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Solve each proportion by finding the missing term.

a) [tex]\(\frac{7}{7} = \frac{8}{28}\)[/tex]

b) [tex]\(\frac{3}{8} = \frac{-9}{24}\)[/tex]

c) [tex]\(\frac{4}{5} = \frac{20}{\square}\)[/tex]

d) [tex]\(\frac{3}{5} = \frac{18}{\square}\)[/tex]

e) [tex]\(\frac{4}{1} = \frac{20}{50}\)[/tex]

f) [tex]\(\frac{3}{15} = \frac{\square}{30}\)[/tex]

Answer :

Below is a step‐by‐step explanation for each part:

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Part (a)
We are given
[tex]$$\frac{7}{7}=\frac{8}{28}.$$[/tex]

First, simplify the left-hand fraction:
[tex]$$\frac{7}{7}=1.$$[/tex]

Now, simplify the right-hand fraction:
[tex]$$\frac{8}{28}=\frac{2}{7}\approx0.2857.$$[/tex]

Since
[tex]$$1\neq0.2857,$$[/tex]
the two fractions are not equivalent.

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Part (b)
We are given
[tex]$$\frac{3}{8}=\frac{-9}{24}.$$[/tex]

Calculate the first fraction:
[tex]$$\frac{3}{8}=0.375.$$[/tex]

Now, calculate the second fraction:
[tex]$$\frac{-9}{24}=-0.375.$$[/tex]

Since
[tex]$$0.375\neq-0.375,$$[/tex]
the two fractions are not equivalent.

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Part (c)
We need to find the missing term in
[tex]$$\frac{4}{5}=\frac{20}{\square}.$$[/tex]

Let the missing number be [tex]$x$[/tex]. Cross multiply:
[tex]$$4x=5\times20.$$[/tex]

That is,
[tex]$$4x=100.$$[/tex]

Solve for [tex]$x$[/tex]:
[tex]$$x=\frac{100}{4}=25.$$[/tex]

Thus, the missing term is [tex]$25$[/tex].

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Part (d)
We need to find the missing term in
[tex]$$\frac{3}{5}=\frac{18}{\square}.$$[/tex]

Let the missing number be [tex]$x$[/tex]. Cross multiply:
[tex]$$3x=5\times18.$$[/tex]

That is,
[tex]$$3x=90.$$[/tex]

Solve for [tex]$x$[/tex]:
[tex]$$x=\frac{90}{3}=30.$$[/tex]

Thus, the missing term is [tex]$30$[/tex].

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Part (e)
We are given
[tex]$$\frac{4}{1}=\frac{20}{50}.$$[/tex]

Calculate the left-hand side:
[tex]$$\frac{4}{1}=4.$$[/tex]

Now, simplify the right-hand side:
[tex]$$\frac{20}{50}=0.4.$$[/tex]

Since
[tex]$$4\neq0.4,$$[/tex]
the two fractions are not equivalent.

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Part (f)
We need to find the missing term in
[tex]$$\frac{3}{15}=\frac{\square}{30}.$$[/tex]

Let the missing number be [tex]$x$[/tex]. Cross multiply:
[tex]$$3\times30=15x.$$[/tex]

That gives,
[tex]$$90=15x.$$[/tex]

Solve for [tex]$x$[/tex]:
[tex]$$x=\frac{90}{15}=6.$$[/tex]

Thus, the missing term is [tex]$6$[/tex].

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Final Answers:

a) The two fractions are not equivalent.
b) The two fractions are not equivalent.
c) The missing term is [tex]$25$[/tex].
d) The missing term is [tex]$30$[/tex].
e) The two fractions are not equivalent.
f) The missing term is [tex]$6$[/tex].

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