Word Problem Involving Add or Subtract Fractions With Different Denominators

Jamie bought a box of fruit weighing 3$\frac{2}{5}$ kilograms. If she bought a second box that weighed 7$\frac{1}{3}$ kilograms, what is the combined weight of both boxes?

Solution

Step 1:

Weight of the first box of fruit = 3$\frac{2}{5}$ kilograms

Weight of the second box of fruit = 7$\frac{1}{3}$ kilograms

The combined of the two boxes of fruit = 3$\frac{2}{5}$ + 7$\frac{1}{3}$ = $\frac{17}{5}$ + $\frac{22}{3}$

Step 2:

The denominators are different. So the LCD of the fractions or LCM of denominators 3 and 5 is 15.

Rewriting to get equivalent fractions with LCD as denominator

$\frac{17×3}{5×3}$ + $\frac{22×5}{3×5}$ = $\frac{51}{15}$ + $\frac{110}{15}$ = $\frac{(51+110)}{15}$ = $\frac{161}{15}$ = 10$\frac{11}{15}$

During the weekend, Nancy spent a total 5$\frac{1}{3}$ hours studying. If she spent 3$\frac{1}{4}$ hours studying on Saturday, how long did she study on Sunday?

Solution

Step 1:

Time spent studying on the weekend = 5$\frac{1}{3}$ hours

Time spent studying on Saturday = 3$\frac{1}{4}$ hours

Time spent studying on Sunday =

Time spent studying on the weekend − Time spent studying on Saturday

= 5$\frac{1}{3}$ − 3$\frac{1}{4}$ = $\frac{16}{3}$$\frac{13}{4} Step 2: LCD of the fractions or the LCM of the denominators 3 and 4 is 12 Rewriting to get equivalent fractions with LCD as denominator \frac{16×4}{3×4}$$\frac{13×3}{4×3}$ = $\frac{64}{12}$$\frac{39}{12} = \frac{64−39}{12} = \frac{25}{12} = 2\frac{1}{12} hours So, the time spent studying on Sunday = 2\frac{1}{12} hours Marcos bought apples that weighed 6\frac{2}{3} kilograms. If he gave away 3\frac{1}{5} kilograms of apples to his friends, how many kilograms of apples does he have left? Solution Step 1: Weight of the apples bought = 6\frac{2}{3} kilograms Weight of the apples given to friends = 3\frac{1}{5} kilograms Weight of the apples left = Weight of the apples bought − Weight of the apples given to friends = 6\frac{2}{3} − 3\frac{1}{5} = \frac{20}{3}$$\frac{16}{5}$

Step 2:

LCD of the fractions or LCM of the denominators 3 and 5 is 15

Rewriting to get equivalent fractions with LCD as denominator

$\frac{20×5}{3×5}$$\frac{16×3}{5×3} = \frac{100}{15}$$\frac{48}{15}$ = $\frac{100−48}{15}$ = $\frac{52}{15}$ = 3$\frac{7}{15}$ kilograms

So, the weight of the apples left = 3$\frac{7}{15}$ kilograms

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