Combining fractions

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At a coffee shop, Kinfe makes a drink by combining $\frac {2}{5}$ of a cup of coffee with $\frac {3}{4}$ of a cup of milk. How many cups of coffee and milk are in this drink all together?

(a): Is this an addition problem for $\frac {2}{5} + \frac {3}{4}$ ? Explain how you know. If this is not a story problem for $\frac {2}{5} + \frac {3}{4}$ , explain how you would adjust the existing story problem so that it is a problem for $\frac {2}{5} + \frac {3}{4}$ .
(b): Solve the problem for $\frac {2}{5} + \frac {3}{4}$ using a picture. Be sure to explain why your solution makes sense using the meaning of addition and the meaning of fractions.

At a smoothie shop, Ileana makes a drink by combining $\frac {3}{5}$ of a cup of strawberries with $\frac {4}{7}$ of an ounce of bananas. How many cups of strawberries and bananas are in this drink all together?

(a): Is this an addition problem for $\frac {3}{5} + \frac {4}{7}$ ? Explain how you know. If this is not a story problem for $\frac {3}{5} + \frac {4}{7}$ , explain how you would adjust the existing story problem so that it is a problem for $\frac {3}{5} + \frac {4}{7}$ .
(b): Solve the problem for $\frac {3}{5} + \frac {4}{7}$ using a picture. Be sure to explain why your solution makes sense using the meaning of addition and the meaning of fractions.

At a tea shop, Joey must remove $\frac {1}{4}$ of the liquid from a bowl that contains $\frac {5}{8}$ of a gallon of water. How much liquid will Joey remove from the bowl?

(a): Is this a subtraction problem for $\frac {5}{8} - \frac {1}{4}$ ? Explain how you know. If this is not a story problem for $\frac {5}{8} - \frac {1}{4}$ , explain how you would adjust the existing story problem so that it is a problem for $\frac {5}{8} - \frac {1}{4}$ .
(b): Solve the problem for $\frac {5}{8} - \frac {1}{4}$ using a picture. Be sure to explain why your solution makes sense using the meaning of subtraction and the meaning of fractions.

At a milkshake shop, Lara has two gallons of ice cream in front of her. She has sold $\frac {5}{7}$ of the first gallon and $\frac {2}{9}$ of the second gallon. How much of the total two gallons of ice cream has Lara sold?

(a): Is this a subtraction problem for $\frac {5}{7} - \frac {2}{9}$ ? Explain how you know. If this is not a story problem for $\frac {5}{7} - \frac {2}{9}$ , explain how you would adjust the existing story problem so that it is a problem for $\frac {5}{7} - \frac {2}{9}$ .
(b): Solve the problem for $\frac {5}{7} - \frac {2}{9}$ using a picture. Be sure to explain why your solution makes sense using the meaning of subtraction and the meaning of fractions.

Based on our work in this activity, why does it make sense to make common denominators when adding or subtracting fractions?

2025-09-21 04:39:04