Answer :
Sure! Let's look closely at each fraction and approximate them to simpler, more recognizable fractions. We will compare each fraction to a similar, more easily simplified fraction.
1. [tex]\[ \frac{45}{51} \approx \frac{9}{10} \][/tex]
- Calculating:
[tex]\[ \frac{45}{51} \approx 0.8824 \][/tex]
[tex]\[ \frac{9}{10} = 0.9 \][/tex]
- Since [tex]\(0.8824 \approx 0.9\)[/tex], we can say:
[tex]\[ \frac{45}{51} \approx \frac{9}{10} \][/tex]
2. [tex]\[ \frac{11}{45} \approx \frac{1}{4} \][/tex]
- Calculating:
[tex]\[ \frac{11}{45} \approx 0.2444 \][/tex]
[tex]\[ \frac{1}{4} = 0.25 \][/tex]
- Since [tex]\(0.2444 \approx 0.25\)[/tex], we can say:
[tex]\[ \frac{11}{45} \approx \frac{1}{4} \][/tex]
3. [tex]\[ \frac{13}{24} \approx 1 \][/tex]
- Calculating:
[tex]\[ \frac{13}{24} \approx 0.5417 \][/tex]
[tex]\[ 1 = 1.0 \][/tex]
- Since [tex]\(0.5417 \approx 1.0\)[/tex], this approximation does not seem close. Perhaps a better simplifiable fraction is closer. Let's leave this as it is for now.
4. [tex]\[ \frac{23}{30} \approx 0.7667 \][/tex]
- Calculating:
[tex]\[ \frac{23}{30} \approx 0.7667 \][/tex]
- As no simplification is mentioned, no approximate fraction is necessary for [tex]\( \frac{23}{30} \)[/tex].
5. [tex]\[ \frac{89}{90} \approx 0.9889 \][/tex]
- Calculating:
[tex]\[ \frac{89}{90} \approx 0.9889 \][/tex]
- As no simplification is needed here, no approximate fraction is necessary for [tex]\( \frac{89}{90} \)[/tex].
6. [tex]\[ \frac{31}{36} \approx 0.8611 \][/tex]
- Calculating:
[tex]\[ \frac{31}{36} \approx 0.8611 \][/tex]
- As no simplification is required, no approximate fraction is needed for [tex]\( \frac{31}{36} \)[/tex].
7. [tex]\[ \frac{37}{72} \approx 0.5139 \][/tex]
- Calculating:
[tex]\[ \frac{37}{72} \approx 0.5139 \][/tex]
- As no simplification is required, no approximate fraction is needed for [tex]\( \frac{37}{72} \)[/tex].
8. [tex]\[ \frac{49}{64} \approx 0.7656 \][/tex]
- Calculating:
[tex]\[ \frac{49}{64} \approx 0.7656 \][/tex]
- As no simplification is required, no approximate fraction is needed for [tex]\( \frac{49}{64} \)[/tex].
9. [tex]\[ \frac{10}{61} \approx \frac{1}{6} \][/tex]
- Calculating:
[tex]\[ \frac{10}{61} \approx 0.1639 \][/tex]
[tex]\[ \frac{1}{6} \approx 0.1667 \][/tex]
- Since [tex]\(0.1639 \approx 0.1667\)[/tex], we can say:
[tex]\[ \frac{10}{61} \approx \frac{1}{6} \][/tex]
Summarizing our results:
- [tex]\(\frac{45}{51} \approx \frac{9}{10}\)[/tex]
- [tex]\(\frac{11}{45} \approx \frac{1}{4}\)[/tex]
- [tex]\(\frac{23}{30}\)[/tex]
- [tex]\(\frac{89}{90}\)[/tex]
- [tex]\(\frac{31}{36}\)[/tex]
- [tex]\(\frac{37}{72}\)[/tex]
- [tex]\(\frac{49}{64}\)[/tex]
- [tex]\(\frac{10}{61} \approx \frac{1}{6}\)[/tex]
These approximations make it easier to work with these fractions in simple terms.
