mahavirnaagar5
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Reduce the following fractions to simplest form:

(a) [tex] \frac{48}{60} [/tex]
(b) [tex] \frac{150}{60} [/tex]
(c) [tex] \frac{84}{98} [/tex]
(d) [tex] \frac{12}{52} [/tex]
(e) [tex] \frac{7}{28} [/tex]

Sagot :

GinnyAnswer
Certainly! Let's reduce each of the given fractions to their simplest form step by step.

### (a) [tex]\(\frac{48}{60}\)[/tex]
To reduce [tex]\(\frac{48}{60}\)[/tex]:

1. Find the greatest common divisor (GCD) of 48 and 60.
2. The GCD of 48 and 60 is 12.
3. Divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{48 \div 12}{60 \div 12} = \frac{4}{5} \][/tex]

So, [tex]\(\frac{48}{60}\)[/tex] simplifies to [tex]\(\frac{4}{5}\)[/tex].

### (b) [tex]\(\frac{150}{60}\)[/tex]
To reduce [tex]\(\frac{150}{60}\)[/tex]:

1. Find the greatest common divisor (GCD) of 150 and 60.
2. The GCD of 150 and 60 is 30.
3. Divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{150 \div 30}{60 \div 30} = \frac{5}{2} \][/tex]

So, [tex]\(\frac{150}{60}\)[/tex] simplifies to [tex]\(\frac{5}{2}\)[/tex].

### (c) [tex]\(\frac{84}{98}\)[/tex]
To reduce [tex]\(\frac{84}{98}\)[/tex]:

1. Find the greatest common divisor (GCD) of 84 and 98.
2. The GCD of 84 and 98 is 14.
3. Divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{84 \div 14}{98 \div 14} = \frac{6}{7} \][/tex]

So, [tex]\(\frac{84}{98}\)[/tex] simplifies to [tex]\(\frac{6}{7}\)[/tex].

### (d) [tex]\(\frac{12}{52}\)[/tex]
To reduce [tex]\(\frac{12}{52}\)[/tex]:

1. Find the greatest common divisor (GCD) of 12 and 52.
2. The GCD of 12 and 52 is 4.
3. Divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{12 \div 4}{52 \div 4} = \frac{3}{13} \][/tex]

So, [tex]\(\frac{12}{52}\)[/tex] simplifies to [tex]\(\frac{3}{13}\)[/tex].

### (e) [tex]\(\frac{7}{28}\)[/tex]
To reduce [tex]\(\frac{7}{28}\)[/tex]:

1. Find the greatest common divisor (GCD) of 7 and 28.
2. The GCD of 7 and 28 is 7.
3. Divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{7 \div 7}{28 \div 7} = \frac{1}{4} \][/tex]

So, [tex]\(\frac{7}{28}\)[/tex] simplifies to [tex]\(\frac{1}{4}\)[/tex].

To summarize, the simplified forms of the given fractions are:
- [tex]\(\frac{48}{60} = \frac{4}{5}\)[/tex]
- [tex]\(\frac{150}{60} = \frac{5}{2}\)[/tex]
- [tex]\(\frac{84}{98} = \frac{6}{7}\)[/tex]
- [tex]\(\frac{12}{52} = \frac{3}{13}\)[/tex]
- [tex]\(\frac{7}{28} = \frac{1}{4}\)[/tex]
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