vestirme4

2021-11-07

Julia bought $5\frac{3}{4}$ pounds of potatoes at the farmers market. Leeyana bought $\frac{1}{5}$ pounds of potatoes. Gabriela bought $1\frac{1}{2}$ pounds of potatoes. How many pounds of potatoes did they buy in all?

rogreenhoxa8

Step 1
The addition(subtraction) between two like fractions can be done by adding(subtracting) the numerators of both fractions by fixing same denominator to the result. Like fractions are the fraction with the same denominator.
For the addition (subtraction) between two unlike fractions, first we have to convert both denominators of the fractions to the same value. This can be done by finding the LCM(Least Common multiple) of the denominators of the fractions. We can multiply and divide both the fractions by suitable constant to produce the same value in both denominators.
The mixed fraction can be converted to an improper fraction as,
$\text{whole}\frac{\nu mera\to r}{denomina\to r}=\frac{\left(\text{whole}×\text{denominator}\right)+\text{numerator}}{\text{denominator}}$
Step 2
The number of pounds of potatoes bought by Julia is $5\frac{3}{4}$
The number of pounds of potatoes bought by Leeyana is $\frac{1}{5}$
The number of pounds of potatoes bought by Gabriela is $1\frac{1}{2}$
The total number of pounds of potatoes bought by Julia, Leeyana, and Gabriela is (1) $5\frac{3}{4}+\frac{1}{5}+1\frac{1}{2}$
Now convert the mixed fractions to an improper fractions,
$5\frac{3}{4}=\frac{\left(5×4\right)+3}{4}$
$=\frac{20+3}{4}$
$=\frac{23}{4}$
$1\frac{1}{2}=\frac{\left(1×2\right)+1}{2}$
$=\frac{2+1}{2}$
$=\frac{3}{2}$
Now we can simplify the addition expression (1),
$5\frac{3}{4}+\frac{1}{5}+1\frac{1}{2}=\frac{23}{4}+\frac{1}{5}+\frac{3}{2}$
$=\left(\frac{23}{4}+\frac{3}{2}\right)+\frac{1}{5}$
$=\left(\frac{23}{4}+\frac{3}{2}×\frac{2}{2}\right)+\frac{1}{5}$
$=\frac{23}{4}+\frac{6}{4}+\frac{1}{5}$
$=\frac{29}{4}+\frac{1}{5}$
$=\frac{29}{4}×\frac{5}{5}+\frac{1}{5}×\frac{4}{4}$

$=\frac{149}{20}$
$=7\frac{9}{20}$
Hence the total number of pounds of potatoes bought by Julie, Leeyana, and Gabriela is $7\frac{9}{20}$ pounds.

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