Question

solve by renaming simplify if needed
1 $6\frac{3}{8}-1\frac{3}{4}=$
$5\frac{11}{8}-1\frac{6}{8}=4\frac{5}{8}$
2 $5\frac{2}{10}-2\frac{4}{5}=$
3 $9\frac{5}{6}-3\frac{2}{3}=$
$-$ $=$
4 $4\frac{1}{5}-1\frac{7}{10}=$
$-$ $=$

Explanation:

Step1: Rename first mixed number

Problem 1:

$6\frac{3}{8} = 5\frac{11}{8}$

Problem 2:

$5\frac{2}{10} = 4\frac{12}{10}$

Problem 3:

$9\frac{5}{6} = 9\frac{5}{6}$, $3\frac{2}{3}=3\frac{4}{6}$; no rename needed for first term, adjust second term's denominator

Problem 4:

$4\frac{1}{5} = 4\frac{2}{10} = 3\frac{12}{10}$

Step2: Subtract whole & fractional parts

Problem 1:

$5\frac{11}{8} - 1\frac{3}{8} = (5-1) + \frac{11-3}{8} = 4 + \frac{8}{8}$

Problem 2:

$4\frac{12}{10} - 2\frac{9}{10} = (4-2) + \frac{12-9}{10} = 2 + \frac{3}{10}$

Problem 3:

$9\frac{5}{6} - 3\frac{4}{6} = (9-3) + \frac{5-4}{6} = 6 + \frac{1}{6}$

Problem 4:

$3\frac{12}{10} - 1\frac{9}{10} = (3-1) + \frac{12-9}{10} = 2 + \frac{3}{10}$

Step3: Simplify final results

Problem 1:

$4 + \frac{8}{8} = 4 + 1 = 5$ Correction: Original step had error, correct calculation: $5\frac{11}{8}-1\frac{3}{8}=4+\frac{8}{8}=5$

Problem 2:

$2\frac{3}{10}$ (already simplified)

Problem 3:

$6\frac{1}{6}$ (already simplified)

Problem 4:

$2\frac{3}{10}$ (already simplified)

Note: The original first problem's handwritten work had an error in renaming; $6\frac{3}{8}$ renames to $5\frac{11}{8}$, not $5\frac{8}{8}$, leading to the correct answer of 5 instead of $4\frac{8}{8}$.

Answer:

1. $4\frac{7}{8}$
2. $2\frac{3}{10}$
3. $6\frac{1}{6}$
4. $2\frac{3}{10}$