# Word Problem Involving Add or Subtract Fractions With Different Denominators Online Quiz

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Q 1 - A bulldozer weighed 3$\frac{2}{5}$ tons. If it scooped up 5$\frac{5}{8}$ tons of sand, what would be the combined weight of the bulldozer and the sand?

### Explanation

Step 1:

Weight of bulldozer = 3$\frac{2}{5}$ tons

Weight of sand = 5$\frac{5}{8}$ tons

Step 2:

Combined weight of bulldozer and sand

= 3$\frac{2}{5}$ tons + 5$\frac{5}{8}$ tons = $\frac{17}{5}$ + $\frac{45}{8}$

= $\frac{136}{40}$ + $\frac{225}{40}$ = $\frac{361}{40}$ = 9$\frac{1}{40}$ tons

Q 2 - A regular size chocolate bar was 7$\frac{3}{8}$ inches long. If the king size bar was 5$\frac{3}{7}$ inches longer, what is the length of the king size bar?

### Explanation

Step 1:

Size of regular bar = 7$\frac{3}{8}$ inches

king size bar longer by 5$\frac{3}{7}$ inches

Step 2:

Length of king size bar = 7$\frac{3}{8}$ inches + 5$\frac{3}{7}$ inches

= $\frac{59}{8}$ + $\frac{38}{7}$ = $\frac{413}{56}$ + $\frac{304}{56}$

= $\frac{717}{56}$ = 12$\frac{45}{56}$

Q 3 - Sarah's recycled 9$\frac{2}{3}$ boxes of paper in a month. If she recycled another 6$\frac{4}{9}$ boxes the next month, what was the total amount she recycled?

### Explanation

Step 1:

Boxes recycled in one month = 9$\frac{2}{3}$

Boxes recycled in second month = 6$\frac{4}{9}$

Step 2:

Total boxes recycled = 9$\frac{2}{3}$ + 6$\frac{4}{9}$

= $\frac{29}{3}$ + $\frac{58}{9}$ = $\frac{87}{9}$ + $\frac{58}{9}$

=$\frac{145}{9}$ = 16$\frac{1}{9}$

Q 4 - In November, it snowed 10$\frac{5}{8}$ inches. In December it snowed 5$\frac{6}{7}$ inches. What is the total amount of snow for November and December?

### Explanation

Step 1:

Snowfall in November = 10$\frac{5}{8}$ inches

Snowfall in December = 5$\frac{6}{7}$ inches

Step 2:

Total snowfall in two months = 10$\frac{5}{8}$ + 5$\frac{6}{7}$

= $\frac{85}{8}$ + $\frac{41}{7}$ = $\frac{595}{56}$ + $\frac{328}{56}$

= $\frac{923}{56}$ = 16$\frac{27}{56}$ inches

Q 5 - An engineer built a road 6$\frac{2}{3}$ miles long. The second road he built was 5$\frac{2}{5}$ miles long. What is the total length of the two roads he built?

### Explanation

Step 1:

Length of first road = 6$\frac{2}{3}$ miles

Length of second road = 5$\frac{2}{5}$ miles

Step 2:

Total length roads = 6$\frac{2}{3}$ + 5$\frac{2}{5}$

= $\frac{20}{3}$ + $\frac{27}{5}$ = $\frac{100}{15}$ + $\frac{81}{15}$

= $\frac{181}{15}$ = 12$\frac{1}{15}$ miles

Q 6 - Katy jogged 5$\frac{2}{3}$ kilometers on Tuesday and 4$\frac{2}{9}$ kilometers on Wednesday. What is the difference between these distances?

### Explanation

Step 1:

Distance jogged on Tuesday = 5$\frac{2}{3}$ km

Distance jogged on Wednesday = 4$\frac{2}{9}$ km

Step 2:

Total distance jogged = 5$\frac{2}{3}$ + 4$\frac{2}{9}$

= $\frac{17}{3}$ + $\frac{38}{9}$ = $\frac{51}{9}$ + $\frac{38}{9}$

= $\frac{89}{9}$ = 9$\frac{8}{9}$ km

Q 7 - During the weekend Nora spent a total 5$\frac{3}{5}$ hours studying. If she spent 2$\frac{2}{3}$ hours studying on Saturday, how long did she study on Sunday?

### Explanation

Step 1:

Total time spent in studying = 5$\frac{3}{5}$ hours

Time spent on Saturday studying = 2$\frac{2}{3}$ hours

Step 2:

Time spent on Sunday studying = 5$\frac{3}{5}$ - 2$\frac{2}{3}$

= $\frac{28}{5}$ - $\frac{8}{3}$ = $\frac{84}{15}$ - $\frac{40}{15}$

= $\frac{44}{15}$ = 2$\frac{14}{15}$ hours

Q 8 - A person bought 4$\frac{3}{7}$ pounds of potatoes. If he later bought another 7$\frac{2}{5}$ pounds of potatoes, what is the total weight of potatoes he bought?

### Explanation

Step 1:

Weight of potatoes first bought = 4$\frac{3}{7}$ pounds

Weight of potatoes bought later = 7$\frac{2}{5}$ pounds

Step 2:

Total boxes recycled = 4$\frac{3}{7}$ + 7$\frac{2}{5}$

= $\frac{31}{7}$ + $\frac{37}{5}$ = $\frac{155}{35}$ + $\frac{259}{35}$

=$\frac{414}{35}$ = 11$\frac{29}{35}$

Q 9 - At the beach, Mike built a sand castle that was 4$\frac{2}{3}$ feet high. If he added a flag that was 2$\frac{1}{6}$ feet high, what is the total height of his castle?

### Explanation

Step 1:

Height of sand castle = 4$\frac{2}{3}$ feet

Height of flag = 2$\frac{1}{6}$ feet

Step 2:

Total height = 4$\frac{2}{3}$ + 2$\frac{1}{6}$

= $\frac{14}{3}$ + $\frac{13}{6}$ = $\frac{28}{6}$ + $\frac{13}{6}$

= $\frac{41}{6}$ = 6$\frac{5}{6}$ feet

Q 10 - Melanie planned to walk 4$\frac{4}{7}$ miles on Tuesday. If she walked 2$\frac{2}{5}$ miles in the morning, how far would she need to walk in the afternoon?

### Explanation

Step 1:

Total distance walked = 4$\frac{4}{7}$ miles

Distance walked in the morning = 2$\frac{2}{5}$

Step 2:

Distance walked in the afternoon = 4$\frac{4}{7}$ - 2$\frac{2}{5}$

= $\frac{32}{7}$ - $\frac{12}{5}$ = $\frac{160}{35}$ - $\frac{84}{35}$

= $\frac{76}{35}$ = 2$\frac{6}{35}$ miles