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Simplify each fraction to its lowest terms.

1. [tex]\(- \frac{18}{54} = \frac{9 \times 2}{9 \times 6} = \frac{1}{3}\)[/tex]

2. [tex]\(- \frac{39}{52} = \frac{13 \times 3}{13 \times 4} = \frac{3}{4}\)[/tex]

3. [tex]\(- \frac{45}{60} = \frac{5 \times 9}{5 \times 12} = \frac{3}{4}\)[/tex]

4. [tex]\(- \frac{48}{60} = \frac{6 \times 8}{6 \times 10} = \frac{4}{5}\)[/tex]

5. [tex]\(- \frac{42}{63} = \frac{7 \times 6}{7 \times 9} = \frac{2}{3}\)[/tex]

6. [tex]\(- \frac{48}{64} = \frac{4 \times 12}{4 \times 16} = \frac{3}{4}\)[/tex]

Answer :

Let's simplify each of the fractions to their lowest terms:

1. Fraction: [tex]\(-\frac{18}{54}\)[/tex]

- The greatest common divisor (GCD) of 18 and 54 is 18.
- Divide both the numerator and the denominator by 18:
[tex]\[
\frac{18 \div 18}{54 \div 18} = \frac{1}{3}
\][/tex]

2. Fraction: [tex]\(-\frac{39}{52}\)[/tex]

- The greatest common divisor of 39 and 52 is 13.
- Divide both the numerator and the denominator by 13:
[tex]\[
\frac{39 \div 13}{52 \div 13} = \frac{3}{4}
\][/tex]

3. Fraction: [tex]\(-\frac{45}{60}\)[/tex]

- The greatest common divisor of 45 and 60 is 15.
- Divide both the numerator and the denominator by 15:
[tex]\[
\frac{45 \div 15}{60 \div 15} = \frac{3}{4}
\][/tex]

4. Fraction: [tex]\(-\frac{48}{60}\)[/tex]

- The greatest common divisor of 48 and 60 is 12.
- Divide both the numerator and the denominator by 12:
[tex]\[
\frac{48 \div 12}{60 \div 12} = \frac{4}{5}
\][/tex]

5. Fraction: [tex]\(-\frac{42}{63}\)[/tex]

- The greatest common divisor of 42 and 63 is 21.
- Divide both the numerator and the denominator by 21:
[tex]\[
\frac{42 \div 21}{63 \div 21} = \frac{2}{3}
\][/tex]

6. Fraction: [tex]\(-\frac{48}{64}\)[/tex]

- The greatest common divisor of 48 and 64 is 16.
- Divide both the numerator and the denominator by 16:
[tex]\[
\frac{48 \div 16}{64 \div 16} = \frac{3}{4}
\][/tex]

So, the simplified fractions are:

- [tex]\(-\frac{18}{54} = \frac{1}{3}\)[/tex]
- [tex]\(-\frac{39}{52} = \frac{3}{4}\)[/tex]
- [tex]\(-\frac{45}{60} = \frac{3}{4}\)[/tex]
- [tex]\(-\frac{48}{60} = \frac{4}{5}\)[/tex]
- [tex]\(-\frac{42}{63} = \frac{2}{3}\)[/tex]
- [tex]\(-\frac{48}{64} = \frac{3}{4}\)[/tex]

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