Answer :
Sure! Let's solve the problem of subtracting the two mixed numbers: [tex]\(5 \frac{13}{15}\)[/tex] and [tex]\(2 \frac{3}{5}\)[/tex].
### Step-by-Step Solution:
1. Convert Mixed Numbers to Improper Fractions:
- First, we need to convert each mixed number into an improper fraction for easier subtraction.
For [tex]\(5 \frac{13}{15}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(5 \times 15 = 75\)[/tex].
- Add the numerator: [tex]\(75 + 13 = 88\)[/tex].
- The improper fraction is [tex]\(\frac{88}{15}\)[/tex].
For [tex]\(2 \frac{3}{5}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(2 \times 5 = 10\)[/tex].
- Add the numerator: [tex]\(10 + 3 = 13\)[/tex].
- The improper fraction is [tex]\(\frac{13}{5}\)[/tex].
2. Find a Common Denominator:
- To subtract the fractions, they must have the same denominator.
- The denominators here are 15 and 5. The least common multiple of 15 and 5 is 15.
3. Convert to a Common Denominator:
- [tex]\(\frac{88}{15}\)[/tex] is already over 15.
- Convert [tex]\(\frac{13}{5}\)[/tex] to a denominator of 15:
- Multiply both the numerator and the denominator by 3: [tex]\(\frac{13 \times 3}{5 \times 3} = \frac{39}{15}\)[/tex].
4. Subtract the Fractions:
- Now subtract [tex]\(\frac{39}{15}\)[/tex] from [tex]\(\frac{88}{15}\)[/tex] by subtracting the numerators:
- [tex]\(\frac{88 - 39}{15} = \frac{49}{15}\)[/tex].
5. Convert the Result Back to a Mixed Number:
- Divide the numerator by the denominator: 49 ÷ 15 equals 3 with a remainder of 4.
- So, [tex]\(\frac{49}{15}\)[/tex] as a mixed number is [tex]\(3 \frac{4}{15}\)[/tex].
Therefore, the result of [tex]\(5 \frac{13}{15} - 2 \frac{3}{5}\)[/tex] is [tex]\(3 \frac{4}{15}\)[/tex].
### Step-by-Step Solution:
1. Convert Mixed Numbers to Improper Fractions:
- First, we need to convert each mixed number into an improper fraction for easier subtraction.
For [tex]\(5 \frac{13}{15}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(5 \times 15 = 75\)[/tex].
- Add the numerator: [tex]\(75 + 13 = 88\)[/tex].
- The improper fraction is [tex]\(\frac{88}{15}\)[/tex].
For [tex]\(2 \frac{3}{5}\)[/tex]:
- Multiply the whole number by the denominator: [tex]\(2 \times 5 = 10\)[/tex].
- Add the numerator: [tex]\(10 + 3 = 13\)[/tex].
- The improper fraction is [tex]\(\frac{13}{5}\)[/tex].
2. Find a Common Denominator:
- To subtract the fractions, they must have the same denominator.
- The denominators here are 15 and 5. The least common multiple of 15 and 5 is 15.
3. Convert to a Common Denominator:
- [tex]\(\frac{88}{15}\)[/tex] is already over 15.
- Convert [tex]\(\frac{13}{5}\)[/tex] to a denominator of 15:
- Multiply both the numerator and the denominator by 3: [tex]\(\frac{13 \times 3}{5 \times 3} = \frac{39}{15}\)[/tex].
4. Subtract the Fractions:
- Now subtract [tex]\(\frac{39}{15}\)[/tex] from [tex]\(\frac{88}{15}\)[/tex] by subtracting the numerators:
- [tex]\(\frac{88 - 39}{15} = \frac{49}{15}\)[/tex].
5. Convert the Result Back to a Mixed Number:
- Divide the numerator by the denominator: 49 ÷ 15 equals 3 with a remainder of 4.
- So, [tex]\(\frac{49}{15}\)[/tex] as a mixed number is [tex]\(3 \frac{4}{15}\)[/tex].
Therefore, the result of [tex]\(5 \frac{13}{15} - 2 \frac{3}{5}\)[/tex] is [tex]\(3 \frac{4}{15}\)[/tex].
