13. Convert [tex]$20 \frac{2}{5} \%$[/tex] into a fraction.
14. Convert [tex]$0.02 \%$[/tex] into a decimal.
15. Find the L.C.M. of 48, 72, and 144.
16. Write MDC XLVII in ordinary number.
11. Solve for [tex]$x: 3 x-\frac{3}{5}=x+2 \frac{1}{5}$[/tex]
Answer (1)
Convert the percentage to a fraction: 20 5 2 % = 500 102 = 250 51 .
Convert the percentage to a decimal: 0.02% = 0.0002 .
Find the LCM of 48, 72, and 144: L CM ( 48 , 72 , 144 ) = 2 4 × 3 2 = 144 .
Convert the Roman numeral to an ordinary number: M D CX L V II = 1000 + 500 + 100 + 40 + 7 = 1647 .
Solve the linear equation for x: 3 x − 5 3 = x + 2 5 1 ⟹ x = 10 14 = 5 7 .
Explanation
Problem Analysis We need to solve five independent math problems:
Convert 20 f r a c 2 5 % into a fraction.
Convert 0.02% into a decimal.
Find the Least Common Multiple (LCM) of 48, 72, and 144.
Convert the Roman numeral MDCXLVII into an ordinary number.
Solve the equation 3 x − f r a c 3 5 = x + 2 f r a c 1 5 for x .
Converting Percentage to Fraction Let's convert 20 5 2 % to a fraction. First, convert the mixed number to an improper fraction: 20 5 2 = 5 20 × 5 + 2 = 5 102 .
Then, divide by 100 to convert the percentage to a fraction: 5 102 /100 = 500 102 .
Finally, simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 2: 500 102 = 500 ÷ 2 102 ÷ 2 = 250 51 .
Converting Percentage to Decimal Now, let's convert 0.02% to a decimal. To do this, we divide by 100: 100 0.02 = 0.0002 .
Finding the Least Common Multiple (LCM) Next, we find the LCM of 48, 72, and 144. First, find the prime factorization of each number: 48 = 2 4 × 3 72 = 2 3 × 3 2 144 = 2 4 × 3 2 The LCM is the product of the highest powers of all prime factors present in the numbers: L CM ( 48 , 72 , 144 ) = 2 4 × 3 2 = 16 × 9 = 144 .
Converting Roman Numerals to Ordinary Numbers Now, let's convert MDCXLVII to an ordinary number. We have: M = 1000 D = 500 C = 100 XL = 40 VII = 7 Adding the values, we get: 1000 + 500 + 100 + 40 + 7 = 1647 .
Solving for x Finally, let's solve for x in the equation 3 x − 5 3 = x + 2 5 1 . First, convert the mixed number to an improper fraction: 2 5 1 = 5 11 .
Then, rewrite the equation as: 3 x − 5 3 = x + 5 11 .
Subtract x from both sides: 2 x − 5 3 = 5 11 .
Add 5 3 to both sides: 2 x = 5 14 .
Divide both sides by 2: x = 10 14 = 5 7 .
Final Answers Therefore, the solutions are:
250 51
0.0002
144
1647
5 7
Examples
These math problems are fundamental and have many real-life applications. For instance, converting percentages is used in calculating discounts or interest rates. Finding the LCM is useful in scheduling events that occur at different intervals. Roman numerals, while less common today, are still used in clock faces and historical documents. Solving linear equations is a basic skill used in various fields like engineering, economics, and computer science. Understanding these concepts provides a solid foundation for more advanced mathematical studies and practical problem-solving.
