Certainly! Let's address each part of the question step-by-step:
### Given:
- Potatoes: [tex]\(2 \frac{1}{2}\)[/tex] kg
- Tomatoes: [tex]\(2 \frac{1}{4}\)[/tex] kg
#### a) Find the total weight of vegetables bought by her.
First, we convert the mixed fractions into improper fractions:
- For potatoes:
[tex]\[
2 \frac{1}{2} = 2 + \frac{1}{2} = \frac{4}{2} + \frac{1}{2} = \frac{5}{2} \text{ kg}
\][/tex]
- For tomatoes:
[tex]\[
2 \frac{1}{4} = 2 + \frac{1}{4} = \frac{8}{4} + \frac{1}{4} = \frac{9}{4} \text{ kg}
\][/tex]
Now, add the weights of the potatoes and tomatoes:
[tex]\[
\frac{5}{2} + \frac{9}{4} = \frac{10}{4} + \frac{9}{4} = \frac{19}{4} \text{ kg}
\][/tex]
Converting the improper fraction back to a mixed number:
[tex]\[
\frac{19}{4} = 4 \frac{3}{4} \text{ kg} = 4.75 \text{ kg}
\][/tex]
So, the total weight of vegetables bought is [tex]\(4.75\)[/tex] kg.
#### b) Convert the fractions into the like fractions.
To combine fractions, we find a common denominator. Here, the denominators are 2 and 4, so the least common denominator is 4. We convert the fractions:
- Potatoes:
[tex]\[
\frac{5}{2} = \frac{5 \times 2}{2 \times 2} = \frac{10}{4}
\][/tex]
- Tomatoes:
[tex]\[
\frac{9}{4} \text{ (already has the denominator 4)}
\][/tex]
So, the converted like fractions are:
[tex]\[
\frac{10}{4} \text{ for potatoes and } \frac{9}{4} \text{ for tomatoes}
\][/tex]
#### c) Which vegetable did she buy more and by how much?
Comparing the improper fractions:
[tex]\[
\text{For potatoes: } \frac{10}{4} \text{ (2.5 kg)}
\][/tex]
[tex]\[
\text{For tomatoes: } \frac{9}{4} \text{ (2.25 kg)}
\][/tex]
Since [tex]\(\frac{10}{4}\)[/tex] is greater than [tex]\(\frac{9}{4}\)[/tex]:
Mrs. Mahato bought more potatoes.
To find out by how much more:
[tex]\[
\frac{10}{4} - \frac{9}{4} = \frac{1}{4} \text{ kg} = 0.25 \text{ kg}
\][/tex]
### Summary:
a) The total weight of vegetables bought by her is [tex]\(4.75\)[/tex] kg.
b) The like fractions are [tex]\(\frac{10}{4}\)[/tex] for potatoes and [tex]\(\frac{9}{4}\)[/tex] for tomatoes.
c) She bought more potatoes, specifically [tex]\(0.25\)[/tex] kg more.
