Word Problem Involving Add or Subtract Fractions With Different Denominators

Jamie bought a box of fruit weighing 325$\frac{2}{5}$ kilograms. If she bought a second box that weighed 713$\frac{1}{3}$ kilograms, what is the combined weight of both boxes?

Solution

Step 1:

Weight of the first box of fruit = 325$\frac{2}{5}$ kilograms

Weight of the second box of fruit = 713$\frac{1}{3}$ kilograms

The combined of the two boxes of fruit = 325$\frac{2}{5}$ + 713$\frac{1}{3}$ = 175$\frac{17}{5}$ + 223$\frac{22}{3}$

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

17×35×3$\frac{17\times 3}{5\times 3}$ + 22×53×5$\frac{22\times 5}{3\times 5}$ = 5115$\frac{51}{15}$ + 11015$\frac{110}{15}$ = (51+110)15$\frac{(51+110)}{15}$ = 16115$\frac{161}{15}$ = 101115$\frac{11}{15}$

During the weekend, Nancy spent a total 513$\frac{1}{3}$ hours studying. If she spent 314$\frac{1}{4}$ hours studying on Saturday, how long did she study on Sunday?

Solution

Step 1:

Time spent studying on the weekend = 513$\frac{1}{3}$ hours

Time spent studying on Saturday = 314$\frac{1}{4}$ hours

Time spent studying on Sunday =

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

= 513$\frac{1}{3}$ − 314$\frac{1}{4}$ = 163$\frac{16}{3}$ − 134$\frac{13}{4}$

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

16×43×4$\frac{16\times 4}{3\times 4}$ − 13×34×3$\frac{13\times 3}{4\times 3}$ = 6412$\frac{64}{12}$ − 3912$\frac{39}{12}$ = 64−3912$\frac{64-39}{12}$ = 2512$\frac{25}{12}$ = 2112$\frac{1}{12}$ hours

So, the time spent studying on Sunday = 2112$\frac{1}{12}$ hours

Marcos bought apples that weighed 623$\frac{2}{3}$ kilograms. If he gave away 315$\frac{1}{5}$ kilograms of apples to his friends, how many kilograms of apples does he have left?

Solution

Step 1:

Weight of the apples bought = 623$\frac{2}{3}$ kilograms

Weight of the apples given to friends = 315$\frac{1}{5}$ kilograms

Weight of the apples left =

Weight of the apples bought − Weight of the apples given to friends

= 623$\frac{2}{3}$ − 315$\frac{1}{5}$ = 203$\frac{20}{3}$ − 165$\frac{16}{5}$

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

20×53×5$\frac{20\times 5}{3\times 5}$ − 16×35×3$\frac{16\times 3}{5\times 3}$ = 10015$\frac{100}{15}$ − 4815$\frac{48}{15}$ = 100−4815$\frac{100-48}{15}$ = 5215$\frac{52}{15}$ = 3715$\frac{7}{15}$ kilograms

So, the weight of the apples left = 3715$\frac{7}{15}$ kilograms