3. $4\\frac{3}{4}+3\\frac{1}{2}$ 8 $\\frac{1}{4}$\n2. $3\\frac{5}{6}-1\\frac{1}{6}=2\\frac{2}{3}$\n5…

3. $4\\frac{3}{4}+3\\frac{1}{2}$ 8 $\\frac{1}{4}$\n2. $3\\frac{5}{6}-1\\frac{1}{6}=2\\frac{2}{3}$\n5. $5\\frac{9}{10}+8\\frac{2}{5}$ 14 $\\frac{3}{10}$\n4. $6\\frac{3}{8}-2\\frac{1}{4}=4\\frac{1}{8}$\n7. $7\\frac{5}{12}-3\\frac{3}{4}$ 3 $\\frac{2}{3}$\n6. $3\\frac{5}{8}-2\\frac{7}{8}$ 1 $\\frac{3}{4}$ 3 $\\frac{1}{10}$\n9. $6 - 2\\frac{3}{4}$ 3 $\\frac{1}{4}$\n8. $1\\frac{3}{5}+2\\frac{5}{6}$ 4 $\\frac{13}{30}$\n10. $3\\frac{1}{2}+2\\frac{5}{8}-4\\frac{1}{4}$ 1 $\\frac{7}{8}$\n11. geometry find the perimeter of the triangle.\n1 $\\frac{5}{6}$ in.\n1 $\\frac{1}{6}$ in.\n2 $\\frac{2}{3}$ in.\n= 5 $\\frac{2}{3}$ in\n12. knitting nastia knitted two scarves for her dolls. one was 8 $\\frac{3}{4}$ inches long. the other was 1 $\\frac{1}{2}$ inches shorter than the first. how long was the second scarf?\ncourse 2 · chapter 4 rational numbers

3. $4\\frac{3}{4}+3\\frac{1}{2}$ 8 $\\frac{1}{4}$\n2. $3\\frac{5}{6}-1\\frac{1}{6}=2\\frac{2}{3}$\n5. $5\\frac{9}{10}+8\\frac{2}{5}$ 14 $\\frac{3}{10}$\n4. $6\\frac{3}{8}-2\\frac{1}{4}=4\\frac{1}{8}$\n7. $7\\frac{5}{12}-3\\frac{3}{4}$ 3 $\\frac{2}{3}$\n6. $3\\frac{5}{8}-2\\frac{7}{8}$ 1 $\\frac{3}{4}$ 3 $\\frac{1}{10}$\n9. $6 - 2\\frac{3}{4}$ 3 $\\frac{1}{4}$\n8. $1\\frac{3}{5}+2\\frac{5}{6}$ 4 $\\frac{13}{30}$\n10. $3\\frac{1}{2}+2\\frac{5}{8}-4\\frac{1}{4}$ 1 $\\frac{7}{8}$\n11. geometry find the perimeter of the triangle.\n1 $\\frac{5}{6}$ in.\n1 $\\frac{1}{6}$ in.\n2 $\\frac{2}{3}$ in.\n= 5 $\\frac{2}{3}$ in\n12. knitting nastia knitted two scarves for her dolls. one was 8 $\\frac{3}{4}$ inches long. the other was 1 $\\frac{1}{2}$ inches shorter than the first. how long was the second scarf?\ncourse 2 · chapter 4 rational numbers

Answer

Explanation:

Step1: Convert mixed - numbers to improper fractions

For the triangle with side lengths (1\frac{5}{6}=\frac{6\times1 + 5}{6}=\frac{11}{6}) inches, (1\frac{1}{6}=\frac{6\times1+1}{6}=\frac{7}{6}) inches and (2\frac{2}{3}=\frac{3\times2 + 2}{3}=\frac{8}{3}=\frac{16}{6}) inches.

Step2: Calculate the perimeter

The perimeter (P) of a triangle is the sum of its side - lengths. So (P=\frac{11}{6}+\frac{7}{6}+\frac{16}{6}=\frac{11 + 7+16}{6}=\frac{34}{6}=\frac{17}{3}=5\frac{2}{3}) inches.

For the knitting problem:

Step1: Convert mixed - numbers to improper fractions

The first scarf length is (8\frac{3}{4}=\frac{4\times8 + 3}{4}=\frac{35}{4}) inches, and the second scarf is (1\frac{1}{2}=\frac{2\times1+1}{2}=\frac{3}{2}=\frac{6}{4}) inches shorter.

Step2: Subtract to find the length of the second scarf

The length of the second scarf (L=\frac{35}{4}-\frac{6}{4}=\frac{35 - 6}{4}=\frac{29}{4}=7\frac{1}{4}) inches.

Answer:

  1. The perimeter of the triangle is (5\frac{2}{3}) inches.
  2. The length of the second scarf is (7\frac{1}{4}) inches.