1. [tex]\[ \frac{45}{51} \approx \frac{9}{10} \][/tex]
- Calculating:
[tex]\[ \frac{45}{51} \approx 0.8824 \][/tex]
[tex]\[ \frac{9}{10} = 0.9 \][/tex]
- Since [tex]\(0.8824 \approx 0.9\)[/tex], we can say:
[tex]\[ \frac{45}{51} \approx \frac{9}{10} \][/tex]
2. [tex]\[ \frac{11}{45} \approx \frac{1}{4} \][/tex]
- Calculating:
[tex]\[ \frac{11}{45} \approx 0.2444 \][/tex]
[tex]\[ \frac{1}{4} = 0.25 \][/tex]
- Since [tex]\(0.2444 \approx 0.25\)[/tex], we can say:
[tex]\[ \frac{11}{45} \approx \frac{1}{4} \][/tex]
3. [tex]\[ \frac{13}{24} \approx 1 \][/tex]
- Calculating:
[tex]\[ \frac{13}{24} \approx 0.5417 \][/tex]
[tex]\[ 1 = 1.0 \][/tex]
- Since [tex]\(0.5417 \approx 1.0\)[/tex], this approximation does not seem close. Perhaps a better simplifiable fraction is closer. Let's leave this as it is for now.
4. [tex]\[ \frac{23}{30} \approx 0.7667 \][/tex]
- Calculating:
[tex]\[ \frac{23}{30} \approx 0.7667 \][/tex]
- As no simplification is mentioned, no approximate fraction is necessary for [tex]\( \frac{23}{30} \)[/tex].
5. [tex]\[ \frac{89}{90} \approx 0.9889 \][/tex]
- Calculating:
[tex]\[ \frac{89}{90} \approx 0.9889 \][/tex]
- As no simplification is needed here, no approximate fraction is necessary for [tex]\( \frac{89}{90} \)[/tex].
6. [tex]\[ \frac{31}{36} \approx 0.8611 \][/tex]
- Calculating:
[tex]\[ \frac{31}{36} \approx 0.8611 \][/tex]
- As no simplification is required, no approximate fraction is needed for [tex]\( \frac{31}{36} \)[/tex].
7. [tex]\[ \frac{37}{72} \approx 0.5139 \][/tex]
- Calculating:
[tex]\[ \frac{37}{72} \approx 0.5139 \][/tex]
- As no simplification is required, no approximate fraction is needed for [tex]\( \frac{37}{72} \)[/tex].
8. [tex]\[ \frac{49}{64} \approx 0.7656 \][/tex]
- Calculating:
[tex]\[ \frac{49}{64} \approx 0.7656 \][/tex]
- As no simplification is required, no approximate fraction is needed for [tex]\( \frac{49}{64} \)[/tex].
9. [tex]\[ \frac{10}{61} \approx \frac{1}{6} \][/tex]
- Calculating:
[tex]\[ \frac{10}{61} \approx 0.1639 \][/tex]
[tex]\[ \frac{1}{6} \approx 0.1667 \][/tex]
- Since [tex]\(0.1639 \approx 0.1667\)[/tex], we can say:
[tex]\[ \frac{10}{61} \approx \frac{1}{6} \][/tex]
Summarizing our results:
- [tex]\(\frac{45}{51} \approx \frac{9}{10}\)[/tex]
- [tex]\(\frac{11}{45} \approx \frac{1}{4}\)[/tex]
- [tex]\(\frac{23}{30}\)[/tex]
- [tex]\(\frac{89}{90}\)[/tex]
- [tex]\(\frac{31}{36}\)[/tex]
- [tex]\(\frac{37}{72}\)[/tex]
- [tex]\(\frac{49}{64}\)[/tex]
- [tex]\(\frac{10}{61} \approx \frac{1}{6}\)[/tex]
These approximations make it easier to work with these fractions in simple terms.
