
