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Answer :
Sure! Let's simplify each of the given fractions step-by-step and find two equivalent fractions for each.
a) [tex]\( \frac{24}{30} \)[/tex]
1. First, find the greatest common divisor (GCD) of 24 and 30. The GCD is the largest number that divides both 24 and 30 without leaving a remainder.
The GCD of 24 and 30 is 6.
2. Simplify the fraction by dividing both the numerator and the denominator by the GCD.
[tex]\[
\frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
3. After simplifying, the fraction [tex]\( \frac{24}{30} \)[/tex] is equivalent to [tex]\( \frac{4}{5} \)[/tex].
b) [tex]\( \frac{18}{24} \)[/tex]
1. Find the greatest common divisor (GCD) of 18 and 24.
The GCD of 18 and 24 is 6.
2. Simplify the fraction by dividing both the numerator and the denominator by the GCD.
[tex]\[
\frac{18 \div 6}{24 \div 6} = \frac{3}{4}
\][/tex]
3. After simplifying, the fraction [tex]\( \frac{18}{24} \)[/tex] is equivalent to [tex]\( \frac{3}{4} \)[/tex].
c) [tex]\( \frac{36}{24} \)[/tex]
1. Find the greatest common divisor (GCD) of 36 and 24.
The GCD of 36 and 24 is 12.
2. Simplify the fraction by dividing both the numerator and the denominator by the GCD.
[tex]\[
\frac{36 \div 12}{24 \div 12} = \frac{3}{2}
\][/tex]
3. After simplifying, the fraction [tex]\( \frac{36}{24} \)[/tex] is equivalent to [tex]\( \frac{3}{2} \)[/tex].
So, the simplified equivalent fractions are:
- [tex]\( \frac{24}{30} \)[/tex] is equivalent to [tex]\( \frac{4}{5} \)[/tex].
- [tex]\( \frac{18}{24} \)[/tex] is equivalent to [tex]\( \frac{3}{4} \)[/tex].
- [tex]\( \frac{36}{24} \)[/tex] is equivalent to [tex]\( \frac{3}{2} \)[/tex].
a) [tex]\( \frac{24}{30} \)[/tex]
1. First, find the greatest common divisor (GCD) of 24 and 30. The GCD is the largest number that divides both 24 and 30 without leaving a remainder.
The GCD of 24 and 30 is 6.
2. Simplify the fraction by dividing both the numerator and the denominator by the GCD.
[tex]\[
\frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
3. After simplifying, the fraction [tex]\( \frac{24}{30} \)[/tex] is equivalent to [tex]\( \frac{4}{5} \)[/tex].
b) [tex]\( \frac{18}{24} \)[/tex]
1. Find the greatest common divisor (GCD) of 18 and 24.
The GCD of 18 and 24 is 6.
2. Simplify the fraction by dividing both the numerator and the denominator by the GCD.
[tex]\[
\frac{18 \div 6}{24 \div 6} = \frac{3}{4}
\][/tex]
3. After simplifying, the fraction [tex]\( \frac{18}{24} \)[/tex] is equivalent to [tex]\( \frac{3}{4} \)[/tex].
c) [tex]\( \frac{36}{24} \)[/tex]
1. Find the greatest common divisor (GCD) of 36 and 24.
The GCD of 36 and 24 is 12.
2. Simplify the fraction by dividing both the numerator and the denominator by the GCD.
[tex]\[
\frac{36 \div 12}{24 \div 12} = \frac{3}{2}
\][/tex]
3. After simplifying, the fraction [tex]\( \frac{36}{24} \)[/tex] is equivalent to [tex]\( \frac{3}{2} \)[/tex].
So, the simplified equivalent fractions are:
- [tex]\( \frac{24}{30} \)[/tex] is equivalent to [tex]\( \frac{4}{5} \)[/tex].
- [tex]\( \frac{18}{24} \)[/tex] is equivalent to [tex]\( \frac{3}{4} \)[/tex].
- [tex]\( \frac{36}{24} \)[/tex] is equivalent to [tex]\( \frac{3}{2} \)[/tex].
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