Question

1. jackie brought \\(\frac{3}{4}\\) of a gallon of iced tea to the party. bill brought \\(\frac{7}{8}\\) of a gallon of iced tea to the same party. how much iced tea did jackie and bill bring to the party?

1. madame curie made some radium in her lab. she used \\(\frac{2}{5}\\) kg of the radium in an experiment and had \\(1\frac{1}{4}\\) kg left. how much radium did she have at first? (extension: if she performed the experiment twice, how much radium would she have left?)

Explanation:

Problem 3

Step1: Find common denominator

Convert $\frac{3}{4}$ to eighth: $\frac{3}{4} = \frac{3\times2}{4\times2} = \frac{6}{8}$

Step2: Add the two fractions

Sum the amounts: $\frac{6}{8} + \frac{7}{8} = \frac{13}{8}$

Step3: Simplify to mixed number

Rewrite improper fraction: $\frac{13}{8} = 1\frac{5}{8}$

Step1: Convert mixed number to fraction

$1\frac{1}{4} = \frac{4\times1 + 1}{4} = \frac{5}{4}$

Step2: Find common denominator

Convert $\frac{5}{4}$ to twentieths: $\frac{5}{4} = \frac{5\times5}{4\times5} = \frac{25}{20}$; Convert $\frac{2}{5}$ to twentieths: $\frac{2}{5} = \frac{2\times4}{5\times4} = \frac{8}{20}$

Step3: Add the two fractions

Total initial amount: $\frac{25}{20} + \frac{8}{20} = \frac{33}{20}$

Step4: Simplify to mixed number

Rewrite improper fraction: $\frac{33}{20} = 1\frac{13}{20}$

Step1: Calculate total used radium

Two uses: $2\times\frac{2}{5} = \frac{4}{5}$

Step2: Convert to common denominator

Convert $\frac{33}{20}$ and $\frac{4}{5}$: $\frac{4}{5} = \frac{16}{20}$

Step3: Subtract used from initial

Remaining radium: $\frac{33}{20} - \frac{16}{20} = \frac{17}{20}$

Answer:

$1\frac{5}{8}$ gallons

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Problem 4 (Main Question)