IDNLearn.com is designed to help you find accurate answers with ease. Our platform offers reliable and comprehensive answers to help you make informed decisions quickly and easily.

Joanna bought the following amounts of fruit:

- [tex]\(1 \frac{1}{2}\)[/tex] pounds of apples
- [tex]\(\frac{3}{4}\)[/tex] of a pound of strawberries
- [tex]\(\frac{1}{2}\)[/tex] of a pound of grapes
- [tex]\(1 \frac{3}{4}\)[/tex] pounds of oranges
- [tex]\(1 \frac{1}{4}\)[/tex] pounds of pears

How many pounds of fruit did Joanna buy in all?

A. 5
B. [tex]\(5 \frac{3}{4}\)[/tex]
C. [tex]\(5 \frac{1}{2}\)[/tex]
D. [tex]\(5 \frac{1}{4}\)[/tex]


Sagot :

To determine the total pounds of fruit Joanna bought, we add up the individual pounds of each fruit.

1. Apples: [tex]\(1 \frac{1}{2}\)[/tex] pounds
- This can be converted into an improper fraction: [tex]\(1 \frac{1}{2} = \frac{3}{2}\)[/tex] pounds.
2. Strawberries: [tex]\(\frac{3}{4}\)[/tex] of a pound.
3. Grapes: [tex]\(\frac{1}{2}\)[/tex] of a pound.
- This can also be written as [tex]\(\frac{2}{4}\)[/tex] to facilitate addition.
4. Oranges: [tex]\(1 \frac{3}{4}\)[/tex] pounds.
- This converts to an improper fraction: [tex]\(1 \frac{3}{4} = \frac{7}{4}\)[/tex] pounds.
5. Pears: [tex]\(1 \frac{1}{4}\)[/tex] pounds.
- This converts to an improper fraction: [tex]\(1 \frac{1}{4} = \frac{5}{4}\)[/tex] pounds.

Next, convert all amounts to either mixed fractions or improper fractions as necessary and sum them up:

[tex]\[ \begin{align*} \text{Apples} &: \frac{3}{2} = \frac{6}{4} \\ \text{Strawberries} &: \frac{3}{4} \\ \text{Grapes} &: \frac{2}{4} \\ \text{Oranges} &: \frac{7}{4} \\ \text{Pears} &: \frac{5}{4} \end{align*} \][/tex]

Combine all fractions over the common denominator 4:

[tex]\[ \frac{6}{4} + \frac{3}{4} + \frac{2}{4} + \frac{7}{4} + \frac{5}{4} = \frac{23}{4} \][/tex]

Convert back to a mixed number:

[tex]\[ \frac{23}{4} = 5 \frac{3}{4} \][/tex]

Thus, the total pounds of fruit Joanna bought is [tex]\(5 \frac{3}{4}\)[/tex] pounds.

So, the correct answer is:
B. [tex]\(5 \frac{3}{4}\)[/tex]