find the sum of following fraction 4 12/20+17/25
The Correct Answer and Explanation is:
To find the sum of the fractions 41220+17254\frac{12}{20} + \frac{17}{25}42012+2517, we first convert the mixed number to an improper fraction, then add the two fractions.
Step 1: Convert the mixed number to an improper fraction
41220=4×20+1220=80+1220=92204\frac{12}{20} = \frac{4 \times 20 + 12}{20} = \frac{80 + 12}{20} = \frac{92}{20}42012=204×20+12=2080+12=2092
Step 2: Find a common denominator for the fractions
We are adding 9220+1725\frac{92}{20} + \frac{17}{25}2092+2517.
To add fractions, they must have a common denominator. The least common denominator (LCD) of 20 and 25 is 100.
Convert both fractions to have the same denominator:
- 9220=92×520×5=460100\frac{92}{20} = \frac{92 \times 5}{20 \times 5} = \frac{460}{100}2092=20×592×5=100460
- 1725=17×425×4=68100\frac{17}{25} = \frac{17 \times 4}{25 \times 4} = \frac{68}{100}2517=25×417×4=10068
Step 3: Add the fractions
460100+68100=460+68100=528100\frac{460}{100} + \frac{68}{100} = \frac{460 + 68}{100} = \frac{528}{100}100460+10068=100460+68=100528
Step 4: Simplify the result
We simplify 528100\frac{528}{100}100528 by dividing both numerator and denominator by their greatest common divisor, which is 4:528÷4100÷4=13225\frac{528 \div 4}{100 \div 4} = \frac{132}{25}100÷4528÷4=25132
Now convert 13225\frac{132}{25}25132 back to a mixed number:132 \div 25 = 5\) remainder \(7\), so \[ \frac{132}{25} = 5\frac{7}{25}
Final Answer:
41220+1725=57254\frac{12}{20} + \frac{17}{25} = 5\frac{7}{25}42012+2517=5257
Explanation (300 words):
To add the mixed number 412204\frac{12}{20}42012 and the fraction 1725\frac{17}{25}2517, we follow a clear sequence of steps. First, we convert the mixed number to an improper fraction. A mixed number combines a whole number and a fraction, so we rewrite it using a single fraction. The denominator of the fraction part is 20. Multiplying the whole number 4 by 20 gives 80. Adding the numerator 12 gives 92. So 412204\frac{12}{20}42012 becomes 9220\frac{92}{20}2092.
Next, we must add 9220+1725\frac{92}{20} + \frac{17}{25}2092+2517. To do this, we need a common denominator. The lowest common denominator of 20 and 25 is 100. We convert both fractions to have 100 as the denominator. Multiply both numerator and denominator of 9220\frac{92}{20}2092 by 5 to get 460100\frac{460}{100}100460. Multiply both numerator and denominator of 1725\frac{17}{25}2517 by 4 to get 68100\frac{68}{100}10068. Now both fractions have the same denominator, so we can add the numerators directly.
Adding 460+68460 + 68460+68 gives 528, so the sum is 528100\frac{528}{100}100528. To simplify, we divide the numerator and denominator by 4. This results in 13225\frac{132}{25}25132. Finally, we convert this improper fraction to a mixed number. Since 25 fits into 132 five times with a remainder of 7, the final answer is 57255\frac{7}{25}5257. This represents the exact sum of the original expression.
