Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.
Sagot :
To determine which of the given fractions are equivalent to [tex]\(\frac{28}{32}\)[/tex], we need to compare them individually. We do this by simplifying [tex]\(\frac{28}{32}\)[/tex] and then checking it against each given fraction.
First, let's simplify [tex]\(\frac{28}{32}\)[/tex].
1. Find the greatest common divisor (GCD) of 28 and 32.
- The factors of 28 are: 1, 2, 4, 7, 14, 28
- The factors of 32 are: 1, 2, 4, 8, 16, 32
- The GCD of 28 and 32 is 4.
2. Divide the numerator and the denominator by the GCD.
[tex]\[ \frac{28 \div 4}{32 \div 4} = \frac{7}{8} \][/tex]
So, [tex]\(\frac{28}{32}\)[/tex] simplifies to [tex]\(\frac{7}{8}\)[/tex].
Next, we need to compare this simplified fraction [tex]\(\frac{7}{8}\)[/tex] with the given fractions:
A. [tex]\(\frac{7}{8}\)[/tex]
- [tex]\(\frac{28}{32} = \frac{7}{8}\)[/tex]
- Therefore, [tex]\(\frac{7}{8}\)[/tex] is equivalent to [tex]\(\frac{28}{32}\)[/tex]. This checks out as True.
B. [tex]\(\frac{13}{16}\)[/tex]
- Compare [tex]\(\frac{7}{8}\)[/tex] with [tex]\(\frac{13}{16}\)[/tex].
- To compare, find a common denominator. The least common denominator (LCD) of 8 and 16 is 16.
- Convert [tex]\(\frac{7}{8}\)[/tex] to an equivalent fraction with a denominator of 16:
[tex]\[ \frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16} \][/tex]
- Compare [tex]\(\frac{14}{16}\)[/tex] with [tex]\(\frac{13}{16}\)[/tex].
- [tex]\(\frac{14}{16} \neq \frac{13}{16}\)[/tex]
- Therefore, [tex]\(\frac{13}{16}\)[/tex] is not equivalent to [tex]\(\frac{28}{32}\)[/tex]. This checks out as False.
C. [tex]\(\frac{14}{16}\)[/tex]
- To compare [tex]\(\frac{7}{8}\)[/tex] with [tex]\(\frac{14}{16}\)[/tex], use the previous result.
- [tex]\(\frac{7}{8} = \frac{14}{16}\)[/tex]
- Therefore, [tex]\(\frac{14}{16}\)[/tex] is equivalent to [tex]\(\frac{28}{32}\)[/tex]. This checks out as True.
D. [tex]\(\frac{7}{12}\)[/tex]
- Compare [tex]\(\frac{7}{8}\)[/tex] with [tex]\(\frac{7}{12}\)[/tex]. To do this, find a common denominator. The least common multiple (LCM) of 8 and 12 is 24.
- Convert both fractions to equivalent fractions with denominator 24:
[tex]\[ \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \][/tex]
[tex]\[ \frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24} \][/tex]
- Compare [tex]\(\frac{21}{24}\)[/tex] with [tex]\(\frac{14}{24}\)[/tex].
- [tex]\(\frac{21}{24} \neq \frac{14}{24}\)[/tex]
- Therefore, [tex]\(\frac{7}{12}\)[/tex] is not equivalent to [tex]\(\frac{28}{32}\)[/tex]. This checks out as False.
In conclusion, the fractions equivalent to [tex]\(\frac{28}{32}\)[/tex] are:
A. [tex]\(\frac{7}{8}\)[/tex]
C. [tex]\(\frac{14}{16}\)[/tex]
First, let's simplify [tex]\(\frac{28}{32}\)[/tex].
1. Find the greatest common divisor (GCD) of 28 and 32.
- The factors of 28 are: 1, 2, 4, 7, 14, 28
- The factors of 32 are: 1, 2, 4, 8, 16, 32
- The GCD of 28 and 32 is 4.
2. Divide the numerator and the denominator by the GCD.
[tex]\[ \frac{28 \div 4}{32 \div 4} = \frac{7}{8} \][/tex]
So, [tex]\(\frac{28}{32}\)[/tex] simplifies to [tex]\(\frac{7}{8}\)[/tex].
Next, we need to compare this simplified fraction [tex]\(\frac{7}{8}\)[/tex] with the given fractions:
A. [tex]\(\frac{7}{8}\)[/tex]
- [tex]\(\frac{28}{32} = \frac{7}{8}\)[/tex]
- Therefore, [tex]\(\frac{7}{8}\)[/tex] is equivalent to [tex]\(\frac{28}{32}\)[/tex]. This checks out as True.
B. [tex]\(\frac{13}{16}\)[/tex]
- Compare [tex]\(\frac{7}{8}\)[/tex] with [tex]\(\frac{13}{16}\)[/tex].
- To compare, find a common denominator. The least common denominator (LCD) of 8 and 16 is 16.
- Convert [tex]\(\frac{7}{8}\)[/tex] to an equivalent fraction with a denominator of 16:
[tex]\[ \frac{7}{8} = \frac{7 \times 2}{8 \times 2} = \frac{14}{16} \][/tex]
- Compare [tex]\(\frac{14}{16}\)[/tex] with [tex]\(\frac{13}{16}\)[/tex].
- [tex]\(\frac{14}{16} \neq \frac{13}{16}\)[/tex]
- Therefore, [tex]\(\frac{13}{16}\)[/tex] is not equivalent to [tex]\(\frac{28}{32}\)[/tex]. This checks out as False.
C. [tex]\(\frac{14}{16}\)[/tex]
- To compare [tex]\(\frac{7}{8}\)[/tex] with [tex]\(\frac{14}{16}\)[/tex], use the previous result.
- [tex]\(\frac{7}{8} = \frac{14}{16}\)[/tex]
- Therefore, [tex]\(\frac{14}{16}\)[/tex] is equivalent to [tex]\(\frac{28}{32}\)[/tex]. This checks out as True.
D. [tex]\(\frac{7}{12}\)[/tex]
- Compare [tex]\(\frac{7}{8}\)[/tex] with [tex]\(\frac{7}{12}\)[/tex]. To do this, find a common denominator. The least common multiple (LCM) of 8 and 12 is 24.
- Convert both fractions to equivalent fractions with denominator 24:
[tex]\[ \frac{7}{8} = \frac{7 \times 3}{8 \times 3} = \frac{21}{24} \][/tex]
[tex]\[ \frac{7}{12} = \frac{7 \times 2}{12 \times 2} = \frac{14}{24} \][/tex]
- Compare [tex]\(\frac{21}{24}\)[/tex] with [tex]\(\frac{14}{24}\)[/tex].
- [tex]\(\frac{21}{24} \neq \frac{14}{24}\)[/tex]
- Therefore, [tex]\(\frac{7}{12}\)[/tex] is not equivalent to [tex]\(\frac{28}{32}\)[/tex]. This checks out as False.
In conclusion, the fractions equivalent to [tex]\(\frac{28}{32}\)[/tex] are:
A. [tex]\(\frac{7}{8}\)[/tex]
C. [tex]\(\frac{14}{16}\)[/tex]
We appreciate your visit. Hopefully, the answers you found were beneficial. Don't hesitate to come back for more information. We hope this was helpful. Please come back whenever you need more information or answers to your queries. Westonci.ca is your go-to source for reliable answers. Return soon for more expert insights.