Verified Answer :
- Add or subtract fractions by finding common denominators or converting them to decimals.
- For additions involving whole numbers and fractions, combine the values directly or convert to a single mixed number or decimal.
- Calculate all expressions to find:
\(\frac{4}{10} + \frac{3}{10} = 0.7; \frac{7}{8} - \frac{2}{8} = 0.625; \frac{4}{10} + \frac{3}{12} = 0.65; 3205 + 24.5 = 3229.5; 62 + 248 = 310; \frac{21}{4} - \frac{33}{4} = -3; \frac{43}{8} + \frac{21}{8} = 8; \frac{92}{6} - \frac{55}{6} = \frac{37}{6}; \frac{32}{5} + \frac{4}{5} = 7.2; \frac{61}{8} - \frac{5}{8} = 7; 127 + \frac{3}{5} = 127.6.\)
- \(\boxed{0.7, 0.625, 0.65, 3229.5, 310, -3, 8, \frac{37}{6}, 7.2, 7, 127.6}\)
Explanation
- Analysis of Arithmetic Expressions
We will evaluate each of the arithmetic expressions provided, working through each step to ensure accuracy. When adding or subtracting fractions with common denominators, we combine the numerators while keeping the denominator the same. For fractions with different denominators, we first find a common denominator or convert them to decimals. For addition with whole numbers, we either convert the whole number to a fraction or add the fractional part to the integer.
- Performing Calculations
We compute the expressions:
- \(\frac{4}{10} + \frac{3}{10} = \frac{7}{10} = 0.7\)
- \(\frac{7}{8} - \frac{2}{8} = \frac{5}{8} = 0.625\)
- \(\frac{4}{10} + \frac{3}{12} = \frac{2}{5} + \frac{1}{4} = \frac{8}{20} + \frac{5}{20} = \frac{13}{20} = 0.65\)
- \(3205 + 24.5 = 3229.5\)
- \(62 + 248 = 310\)
- \(\frac{21}{4} - \frac{33}{4} = \frac{-12}{4} = -3\)
- \(\frac{43}{8} + \frac{21}{8} = \frac{64}{8} = 8\)
- \(\frac{92}{6} - \frac{55}{6} = \frac{37}{6} = 6\frac{1}{6} \approx 6.167\)
- \(\frac{32}{5} + \frac{4}{5} = \frac{36}{5} = 7.2\)
- \(\frac{61}{8} - \frac{5}{8} = \frac{56}{8} = 7\)
- \(127 + \frac{3}{5} = 127 + 0.6 = 127.6\)
- Conclusion of Calculations
The results for the requested expressions are as follows:
- \(\frac{4}{10} + \frac{3}{10} = 0.7\)
- \(\frac{7}{8} - \frac{2}{8} = 0.625\)
- \(\frac{4}{10} + \frac{3}{12} = 0.65\)
- \(3205 + 24.5 = 3229.5\)
- \(62 + 248 = 310\)
- \(\frac{21}{4} - \frac{33}{4} = -3\)
- \(\frac{43}{8} + \frac{21}{8} = 8\)
- \(\frac{92}{6} - \frac{55}{6} = \frac{37}{6}\)
- \(\frac{32}{5} + \frac{4}{5} = 7.2\)
- \(\frac{61}{8} - \frac{5}{8} = 7\)
- \(127 + \frac{3}{5} = 127.6\)
Examples
In everyday life, arithmetic skills are crucial for tasks like budgeting, cooking, or measurement. For instance, if you are following a recipe that calls for different measurements of ingredients like \(\frac{3}{4}\) cup of flour and \(\frac{1}{2}\) cup of sugar, you can use these arithmetic rules to manage your proportions correctly, ensuring your final product is balanced and delicious. Similarly, managing personal finances involves basic arithmetic to sum daily expenses or subtract savings from income.