Question

add the following fractions and reduce to lowest terms. (enter a reduced fraction.)\\(\frac{1}{4} + \frac{3}{8} + \frac{1}{16}\\)\

1. - / 3 points\

crate and barrel shipped three packages to new york weighing \\(45\frac{2}{5}\\), \\(126\frac{3}{4}\\), and \\(88\frac{5}{8}\\) pounds. what was the total weight (in lb) of the shipment? (enter your answer as a simplified mixed number.)

Explanation:

First Problem: Adding Fractions $\boldsymbol{\frac{1}{4} + \frac{3}{8} + \frac{1}{16}}$

Step1: Find a common denominator.

The denominators are 4, 8, and 16. The least common denominator (LCD) is 16.
Rewrite each fraction with the LCD:
$\frac{1}{4} = \frac{1\times4}{4\times4} = \frac{4}{16}$
$\frac{3}{8} = \frac{3\times2}{8\times2} = \frac{6}{16}$
$\frac{1}{16}$ remains as is.

Step2: Add the numerators.

Now add the fractions:
$\frac{4}{16} + \frac{6}{16} + \frac{1}{16} = \frac{4 + 6 + 1}{16} = \frac{11}{16}$

Step1: Separate whole numbers and fractions.

For $45\frac{2}{5}$, $126\frac{3}{4}$, and $88\frac{5}{8}$:
Whole numbers: $45 + 126 + 88$
Fractions: $\frac{2}{5} + \frac{3}{4} + \frac{5}{8}$

Step2: Add the whole numbers.

$45 + 126 + 88 = 259$

Step3: Find a common denominator for fractions.

Denominators: 5, 4, 8. LCD is 40.
Rewrite fractions:
$\frac{2}{5} = \frac{2\times8}{5\times8} = \frac{16}{40}$
$\frac{3}{4} = \frac{3\times10}{4\times10} = \frac{30}{40}$
$\frac{5}{8} = \frac{5\times5}{8\times5} = \frac{25}{40}$

Step4: Add the fractions.

$\frac{16}{40} + \frac{30}{40} + \frac{25}{40} = \frac{16 + 30 + 25}{40} = \frac{71}{40}$

Step5: Convert improper fraction to mixed number and add to whole numbers.

$\frac{71}{40} = 1\frac{31}{40}$
Total weight: $259 + 1\frac{31}{40} = 260\frac{31}{40}$

Answer:

$\frac{11}{16}$

Second Problem: Total Weight of Packages