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Answer :
Sure, let's go through the addition or subtraction of these mixed numbers step-by-step.
We have the following problem:
[tex]\[ 7 \frac{13}{15} - 5 \frac{1}{5} \][/tex]
### Step 1: Convert Mixed Numbers to Improper Fractions
A mixed number consists of a whole number and a fraction. We need to convert these mixed numbers to improper fractions.
For [tex]\( 7 \frac{13}{15} \)[/tex]:
- Multiply the whole number by the denominator: [tex]\( 7 \times 15 = 105 \)[/tex]
- Add the numerator of the fraction: [tex]\( 105 + 13 = 118 \)[/tex]
- Thus, [tex]\( 7 \frac{13}{15} \)[/tex] becomes [tex]\( \frac{118}{15} \)[/tex]
For [tex]\( 5 \frac{1}{5} \)[/tex]:
- Multiply the whole number by the denominator: [tex]\( 5 \times 5 = 25 \)[/tex]
- Add the numerator of the fraction: [tex]\( 25 + 1 = 26 \)[/tex]
- Thus, [tex]\( 5 \frac{1}{5} \)[/tex] becomes [tex]\( \frac{26}{5} \)[/tex]
### Step 2: Find a Common Denominator
To subtract these fractions, they need a common denominator. The denominators are 15 and 5. The least common multiple (LCM) of 15 and 5 is 15.
Now, convert [tex]\(\frac{26}{5}\)[/tex] to a fraction with the denominator 15:
[tex]\[ \frac{26}{5} = \frac{26 \times 3}{5 \times 3} = \frac{78}{15} \][/tex]
### Step 3: Subtract the Fractions
Now we have:
[tex]\[ \frac{118}{15} - \frac{78}{15} \][/tex]
Since the denominators are the same, we can subtract the numerators directly:
[tex]\[ \frac{118 - 78}{15} = \frac{40}{15} \][/tex]
### Step 4: Simplify the Fraction
The fraction [tex]\(\frac{40}{15}\)[/tex] can be simplified by dividing the numerator and the denominator by their greatest common divisor (GCD). The GCD of 40 and 15 is 5:
[tex]\[ \frac{40 \div 5}{15 \div 5} = \frac{8}{3} \][/tex]
So, [tex]\( 7 \frac{13}{15} - 5 \frac{1}{5} = \frac{8}{3} \)[/tex].
Thus, the final answer in lowest terms is:
[tex]\[ \boxed{\frac{8}{3}} \][/tex]
We have the following problem:
[tex]\[ 7 \frac{13}{15} - 5 \frac{1}{5} \][/tex]
### Step 1: Convert Mixed Numbers to Improper Fractions
A mixed number consists of a whole number and a fraction. We need to convert these mixed numbers to improper fractions.
For [tex]\( 7 \frac{13}{15} \)[/tex]:
- Multiply the whole number by the denominator: [tex]\( 7 \times 15 = 105 \)[/tex]
- Add the numerator of the fraction: [tex]\( 105 + 13 = 118 \)[/tex]
- Thus, [tex]\( 7 \frac{13}{15} \)[/tex] becomes [tex]\( \frac{118}{15} \)[/tex]
For [tex]\( 5 \frac{1}{5} \)[/tex]:
- Multiply the whole number by the denominator: [tex]\( 5 \times 5 = 25 \)[/tex]
- Add the numerator of the fraction: [tex]\( 25 + 1 = 26 \)[/tex]
- Thus, [tex]\( 5 \frac{1}{5} \)[/tex] becomes [tex]\( \frac{26}{5} \)[/tex]
### Step 2: Find a Common Denominator
To subtract these fractions, they need a common denominator. The denominators are 15 and 5. The least common multiple (LCM) of 15 and 5 is 15.
Now, convert [tex]\(\frac{26}{5}\)[/tex] to a fraction with the denominator 15:
[tex]\[ \frac{26}{5} = \frac{26 \times 3}{5 \times 3} = \frac{78}{15} \][/tex]
### Step 3: Subtract the Fractions
Now we have:
[tex]\[ \frac{118}{15} - \frac{78}{15} \][/tex]
Since the denominators are the same, we can subtract the numerators directly:
[tex]\[ \frac{118 - 78}{15} = \frac{40}{15} \][/tex]
### Step 4: Simplify the Fraction
The fraction [tex]\(\frac{40}{15}\)[/tex] can be simplified by dividing the numerator and the denominator by their greatest common divisor (GCD). The GCD of 40 and 15 is 5:
[tex]\[ \frac{40 \div 5}{15 \div 5} = \frac{8}{3} \][/tex]
So, [tex]\( 7 \frac{13}{15} - 5 \frac{1}{5} = \frac{8}{3} \)[/tex].
Thus, the final answer in lowest terms is:
[tex]\[ \boxed{\frac{8}{3}} \][/tex]
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