Question

regroup and subtract. simplify if possible.

1. $7\frac{3}{10} - 4\frac{2}{5}$
2. $3\frac{1}{8} - 2\frac{1}{3}$
3. $4\frac{3}{4} - 1\frac{5}{6}$

Explanation:

Step1: Find common denominator (Q12)

The denominator of $\frac{2}{5}$ can be converted to 10: $4\frac{2}{5}=4\frac{4}{10}$

Step2: Subtract mixed numbers (Q12)

$7\frac{3}{10}-4\frac{4}{10}$; regroup $7\frac{3}{10}$ to $6\frac{13}{10}$, then subtract:
$6\frac{13}{10}-4\frac{4}{10}=2\frac{9}{10}$

Step3: Find common denominator (Q13)

Common denominator of 8 and 3 is 24: $3\frac{1}{8}=3\frac{3}{24}$, $2\frac{1}{3}=2\frac{8}{24}$

Step4: Subtract mixed numbers (Q13)

Regroup $3\frac{3}{24}$ to $2\frac{27}{24}$, then subtract:
$2\frac{27}{24}-2\frac{8}{24}=\frac{19}{24}$

Step5: Find common denominator (Q14)

Common denominator of 4 and 6 is 12: $4\frac{3}{4}=4\frac{9}{12}$, $1\frac{5}{6}=1\frac{10}{12}$

Step6: Subtract mixed numbers (Q14)

Regroup $4\frac{9}{12}$ to $3\frac{21}{12}$, then subtract:
$3\frac{21}{12}-1\frac{10}{12}=2\frac{11}{12}$

Answer:

1. $2\frac{9}{10}$
2. $\frac{19}{24}$
3. $2\frac{11}{12}$