Answer :
To determine which fractions are equivalent to [tex]\(\frac{21}{28}\)[/tex], we need to simplify [tex]\(\frac{21}{28}\)[/tex] and then compare this simplified form to the other fractions.
### Step 1: Simplify [tex]\(\frac{21}{28}\)[/tex]
1. Find the greatest common divisor (GCD) of 21 and 28.
- The factors of 21 are 1, 3, 7, 21.
- The factors of 28 are 1, 2, 4, 7, 14, 28.
- The greatest common factor is 7.
2. Divide both the numerator and the denominator of [tex]\(\frac{21}{28}\)[/tex] by 7:
[tex]\[ \frac{21 \div 7}{28 \div 7} = \frac{3}{4} \][/tex]
So, [tex]\(\frac{21}{28}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex].
### Step 2: Simplify and compare each of the given fractions
1. [tex]\(\frac{42}{56}\)[/tex]
- GCD of 42 and 56 is 14.
- Simplify: [tex]\(\frac{42 \div 14}{56 \div 14} = \frac{3}{4}\)[/tex]
- Equivalent to [tex]\(\frac{21}{28}\)[/tex]?
2. [tex]\(\frac{3}{4}\)[/tex]
- Already in simplest form.
- Equivalent to [tex]\(\frac{21}{28}\)[/tex]?
3. [tex]\(\frac{3}{9}\)[/tex]
- GCD of 3 and 9 is 3.
- Simplify: [tex]\(\frac{3 \div 3}{9 \div 3} = \frac{1}{3}\)[/tex]
- Not equivalent to [tex]\(\frac{21}{28}\)[/tex]?
4. [tex]\(\frac{3}{7}\)[/tex]
- Already in simplest form.
- Not equivalent to [tex]\(\frac{21}{28}\)[/tex]?
### Step 3: Conclusion
Comparing all the simplified forms, we find that [tex]\(\frac{42}{56}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex] both simplify to [tex]\(\frac{3}{4}\)[/tex], which is equivalent to [tex]\(\frac{21}{28}\)[/tex]. Therefore, the two fractions equivalent to [tex]\(\frac{21}{28}\)[/tex] are:
[tex]\[ \boxed{\frac{42}{56} \quad \text{and} \quad \frac{3}{4}} \][/tex]
### Step 1: Simplify [tex]\(\frac{21}{28}\)[/tex]
1. Find the greatest common divisor (GCD) of 21 and 28.
- The factors of 21 are 1, 3, 7, 21.
- The factors of 28 are 1, 2, 4, 7, 14, 28.
- The greatest common factor is 7.
2. Divide both the numerator and the denominator of [tex]\(\frac{21}{28}\)[/tex] by 7:
[tex]\[ \frac{21 \div 7}{28 \div 7} = \frac{3}{4} \][/tex]
So, [tex]\(\frac{21}{28}\)[/tex] simplifies to [tex]\(\frac{3}{4}\)[/tex].
### Step 2: Simplify and compare each of the given fractions
1. [tex]\(\frac{42}{56}\)[/tex]
- GCD of 42 and 56 is 14.
- Simplify: [tex]\(\frac{42 \div 14}{56 \div 14} = \frac{3}{4}\)[/tex]
- Equivalent to [tex]\(\frac{21}{28}\)[/tex]?
2. [tex]\(\frac{3}{4}\)[/tex]
- Already in simplest form.
- Equivalent to [tex]\(\frac{21}{28}\)[/tex]?
3. [tex]\(\frac{3}{9}\)[/tex]
- GCD of 3 and 9 is 3.
- Simplify: [tex]\(\frac{3 \div 3}{9 \div 3} = \frac{1}{3}\)[/tex]
- Not equivalent to [tex]\(\frac{21}{28}\)[/tex]?
4. [tex]\(\frac{3}{7}\)[/tex]
- Already in simplest form.
- Not equivalent to [tex]\(\frac{21}{28}\)[/tex]?
### Step 3: Conclusion
Comparing all the simplified forms, we find that [tex]\(\frac{42}{56}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex] both simplify to [tex]\(\frac{3}{4}\)[/tex], which is equivalent to [tex]\(\frac{21}{28}\)[/tex]. Therefore, the two fractions equivalent to [tex]\(\frac{21}{28}\)[/tex] are:
[tex]\[ \boxed{\frac{42}{56} \quad \text{and} \quad \frac{3}{4}} \][/tex]
