50+ Mixed Operation Word Problems worksheets for 7th Grade on ... - Free Printable

Let's solve each of these multi-step word problems involving rational numbers step by step.

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1. Sophie went to the lake with her family. First, they spent 1 1/4 hours fishing. Then, they spent twice as much time swimming. How much time did they spend fishing and swimming in all?

Step 1: Convert mixed number to improper fraction
$ 1 \frac{1}{4} = \frac{5}{4} $ hours (fishing)

Step 2: Swimming time is twice the fishing time
$ 2 \times \frac{5}{4} = \frac{10}{4} = \frac{5}{2} $ hours

Step 3: Add fishing and swimming times
$ \frac{5}{4} + \frac{5}{2} = \frac{5}{4} + \frac{10}{4} = \frac{15}{4} $

Convert to mixed number:
$ \frac{15}{4} = 3 \frac{3}{4} $

✔ Answer: $ \boxed{3 \frac{3}{4}} $ hours

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2. Kelly made fruit punch to serve at a party for her chess team. She mixed 1 2/5 liters of cranberry juice and 1 3/5 liters of pineapple juice together. Then, she split the fruit punch evenly among 9 glasses. How much fruit punch did Kelly pour into each glass?

Step 1: Convert mixed numbers to improper fractions
- $ 1 \frac{2}{5} = \frac{7}{5} $
- $ 1 \frac{3}{5} = \frac{8}{5} $

Step 2: Add the juices
$ \frac{7}{5} + \frac{8}{5} = \frac{15}{5} = 3 $ liters total

Step 3: Divide by 9 glasses
$ 3 \div 9 = \frac{3}{9} = \frac{1}{3} $

✔ Answer: $ \boxed{\frac{1}{3}} $ liter per glass

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3. Paul runs a small farm. After the last harvest, he weighed the amount of squash he collected. He had 42.2 total pounds of green and yellow squash. If yellow squash made up 1/5 of the harvest by weight, how many pounds of green squash did he have?

Step 1: Yellow squash = $ \frac{1}{5} $ of total
$ \frac{1}{5} \times 42.2 = \frac{42.2}{5} = 8.44 $ pounds

Step 2: Green squash = total – yellow
$ 42.2 - 8.44 = 33.76 $ pounds

✔ Answer: $ \boxed{33.76} $ pounds

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4. David has 3 1/2 cups of blueberries. He uses 1/4 of a cup of blueberries to make a breakfast smoothie. He uses 1/2 of the remaining blueberries to make blueberry pancakes. How many cups of blueberries does he use for the pancakes?

Step 1: Convert mixed number to improper fraction
$ 3 \frac{1}{2} = \frac{7}{2} $ cups

Step 2: Subtract smoothie portion
$ \frac{7}{2} - \frac{1}{4} = \frac{14}{4} - \frac{1}{4} = \frac{13}{4} $ cups remaining

Step 3: Use half of remaining for pancakes
$ \frac{1}{2} \times \frac{13}{4} = \frac{13}{8} $

Convert to mixed number:
$ \frac{13}{8} = 1 \frac{5}{8} $

✔ Answer: $ \boxed{1 \frac{5}{8}} $ cups

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5. Luther owns a farm where he grows red and green tomatoes. He sells both types of tomatoes for $1.70 per pound. One customer bought 10.6 pounds of red tomatoes and 8.3 pounds of green tomatoes. How much money did Luther earn in all from that sale?

Step 1: Total weight sold
$ 10.6 + 8.3 = 18.9 $ pounds

Step 2: Multiply by price per pound
$ 18.9 \times 1.70 $

Break it down:
- $ 18.9 \times 1.7 = (18 + 0.9) \times 1.7 $
- $ 18 \times 1.7 = 30.6 $
- $ 0.9 \times 1.7 = 1.53 $
- Total = $ 30.6 + 1.53 = 32.13 $

✔ Answer: $ \boxed{32.13} $ dollars

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6. Jasmine is having friends over to watch a football game. She has 2 1/2 hours until her guests arrive. She spends 2/5 of that time cleaning and the rest of the time preparing snacks. How much time does Jasmine spend preparing snacks?

Step 1: Convert $ 2 \frac{1}{2} $ to improper fraction
$ 2 \frac{1}{2} = \frac{5}{2} $ hours

Step 2: Time spent cleaning = $ \frac{2}{5} \times \frac{5}{2} = \frac{10}{10} = 1 $ hour

Step 3: Time left for snacks = total – cleaning
$ \frac{5}{2} - 1 = \frac{5}{2} - \frac{2}{2} = \frac{3}{2} = 1 \frac{1}{2} $

✔ Answer: $ \boxed{1 \frac{1}{2}} $ hours

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✔ Final Answers:

1. $ \boxed{3 \frac{3}{4}} $ hours
2. $ \boxed{\frac{1}{3}} $ liter
3. $ \boxed{33.76} $ pounds
4. $ \boxed{1 \frac{5}{8}} $ cups
5. $ \boxed{32.13} $ dollars
6. $ \boxed{1 \frac{1}{2}} $ hours

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