Let’s solve each of the 6 word problems step by step, showing all work and explaining the reasoning.
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Problem 1:
> Lucy is training for a long distance race. She runs ⁵⁄₇ of a kilometer every day during her first week of training. How many kilometers did she run during that first week?
✔ Key info:
- Runs ⁵⁄₇ km per day
- First week = 7 days
✔ Solution:
Multiply daily distance by number of days:
⁵⁄₇ × 7 = (5 × 7) / 7 = 35 / 7 =
5 kilometers
✔ Answer: 5 kilometers
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Problem 2:
> If it takes Micah 4 minutes to swim ¹⁄₁₀ of a kilometer, how long would it take him to swim 2 kilometers?
✔ Key info:
- Time for ¹⁄₁₀ km = 4 minutes
- Need time for 2 km
✔ Solution:
First, find how many ¹⁄₁₀ km segments are in 2 km:
2 ÷ ¹⁄₁₀ = 2 × 10 =
20 segments
Each segment takes 4 minutes → 20 × 4 =
80 minutes
✔ Answer: 80 minutes
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Problem 3:
> There are 27 players on the JV baseball team. Out of all of the players, ¹⁄₉ of them are left-handed. Of those left-handed players, ²⁄₃ of them are over 6 feet tall. How many players on the JV baseball team are left-handed and over 6 feet tall?
✔ Key info:
- Total players = 27
- Left-handed = ¹⁄₉ of 27
- Of those, ²⁄₃ are over 6 ft tall
✔ Solution:
Step 1: Find number of left-handed players:
¹⁄₉ × 27 = 27 ÷ 9 =
3 left-handed players
Step 2: Find how many of those are over 6 ft:
²⁄₃ × 3 = (2 × 3) / 3 = 6 / 3 =
2 players
✔ Answer: 2 players
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Problem 4:
> Danny ordered 16 pizzas for a party. ³⁄₄ of the pizzas have toppings and the rest are plain. Of the pizzas with toppings, ¹⁄₂ of them have olives and the rest have only mushrooms. How many pizzas have only mushrooms?
✔ Key info:
- Total pizzas = 16
- Topped pizzas = ³⁄₄ of 16
- Of topped pizzas, ¹⁄₂ have olives → so ¹⁄₂ have mushrooms
✔ Solution:
Step 1: Topped pizzas = ³⁄₄ × 16 = (3 × 16)/4 = 48/4 =
12 pizzas
Step 2: Pizzas with only mushrooms = ¹⁄₂ of 12 = 12 ÷ 2 =
6 pizzas
✔ Answer: 6 pizzas
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Problem 5:
> There is ⁵⁄₆ of a birthday cake left over from last night’s party. Mariah ate ¹⁄₅ of the leftover cake for breakfast this morning. How much of the cake did she eat?
✔ Key info:
- Leftover cake = ⁵⁄₆
- Mariah ate ¹⁄₅ of that leftover
✔ Solution:
Multiply the fraction of leftover cake by the fraction she ate:
¹⁄₅ × ⁵⁄₆ = (1 × 5) / (5 × 6) = 5 / 30 =
¹⁄₆
(Simplify: 5/30 = 1/6)
✔ Answer: ¹⁄₆ of the cake
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Problem 6:
> Tina is making bags of homemade cookies to share with her coworkers. She plans on making 36 cookies, where each cookie will weigh ²⁄₃ pounds. If she puts 4 cookies in each box, how much will each box weigh?
✔ Key info:
- Each cookie = ²⁄₃ lb
- Each box = 4 cookies
✔ Solution:
Multiply weight per cookie by number of cookies per box:
4 × ²⁄₃ = (4 × 2) / 3 = 8/3 =
2 ²⁄₃ pounds
✔ Answer: 2 ²⁄₃ pounds
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✔ Final Answers:
1.
5 kilometers
2.
80 minutes
3.
2 players
4.
6 pizzas
5.
¹⁄₆ of the cake
6.
2 ²⁄₃ pounds
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Parent Tip: Review the logic above to help your child master the concept of free fifth grade math word problems worksheet.
