Rearrange each of the following in ascending order. \( 1.1 .1756,017 ; 56,525 ; 670,76 ; 8,105 ; 56,106 ; 685,503 ; 7,016 ; 787,874 \) \( 1.1 .2 \frac{5}{7} ; \frac{3}{17} ; \frac{1}{2} ; \frac{7}{9} \) Calculate each of the following without using a calculator. Show all working \( 1.2 .1 \frac{7}{4} \times \frac{2}{5} \) \( \frac{5}{2}\left(\frac{5}{4}+\frac{11}{20}\right) \) \( 1.2 .2 \frac{1}{8} \) of \( 64+118 \div 21-7 \)

Let's solve the problems step by step. ### Part 1: Rearranging Numbers in Ascending Order #### 1.1: Rearranging Decimal Numbers The numbers given are: - \( 1.1756 \) - \( 0.17 \) (interpreting \( 017 \) as \( 0.17 \)) - \( 56.525 \) - \( 670.76 \) - \( 8.105 \) - \( 56.106 \) - \( 685.503 \) - \( 7.016 \) - \( 787.874 \) Now, let's convert them to a consistent format and compare them: - \( 0.17 \) - \( 1.1756 \) - \( 7.016 \) - \( 8.105 \) - \( 56.106 \) - \( 56.525 \) - \( 670.76 \) - \( 685.503 \) - \( 787.874 \) Now, arranging them in ascending order: 1. \( 0.17 \) 2. \( 1.1756 \) 3. \( 7.016 \) 4. \( 8.105 \) 5. \( 56.106 \) 6. \( 56.525 \) 7. \( 670.76 \) 8. \( 685.503 \) 9. \( 787.874 \) #### 1.2: Rearranging Fractions The fractions given are: - \( 1.2 \frac{5}{7} \) (which is \( \frac{12}{7} \)) - \( \frac{3}{17} \) - \( \frac{1}{2} \) - \( \frac{7}{9} \) To compare these fractions, we can convert them to a common denominator or decimal form: - \( \frac{12}{7} \approx 1.714 \) - \( \frac{3}{17} \approx 0.176 \) - \( \frac{1}{2} = 0.5 \) - \( \frac{7}{9} \approx 0.778 \) Now, arranging them in ascending order: 1. \( \frac{3}{17} \) 2. \( \frac{1}{2} \) 3. \( \frac{7}{9} \) 4. \( \frac{12}{7} \) ### Part 2: Calculations #### 2.1: Calculate \( \frac{7}{4} \times \frac{2}{5} \) To multiply fractions, we multiply the numerators and the denominators: \[ \frac{7}{4} \times \frac{2}{5} = \frac{7 \times 2}{4 \times 5} = \frac{14}{20} \] Now, simplify \( \frac{14}{20} \): \[ \frac{14 \div 2}{20 \div 2} = \frac{7}{10} \] #### 2.2: Calculate \( \frac{5}{2}\left(\frac{5}{4}+\frac{11}{20}\right) \) First, we need to add \( \frac{5}{4} \) and \( \frac{11}{20} \). To do this, we find a common denominator, which is \( 20 \): \[ \frac{5}{4} = \frac{5 \times 5}{4 \times 5} = \frac{25}{20} \] Now, add: \[ \frac{25}{20} + \frac{11}{20} = \frac{25 + 11}{20} = \frac{36}{20} \] Now, simplify \( \frac{36}{20} \): \[ \frac{36 \div 4}{20 \div 4} = \frac{9}{5} \] Now, multiply by \( \frac{5}{2} \): \[ \frac{5}{2} \times \frac{9}{5} = \frac{5 \times 9}{2 \times 5} = \frac{9}{2} \] #### 2.3: Calculate \( \frac{1}{8} \) of \( 64 + \frac{118}{21} - 7 \) First, calculate \( 64 + \frac{118}{21} - 7 \): \[ 64 - 7 = 57 \] Now, we need to add \( 57 \) and \( \frac{118}{21} \). Convert \( 57 \) to a fraction with a denominator of \( 21 \): \[ 57 = \frac{57 \times 21}{21} = \frac{1197}{21} \] Now, add: \[ \frac{1197}{21} + \frac{118}{21} = \frac{1197 + 118}{21} = \frac{1315}{21} \] Now, calculate \( \frac{1}{8} \) of \( \frac{1315}{21} \): \[ \frac{1}{8} \times \frac{1315}{21} = \frac{1315}{168} \] ### Summary of Results 1. **Ascending Order of Decimal Numbers**: - \( 0.17, 1.1756, 7.016, 8.105, 56.106, 56.525, 670.76, 685.503, 787.874 \) 2. **Ascending Order of Fractions**: - \( \frac{3}{17}, \frac{1}{2}, \frac{7}{9}, \frac{12}{7} \) 3. **Calculations**: - \( \frac{7}{4} \times \frac{2}{5} = \frac{7}{10} \) - \( \frac{5}{2}\left(\frac{5}{4}+\frac{11}{20}\right) = \frac{9}{2} \) - \( \frac{1}{8} \) of \( 64 + \frac{118}{21} - 7 = \frac{1315}{168} \)