IDNLearn.com makes it easy to find answers and share knowledge with others. Ask your questions and receive accurate, in-depth answers from our knowledgeable community members.
Sagot :
Let's solve each exercise step by step:
### (a) [tex]\(\frac{-1}{2} + \frac{3}{4}\)[/tex]
1. Find a common denominator for [tex]\(\frac{-1}{2}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex]. The common denominator is 4.
2. Convert [tex]\(\frac{-1}{2}\)[/tex] to [tex]\(\frac{-2}{4}\)[/tex].
3. Add [tex]\(\frac{-2}{4} + \frac{3}{4} = \frac{1}{4}\)[/tex].
Therefore, [tex]\(\frac{-1}{2} + \frac{3}{4} = \frac{1}{4}\)[/tex].
### (b) [tex]\(\frac{5}{9} - \frac{4}{3}\)[/tex]
1. Find a common denominator for [tex]\(\frac{5}{9}\)[/tex] and [tex]\(\frac{4}{3}\)[/tex]. The common denominator is 9.
2. Convert [tex]\(\frac{4}{3}\)[/tex] to [tex]\(\frac{12}{9}\)[/tex].
3. Subtract [tex]\(\frac{5}{9} - \frac{12}{9} = \frac{-7}{9}\)[/tex].
Therefore, [tex]\(\frac{5}{9} - \frac{4}{3} = \frac{-7}{9}\)[/tex].
### (c) [tex]\(-1 \frac{1}{3} - 2 \frac{1}{4}\)[/tex]
1. Convert the mixed numbers to improper fractions:
- [tex]\(-1 \frac{1}{3} = \frac{-4}{3}\)[/tex]
- [tex]\(2 \frac{1}{4} = \frac{9}{4}\)[/tex]
2. Find a common denominator for [tex]\(\frac{-4}{3}\)[/tex] and [tex]\(\frac{9}{4}\)[/tex]. The common denominator is 12.
3. Convert the fractions:
- [tex]\(\frac{-4}{3} = \frac{-16}{12}\)[/tex]
- [tex]\(\frac{9}{4} = \frac{27}{12}\)[/tex]
4. Subtract [tex]\(\frac{-16}{12} - \frac{27}{12} = \frac{-43}{12}\)[/tex], which is approximately [tex]\(-3.5833\)[/tex].
Therefore, [tex]\(-1 \frac{1}{3} - 2 \frac{1}{4} = \frac{-43}{12}\)[/tex] or approximately [tex]\(-3.5833\)[/tex].
### (e) [tex]\(\frac{-3}{5} - \left(\frac{-7}{2}\right)\)[/tex]
1. Recognize that subtracting a negative is the same as adding a positive: [tex]\(\frac{-3}{5} + \frac{7}{2}\)[/tex].
2. Find a common denominator for [tex]\(\frac{-3}{5}\)[/tex] and [tex]\(\frac{7}{2}\)[/tex]. The common denominator is 10.
3. Convert the fractions:
- [tex]\(\frac{-3}{5} = \frac{-6}{10}\)[/tex]
- [tex]\(\frac{7}{2} = \frac{35}{10}\)[/tex]
4. Add [tex]\(\frac{-6}{10} + \frac{35}{10} = \frac{29}{10}\)[/tex], which is 2.9.
Therefore, [tex]\(\frac{-3}{5} - \left(\frac{-7}{2}\right) = 2.9\)[/tex].
### (f) [tex]\(16 - 2 \frac{3}{7}\)[/tex]
1. Convert the mixed number to an improper fraction:
- [tex]\(2 \frac{3}{7} = \frac{17}{7}\)[/tex]
2. Recognize that 16 is equivalent to [tex]\(\frac{112}{7}\)[/tex].
3. Subtract [tex]\(\frac{112}{7} - \frac{17}{7} = \frac{95}{7}\)[/tex], which is approximately 13.5714.
Therefore, [tex]\(16 - 2 \frac{3}{7} = \frac{95}{7}\)[/tex] or approximately 13.5714.
### (g) [tex]\(1 \frac{5}{7} - 4\)[/tex]
1. Convert the mixed number to an improper fraction:
- [tex]\(1 \frac{5}{7} = \frac{12}{7}\)[/tex]
2. Recognize that 4 is equivalent to [tex]\(\frac{28}{7}\)[/tex].
3. Subtract [tex]\(\frac{12}{7} - \frac{28}{7} = \frac{-16}{7}\)[/tex], which is approximately [tex]\(-2.2857\)[/tex].
Therefore, [tex]\(1 \frac{5}{7} - 4 = \frac{-16}{7}\)[/tex] or approximately [tex]\(-2.2857\)[/tex].
### (i) [tex]\(\frac{3}{19} + \frac{1}{2}\)[/tex]
1. Find a common denominator for [tex]\(\frac{3}{19}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]. The common denominator is 38.
2. Convert the fractions:
- [tex]\(\frac{3}{19} = \frac{6}{38}\)[/tex]
- [tex]\(\frac{1}{2} = \frac{19}{38}\)[/tex]
3. Add [tex]\(\frac{6}{38} + \frac{19}{38} = \frac{25}{38}\)[/tex], which is approximately 0.6579.
Therefore, [tex]\(\frac{3}{19} + \frac{1}{2} = \frac{25}{38}\)[/tex] or approximately 0.6579.
These are the solutions to the given exercises.
