Question

fractions - add, subtract, multiply, and divide
1 $\frac{17}{3} + \frac{3}{17} =$
2 $\frac{7}{2} + \frac{11}{13} =$
3 $\frac{3}{2} + \frac{20}{3} =$
4 $\frac{13}{14} - \frac{12}{22} =$
5 $\frac{9}{10} - \frac{3}{15} =$
6 $\frac{18}{19} - \frac{5}{6} =$
7 $\frac{12}{15} \times \frac{6}{20} =$
8 $\frac{23}{18} \times \frac{16}{21} =$
9 $\frac{9}{14} \times \frac{22}{24} =$
10 $\frac{26}{52} div \frac{12}{13} =$
11 $\frac{5}{96} div \frac{3}{64} =$
12 $\frac{27}{21} div \frac{44}{14} =$

Explanation:

Problem 1: $\boldsymbol{\frac{17}{3} + \frac{3}{17}}$

Step1: Find a common denominator (3×17 = 51)

$\frac{17}{3} = \frac{17×17}{3×17} = \frac{289}{51}$, $\frac{3}{17} = \frac{3×3}{17×3} = \frac{9}{51}$

Step2: Add the fractions

$\frac{289}{51} + \frac{9}{51} = \frac{289 + 9}{51} = \frac{298}{51}$

Step1: Common denominator (2×13 = 26)

$\frac{7}{2} = \frac{7×13}{2×13} = \frac{91}{26}$, $\frac{11}{13} = \frac{11×2}{13×2} = \frac{22}{26}$

Step2: Add the fractions

$\frac{91}{26} + \frac{22}{26} = \frac{91 + 22}{26} = \frac{113}{26}$

Step1: Common denominator (2×3 = 6)

$\frac{3}{2} = \frac{3×3}{2×3} = \frac{9}{6}$, $\frac{20}{3} = \frac{20×2}{3×2} = \frac{40}{6}$

Step2: Add the fractions

$\frac{9}{6} + \frac{40}{6} = \frac{9 + 40}{6} = \frac{49}{6}$

Answer:

$\frac{298}{51}$ (or $5\frac{43}{51}$)

Problem 2: $\boldsymbol{\frac{7}{2} + \frac{11}{13}}$