6 1/8 – 2 1/12-5 1/10 + 3 7/25 please answer in mixed fraction
The Correct Answer and Explanation is:
Step-by-Step Solution for:
6 1/8 – 2 1/12 – 5 1/10 + 3 7/25
Step 1: Convert all mixed numbers to improper fractions
- 6 1/8 = 6×8+18=498\frac{6 \times 8 + 1}{8} = \frac{49}{8}86×8+1=849
- 2 1/12 = 2×12+112=2512\frac{2 \times 12 + 1}{12} = \frac{25}{12}122×12+1=1225
- 5 1/10 = 5×10+110=5110\frac{5 \times 10 + 1}{10} = \frac{51}{10}105×10+1=1051
- 3 7/25 = 3×25+725=8225\frac{3 \times 25 + 7}{25} = \frac{82}{25}253×25+7=2582
Step 2: Find a common denominator
The denominators are 8, 12, 10, and 25.
The Least Common Denominator (LCD) is 600.
Step 3: Convert each fraction to have the denominator 600
- 498=49×75600=3675600\frac{49}{8} = \frac{49 \times 75}{600} = \frac{3675}{600}849=60049×75=6003675
- 2512=25×50600=1250600\frac{25}{12} = \frac{25 \times 50}{600} = \frac{1250}{600}1225=60025×50=6001250
- 5110=51×60600=3060600\frac{51}{10} = \frac{51 \times 60}{600} = \frac{3060}{600}1051=60051×60=6003060
- 8225=82×24600=1968600\frac{82}{25} = \frac{82 \times 24}{600} = \frac{1968}{600}2582=60082×24=6001968
Step 4: Perform the operations3675600−1250600−3060600+1968600=3675−1250−3060+1968600\frac{3675}{600} – \frac{1250}{600} – \frac{3060}{600} + \frac{1968}{600} = \frac{3675 – 1250 – 3060 + 1968}{600}6003675−6001250−6003060+6001968=6003675−1250−3060+1968
Simplifying the numerator:3675−1250=24252425−3060=−635−635+1968=13333675 – 1250 = 2425 2425 – 3060 = -635 -635 + 1968 = 1333 3675−1250=24252425−3060=−635−635+1968=1333
So the result is:1333600\frac{1333}{600}6001333
Step 5: Convert to a mixed number
Divide 1333 by 600:1333÷600=2 remainder 1331333 ÷ 600 = 2 \text{ remainder } 133 1333÷600=2 remainder 133
So:1333600=2133600\frac{1333}{600} = 2 \frac{133}{600}6001333=2600133
Step 6: Simplify the fractional part
Find the Greatest Common Divisor (GCD) of 133 and 600, which is 1, so the fraction stays the same.
Final Answer:2133600\boxed{2 \frac{133}{600}}2600133
Explanation:
To solve mixed number operations involving subtraction and addition, the first step is converting all mixed numbers to improper fractions. This simplifies the operations since dealing with improper fractions is straightforward when finding common denominators.
The denominators in this case were 8, 12, 10, and 25, with an LCD of 600, which allows all fractions to be expressed with a common denominator. After conversion, arithmetic operations follow the same rules as basic fractions.
The sum simplifies to an improper fraction of 1333600\frac{1333}{600}6001333, which is then rewritten as a mixed number by dividing the numerator by the denominator. The remainder forms the fractional part, and simplifying ensures the fraction is in its simplest form.
This method avoids errors that can happen when mixing whole numbers and fractions separately, providing a clean, accurate final result.
