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a) \(\frac{4}{10} = \)
b) \(\frac{16}{16} = \)
c) \(\frac{1}{5} = \)
d) \(\frac{3}{5} = \)
e) \(\frac{12}{35} = \)
f) \(\frac{8}{30} = \)
g) \(\frac{33}{50} = \)
h) \(\frac{78}{200} = \)
i) \(\frac{32}{40} = \)
j) \(\frac{100}{125} = \)

Answer :

To solve the given fractions, we need to either simplify them to their lowest terms if possible or perform any requested operations like converting them into decimals.

Here’s how you can approach each of them:

a) [tex]\frac{4}{10} =[/tex]

To simplify [tex]\frac{4}{10}[/tex], find the greatest common divisor (GCD) of 4 and 10, which is 2. Divide both the numerator and the denominator by 2:
[tex]\frac{4 \div 2}{10 \div 2} = \frac{2}{5}[/tex]
So, [tex]\frac{4}{10} = \frac{2}{5}[/tex].

b) [tex]\frac{16}{16} =[/tex]

Any number divided by itself equals 1:
[tex]\frac{16}{16} = 1[/tex]

c) [tex]\frac{1}{5} =[/tex]

This fraction is already in its simplest form, so [tex]\frac{1}{5}[/tex] remains [tex]\frac{1}{5}[/tex].

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

This fraction is also already in its simplest form, so [tex]\frac{3}{5}[/tex] remains [tex]\frac{3}{5}[/tex].

e) [tex]\frac{12}{35} =[/tex]

The GCD of 12 and 35 is 1, so this fraction is already in its simplest form:
[tex]\frac{12}{35}[/tex]

f) [tex]\frac{8}{30} =[/tex]

The GCD of 8 and 30 is 2. Simplify by dividing both terms by 2:
[tex]\frac{8 \div 2}{30 \div 2} = \frac{4}{15}[/tex]
So, [tex]\frac{8}{30} = \frac{4}{15}[/tex].

g) [tex]\frac{33}{50} =[/tex]

33 and 50 do not have a common factor other than 1, so the fraction is already in its simplest form:
[tex]\frac{33}{50}[/tex]

h) [tex]\frac{78}{200} =[/tex]

The GCD of 78 and 200 is 2. Simplify by dividing by 2:
[tex]\frac{78 \div 2}{200 \div 2} = \frac{39}{100}[/tex]
Thus, [tex]\frac{78}{200} = \frac{39}{100}[/tex].

i) [tex]\frac{32}{40} =[/tex]

The GCD of 32 and 40 is 8. Simplify by dividing by 8:
[tex]\frac{32 \div 8}{40 \div 8} = \frac{4}{5}[/tex]
So, [tex]\frac{32}{40} = \frac{4}{5}[/tex].

j) [tex]\frac{100}{125} =[/tex]

The GCD of 100 and 125 is 25. Simplify by dividing by 25:
[tex]\frac{100 \div 25}{125 \div 25} = \frac{4}{5}[/tex]
Therefore, [tex]\frac{100}{125} = \frac{4}{5}[/tex].

In summary, each fraction is simplified to show its basic form or needs no simplification if already in the simplest form.

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