Answer :
Sure! Let's go through each part of the question step by step:
### 5) Name three fractions that are equivalent to [tex]\(\frac{2}{3}\)[/tex]:
To find fractions equivalent to [tex]\(\frac{2}{3}\)[/tex], we multiply both the numerator (2) and the denominator (3) by the same number:
- Multiply by 1: [tex]\(\frac{2 \times 1}{3 \times 1} = \frac{2}{3}\)[/tex]
- Multiply by 2: [tex]\(\frac{2 \times 2}{3 \times 2} = \frac{4}{6}\)[/tex]
- Multiply by 3: [tex]\(\frac{2 \times 3}{3 \times 3} = \frac{6}{9}\)[/tex]
So, three fractions equivalent to [tex]\(\frac{2}{3}\)[/tex] are [tex]\(\frac{2}{3}\)[/tex], [tex]\(\frac{4}{6}\)[/tex], and [tex]\(\frac{6}{9}\)[/tex].
### 6) Reduce [tex]\(\frac{9}{12}\)[/tex] to its lowest terms:
To reduce [tex]\(\frac{9}{12}\)[/tex], we find the greatest common divisor (GCD) of 9 and 12, which is 3. Then, we divide both the numerator and the denominator by 3:
[tex]\[
\frac{9 \div 3}{12 \div 3} = \frac{3}{4}
\][/tex]
So, [tex]\(\frac{9}{12}\)[/tex] reduces to [tex]\(\frac{3}{4}\)[/tex].
### 37) Reduce [tex]\(\frac{24}{30}\)[/tex] to its lowest terms:
To reduce [tex]\(\frac{24}{30}\)[/tex], we find the GCD of 24 and 30, which is 6. Then, we divide both the numerator and the denominator by 6:
[tex]\[
\frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
So, [tex]\(\frac{24}{30}\)[/tex] reduces to [tex]\(\frac{4}{5}\)[/tex].
### 8) Write as a mixed number: [tex]\(\frac{12}{5}\)[/tex]
To convert [tex]\(\frac{12}{5}\)[/tex] into a mixed number, we divide 12 by 5:
- 12 divided by 5 is 2 with a remainder of 2.
This gives us the mixed number: [tex]\(2 \frac{2}{5}\)[/tex].
### 9) Write as an improper fraction: [tex]\(3 \frac{1}{4}\)[/tex]
To convert the mixed number [tex]\(3 \frac{1}{4}\)[/tex] into an improper fraction:
- Multiply the whole number (3) by the denominator (4), which is 12.
- Add the numerator (1), which gives us 13.
So, the improper fraction is [tex]\(\frac{13}{4}\)[/tex].
### Circle the fraction with the greatest value: [tex]\(\frac{1}{11}, \frac{1}{6}, \frac{1}{9}\)[/tex]
To compare these fractions, note that a smaller denominator means a larger fraction when the numerators are the same:
- [tex]\(\frac{1}{6} > \frac{1}{9} > \frac{1}{11}\)[/tex]
Therefore, [tex]\(\frac{1}{6}\)[/tex] is the greatest fraction.
I hope this helps! Let me know if you have any more questions.
### 5) Name three fractions that are equivalent to [tex]\(\frac{2}{3}\)[/tex]:
To find fractions equivalent to [tex]\(\frac{2}{3}\)[/tex], we multiply both the numerator (2) and the denominator (3) by the same number:
- Multiply by 1: [tex]\(\frac{2 \times 1}{3 \times 1} = \frac{2}{3}\)[/tex]
- Multiply by 2: [tex]\(\frac{2 \times 2}{3 \times 2} = \frac{4}{6}\)[/tex]
- Multiply by 3: [tex]\(\frac{2 \times 3}{3 \times 3} = \frac{6}{9}\)[/tex]
So, three fractions equivalent to [tex]\(\frac{2}{3}\)[/tex] are [tex]\(\frac{2}{3}\)[/tex], [tex]\(\frac{4}{6}\)[/tex], and [tex]\(\frac{6}{9}\)[/tex].
### 6) Reduce [tex]\(\frac{9}{12}\)[/tex] to its lowest terms:
To reduce [tex]\(\frac{9}{12}\)[/tex], we find the greatest common divisor (GCD) of 9 and 12, which is 3. Then, we divide both the numerator and the denominator by 3:
[tex]\[
\frac{9 \div 3}{12 \div 3} = \frac{3}{4}
\][/tex]
So, [tex]\(\frac{9}{12}\)[/tex] reduces to [tex]\(\frac{3}{4}\)[/tex].
### 37) Reduce [tex]\(\frac{24}{30}\)[/tex] to its lowest terms:
To reduce [tex]\(\frac{24}{30}\)[/tex], we find the GCD of 24 and 30, which is 6. Then, we divide both the numerator and the denominator by 6:
[tex]\[
\frac{24 \div 6}{30 \div 6} = \frac{4}{5}
\][/tex]
So, [tex]\(\frac{24}{30}\)[/tex] reduces to [tex]\(\frac{4}{5}\)[/tex].
### 8) Write as a mixed number: [tex]\(\frac{12}{5}\)[/tex]
To convert [tex]\(\frac{12}{5}\)[/tex] into a mixed number, we divide 12 by 5:
- 12 divided by 5 is 2 with a remainder of 2.
This gives us the mixed number: [tex]\(2 \frac{2}{5}\)[/tex].
### 9) Write as an improper fraction: [tex]\(3 \frac{1}{4}\)[/tex]
To convert the mixed number [tex]\(3 \frac{1}{4}\)[/tex] into an improper fraction:
- Multiply the whole number (3) by the denominator (4), which is 12.
- Add the numerator (1), which gives us 13.
So, the improper fraction is [tex]\(\frac{13}{4}\)[/tex].
### Circle the fraction with the greatest value: [tex]\(\frac{1}{11}, \frac{1}{6}, \frac{1}{9}\)[/tex]
To compare these fractions, note that a smaller denominator means a larger fraction when the numerators are the same:
- [tex]\(\frac{1}{6} > \frac{1}{9} > \frac{1}{11}\)[/tex]
Therefore, [tex]\(\frac{1}{6}\)[/tex] is the greatest fraction.
I hope this helps! Let me know if you have any more questions.