### (a) [tex]\(\frac{-1}{2} + \frac{3}{4}\)[/tex]
1. Find a common denominator for [tex]\(\frac{-1}{2}\)[/tex] and [tex]\(\frac{3}{4}\)[/tex]. The common denominator is 4.
2. Convert [tex]\(\frac{-1}{2}\)[/tex] to [tex]\(\frac{-2}{4}\)[/tex].
3. Add [tex]\(\frac{-2}{4} + \frac{3}{4} = \frac{1}{4}\)[/tex].
Therefore, [tex]\(\frac{-1}{2} + \frac{3}{4} = \frac{1}{4}\)[/tex].
### (b) [tex]\(\frac{5}{9} - \frac{4}{3}\)[/tex]
1. Find a common denominator for [tex]\(\frac{5}{9}\)[/tex] and [tex]\(\frac{4}{3}\)[/tex]. The common denominator is 9.
2. Convert [tex]\(\frac{4}{3}\)[/tex] to [tex]\(\frac{12}{9}\)[/tex].
3. Subtract [tex]\(\frac{5}{9} - \frac{12}{9} = \frac{-7}{9}\)[/tex].
Therefore, [tex]\(\frac{5}{9} - \frac{4}{3} = \frac{-7}{9}\)[/tex].
### (c) [tex]\(-1 \frac{1}{3} - 2 \frac{1}{4}\)[/tex]
1. Convert the mixed numbers to improper fractions:
- [tex]\(-1 \frac{1}{3} = \frac{-4}{3}\)[/tex]
- [tex]\(2 \frac{1}{4} = \frac{9}{4}\)[/tex]
2. Find a common denominator for [tex]\(\frac{-4}{3}\)[/tex] and [tex]\(\frac{9}{4}\)[/tex]. The common denominator is 12.
3. Convert the fractions:
- [tex]\(\frac{-4}{3} = \frac{-16}{12}\)[/tex]
- [tex]\(\frac{9}{4} = \frac{27}{12}\)[/tex]
4. Subtract [tex]\(\frac{-16}{12} - \frac{27}{12} = \frac{-43}{12}\)[/tex], which is approximately [tex]\(-3.5833\)[/tex].
Therefore, [tex]\(-1 \frac{1}{3} - 2 \frac{1}{4} = \frac{-43}{12}\)[/tex] or approximately [tex]\(-3.5833\)[/tex].
### (e) [tex]\(\frac{-3}{5} - \left(\frac{-7}{2}\right)\)[/tex]
1. Recognize that subtracting a negative is the same as adding a positive: [tex]\(\frac{-3}{5} + \frac{7}{2}\)[/tex].
2. Find a common denominator for [tex]\(\frac{-3}{5}\)[/tex] and [tex]\(\frac{7}{2}\)[/tex]. The common denominator is 10.
3. Convert the fractions:
- [tex]\(\frac{-3}{5} = \frac{-6}{10}\)[/tex]
- [tex]\(\frac{7}{2} = \frac{35}{10}\)[/tex]
4. Add [tex]\(\frac{-6}{10} + \frac{35}{10} = \frac{29}{10}\)[/tex], which is 2.9.
Therefore, [tex]\(\frac{-3}{5} - \left(\frac{-7}{2}\right) = 2.9\)[/tex].
### (f) [tex]\(16 - 2 \frac{3}{7}\)[/tex]
1. Convert the mixed number to an improper fraction:
- [tex]\(2 \frac{3}{7} = \frac{17}{7}\)[/tex]
2. Recognize that 16 is equivalent to [tex]\(\frac{112}{7}\)[/tex].
3. Subtract [tex]\(\frac{112}{7} - \frac{17}{7} = \frac{95}{7}\)[/tex], which is approximately 13.5714.
Therefore, [tex]\(16 - 2 \frac{3}{7} = \frac{95}{7}\)[/tex] or approximately 13.5714.
### (g) [tex]\(1 \frac{5}{7} - 4\)[/tex]
1. Convert the mixed number to an improper fraction:
- [tex]\(1 \frac{5}{7} = \frac{12}{7}\)[/tex]
2. Recognize that 4 is equivalent to [tex]\(\frac{28}{7}\)[/tex].
3. Subtract [tex]\(\frac{12}{7} - \frac{28}{7} = \frac{-16}{7}\)[/tex], which is approximately [tex]\(-2.2857\)[/tex].
Therefore, [tex]\(1 \frac{5}{7} - 4 = \frac{-16}{7}\)[/tex] or approximately [tex]\(-2.2857\)[/tex].
### (i) [tex]\(\frac{3}{19} + \frac{1}{2}\)[/tex]
1. Find a common denominator for [tex]\(\frac{3}{19}\)[/tex] and [tex]\(\frac{1}{2}\)[/tex]. The common denominator is 38.
2. Convert the fractions:
- [tex]\(\frac{3}{19} = \frac{6}{38}\)[/tex]
- [tex]\(\frac{1}{2} = \frac{19}{38}\)[/tex]
3. Add [tex]\(\frac{6}{38} + \frac{19}{38} = \frac{25}{38}\)[/tex], which is approximately 0.6579.
Therefore, [tex]\(\frac{3}{19} + \frac{1}{2} = \frac{25}{38}\)[/tex] or approximately 0.6579.
These are the solutions to the given exercises.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. For dependable answers, trust IDNLearn.com. Thank you for visiting, and we look forward to assisting you again.
