CALCULATE THE EXACT VALUE OF 3 1/5 – 2/3 divided by 2 4/5
The Correct Answer and Explanation is:
To solve 315−23÷2453 \frac{1}{5} – \frac{2}{3} \div 2 \frac{4}{5}351−32÷254, let’s break it down step by step.
Step 1: Convert the mixed numbers to improper fractions.
- 315=3×5+15=1653 \frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{16}{5}351=53×5+1=516
- 245=2×5+45=1452 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{14}{5}254=52×5+4=514
Now the expression becomes:165−23÷145\frac{16}{5} – \frac{2}{3} \div \frac{14}{5}516−32÷514
Step 2: Division of fractions.
To divide by a fraction, multiply by its reciprocal:23÷145=23×514=2×53×14=1042\frac{2}{3} \div \frac{14}{5} = \frac{2}{3} \times \frac{5}{14} = \frac{2 \times 5}{3 \times 14} = \frac{10}{42}32÷514=32×145=3×142×5=4210
Simplify the fraction 1042\frac{10}{42}4210:1042=521\frac{10}{42} = \frac{5}{21}4210=215
Now the expression becomes:165−521\frac{16}{5} – \frac{5}{21}516−215
Step 3: Find a common denominator.
The least common denominator (LCD) of 5 and 21 is 105. Now we convert both fractions to have this common denominator.
- 165=16×215×21=336105\frac{16}{5} = \frac{16 \times 21}{5 \times 21} = \frac{336}{105}516=5×2116×21=105336
- 521=5×521×5=25105\frac{5}{21} = \frac{5 \times 5}{21 \times 5} = \frac{25}{105}215=21×55×5=10525
Step 4: Subtract the fractions.
Now we can subtract the fractions:336105−25105=336−25105=311105\frac{336}{105} – \frac{25}{105} = \frac{336 – 25}{105} = \frac{311}{105}105336−10525=105336−25=105311
Step 5: Convert the improper fraction to a mixed number.
To convert 311105\frac{311}{105}105311 to a mixed number, divide 311 by 105:311÷105=2 remainder 101311 \div 105 = 2 \text{ remainder } 101311÷105=2 remainder 101
Thus, 311105=2101105\frac{311}{105} = 2 \frac{101}{105}105311=2105101.
Final Answer:
The exact value of 315−23÷2453 \frac{1}{5} – \frac{2}{3} \div 2 \frac{4}{5}351−32÷254 is 21011052 \frac{101}{105}2105101.
