Answer :
Sure! Let's work through creating equivalent fractions with common denominators step by step.
### Problem 6:
Fractions: [tex]\( \frac{3}{7} \)[/tex] and [tex]\( \frac{2}{3} \)[/tex]
1. Find the Common Denominator: Multiply the denominators of both fractions:
- [tex]\( 7 \times 3 = 21 \)[/tex]
2. Adjust each fraction to have this common denominator:
- For [tex]\( \frac{3}{7} \)[/tex]: Multiply both the numerator and denominator by 3:
- [tex]\( \frac{3 \times 3}{7 \times 3} = \frac{9}{21} \)[/tex]
- For [tex]\( \frac{2}{3} \)[/tex]: Multiply both the numerator and denominator by 7:
- [tex]\( \frac{2 \times 7}{3 \times 7} = \frac{14}{21} \)[/tex]
So, the equivalent fractions are [tex]\( \frac{9}{21} \)[/tex] and [tex]\( \frac{14}{21} \)[/tex].
### Problem 7:
Fractions: [tex]\( \frac{3}{4} \)[/tex] and [tex]\( \frac{2}{5} \)[/tex]
1. Find the Common Denominator: Multiply the denominators of both fractions:
- [tex]\( 4 \times 5 = 20 \)[/tex]
2. Adjust each fraction to have this common denominator:
- For [tex]\( \frac{3}{4} \)[/tex]: Multiply both the numerator and denominator by 5:
- [tex]\( \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \)[/tex]
- For [tex]\( \frac{2}{5} \)[/tex]: Multiply both the numerator and denominator by 4:
- [tex]\( \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \)[/tex]
So, the equivalent fractions are [tex]\( \frac{15}{20} \)[/tex] and [tex]\( \frac{8}{20} \)[/tex].
### Problem 8:
Fractions: [tex]\( \frac{1}{2} \)[/tex] and [tex]\( \frac{3}{12} \)[/tex]
1. Find the Common Denominator: Multiply the denominators of both fractions:
- [tex]\( 2 \times 12 = 24 \)[/tex]
2. Adjust each fraction to have this common denominator:
- For [tex]\( \frac{1}{2} \)[/tex]: Multiply both the numerator and denominator by 12:
- [tex]\( \frac{1 \times 12}{2 \times 12} = \frac{12}{24} \)[/tex]
- For [tex]\( \frac{3}{12} \)[/tex]: Multiply both the numerator and denominator by 2:
- [tex]\( \frac{3 \times 2}{12 \times 2} = \frac{6}{24} \)[/tex]
So, the equivalent fractions are [tex]\( \frac{12}{24} \)[/tex] and [tex]\( \frac{6}{24} \)[/tex].
These steps show how each pair of fractions is converted into equivalent fractions with a common denominator.
### Problem 6:
Fractions: [tex]\( \frac{3}{7} \)[/tex] and [tex]\( \frac{2}{3} \)[/tex]
1. Find the Common Denominator: Multiply the denominators of both fractions:
- [tex]\( 7 \times 3 = 21 \)[/tex]
2. Adjust each fraction to have this common denominator:
- For [tex]\( \frac{3}{7} \)[/tex]: Multiply both the numerator and denominator by 3:
- [tex]\( \frac{3 \times 3}{7 \times 3} = \frac{9}{21} \)[/tex]
- For [tex]\( \frac{2}{3} \)[/tex]: Multiply both the numerator and denominator by 7:
- [tex]\( \frac{2 \times 7}{3 \times 7} = \frac{14}{21} \)[/tex]
So, the equivalent fractions are [tex]\( \frac{9}{21} \)[/tex] and [tex]\( \frac{14}{21} \)[/tex].
### Problem 7:
Fractions: [tex]\( \frac{3}{4} \)[/tex] and [tex]\( \frac{2}{5} \)[/tex]
1. Find the Common Denominator: Multiply the denominators of both fractions:
- [tex]\( 4 \times 5 = 20 \)[/tex]
2. Adjust each fraction to have this common denominator:
- For [tex]\( \frac{3}{4} \)[/tex]: Multiply both the numerator and denominator by 5:
- [tex]\( \frac{3 \times 5}{4 \times 5} = \frac{15}{20} \)[/tex]
- For [tex]\( \frac{2}{5} \)[/tex]: Multiply both the numerator and denominator by 4:
- [tex]\( \frac{2 \times 4}{5 \times 4} = \frac{8}{20} \)[/tex]
So, the equivalent fractions are [tex]\( \frac{15}{20} \)[/tex] and [tex]\( \frac{8}{20} \)[/tex].
### Problem 8:
Fractions: [tex]\( \frac{1}{2} \)[/tex] and [tex]\( \frac{3}{12} \)[/tex]
1. Find the Common Denominator: Multiply the denominators of both fractions:
- [tex]\( 2 \times 12 = 24 \)[/tex]
2. Adjust each fraction to have this common denominator:
- For [tex]\( \frac{1}{2} \)[/tex]: Multiply both the numerator and denominator by 12:
- [tex]\( \frac{1 \times 12}{2 \times 12} = \frac{12}{24} \)[/tex]
- For [tex]\( \frac{3}{12} \)[/tex]: Multiply both the numerator and denominator by 2:
- [tex]\( \frac{3 \times 2}{12 \times 2} = \frac{6}{24} \)[/tex]
So, the equivalent fractions are [tex]\( \frac{12}{24} \)[/tex] and [tex]\( \frac{6}{24} \)[/tex].
These steps show how each pair of fractions is converted into equivalent fractions with a common denominator.