Answer :
To solve the expression [tex]\(4 \frac{2}{3} \div 1 \frac{13}{15} - 2 \frac{1}{4}\)[/tex], follow these steps:
1. Convert the mixed numbers to improper fractions:
- For [tex]\(4 \frac{2}{3}\)[/tex]: Convert it to an improper fraction.
[tex]\[
4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}
\][/tex]
- For [tex]\(1 \frac{13}{15}\)[/tex]: Convert it to an improper fraction.
[tex]\[
1 \frac{13}{15} = \frac{1 \times 15 + 13}{15} = \frac{15 + 13}{15} = \frac{28}{15}
\][/tex]
- For [tex]\(2 \frac{1}{4}\)[/tex]: Convert it to an improper fraction.
[tex]\[
2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}
\][/tex]
2. Perform the division of the improper fractions:
- Divide [tex]\(\frac{14}{3}\)[/tex] by [tex]\(\frac{28}{15}\)[/tex]. To divide fractions, multiply by the reciprocal of the second fraction.
[tex]\[
\frac{14}{3} \div \frac{28}{15} = \frac{14}{3} \times \frac{15}{28}
\][/tex]
- Simplify:
[tex]\[
\frac{14}{3} \times \frac{15}{28} = \frac{14 \times 15}{3 \times 28} = \frac{210}{84}
\][/tex]
- Further simplifying [tex]\(\frac{210}{84}\)[/tex]:
[tex]\[
\frac{210}{84} = \frac{105}{42} = \frac{35}{14} = \frac{5}{2}
\][/tex]
3. Subtract the third fraction:
- Now, subtract [tex]\(\frac{9}{4}\)[/tex] from [tex]\(\frac{5}{2}\)[/tex]. First, convert [tex]\(\frac{5}{2}\)[/tex] to a fraction with a common denominator:
[tex]\[
\frac{5}{2} = \frac{10}{4}
\][/tex]
- Perform the subtraction:
[tex]\[
\frac{10}{4} - \frac{9}{4} = \frac{1}{4}
\][/tex]
So, the final result of the expression [tex]\(4 \frac{2}{3} \div 1 \frac{13}{15} - 2 \frac{1}{4}\)[/tex] is [tex]\(\boxed{\frac{1}{4}}\)[/tex].
1. Convert the mixed numbers to improper fractions:
- For [tex]\(4 \frac{2}{3}\)[/tex]: Convert it to an improper fraction.
[tex]\[
4 \frac{2}{3} = \frac{4 \times 3 + 2}{3} = \frac{12 + 2}{3} = \frac{14}{3}
\][/tex]
- For [tex]\(1 \frac{13}{15}\)[/tex]: Convert it to an improper fraction.
[tex]\[
1 \frac{13}{15} = \frac{1 \times 15 + 13}{15} = \frac{15 + 13}{15} = \frac{28}{15}
\][/tex]
- For [tex]\(2 \frac{1}{4}\)[/tex]: Convert it to an improper fraction.
[tex]\[
2 \frac{1}{4} = \frac{2 \times 4 + 1}{4} = \frac{8 + 1}{4} = \frac{9}{4}
\][/tex]
2. Perform the division of the improper fractions:
- Divide [tex]\(\frac{14}{3}\)[/tex] by [tex]\(\frac{28}{15}\)[/tex]. To divide fractions, multiply by the reciprocal of the second fraction.
[tex]\[
\frac{14}{3} \div \frac{28}{15} = \frac{14}{3} \times \frac{15}{28}
\][/tex]
- Simplify:
[tex]\[
\frac{14}{3} \times \frac{15}{28} = \frac{14 \times 15}{3 \times 28} = \frac{210}{84}
\][/tex]
- Further simplifying [tex]\(\frac{210}{84}\)[/tex]:
[tex]\[
\frac{210}{84} = \frac{105}{42} = \frac{35}{14} = \frac{5}{2}
\][/tex]
3. Subtract the third fraction:
- Now, subtract [tex]\(\frac{9}{4}\)[/tex] from [tex]\(\frac{5}{2}\)[/tex]. First, convert [tex]\(\frac{5}{2}\)[/tex] to a fraction with a common denominator:
[tex]\[
\frac{5}{2} = \frac{10}{4}
\][/tex]
- Perform the subtraction:
[tex]\[
\frac{10}{4} - \frac{9}{4} = \frac{1}{4}
\][/tex]
So, the final result of the expression [tex]\(4 \frac{2}{3} \div 1 \frac{13}{15} - 2 \frac{1}{4}\)[/tex] is [tex]\(\boxed{\frac{1}{4}}\)[/tex].
