Answered

Connect with a community of experts and enthusiasts on IDNLearn.com. Our Q&A platform is designed to provide quick and accurate answers to any questions you may have.

Here is the corrected and formatted version of the given mathematical expression:

[tex]\[
\begin{array}{l}
3 \cdot 3 \frac{1}{2} \times 3 \frac{2}{5} = \\
4 \frac{3}{5} + 5 \frac{3}{4} \\
\frac{4}{2} \times 3 \frac{4}{7}
\end{array}
\][/tex]

Sagot :

GinnyAnsweridn
Let's solve these expressions one by one.

### Expression 1: [tex]\( 3 \cdot 3 \frac{1}{2} \times 3 \frac{2}{5} \)[/tex]

1. Convert mixed numbers to improper fractions:
- [tex]\( 3 \frac{1}{2} = \frac{7}{2} \)[/tex]
- [tex]\( 3 \frac{2}{5} = \frac{17}{5} \)[/tex]

2. Substitute the improper fractions into the expression:
- [tex]\( 3 \cdot \frac{7}{2} \times \frac{17}{5} \)[/tex]

3. Simplify the expression:
- [tex]\( 3 \cdot \frac{7}{2} = \frac{21}{2} \)[/tex]
- Then multiply: [tex]\( \frac{21}{2} \times \frac{17}{5} = \frac{357}{10} = 35.7 \)[/tex]

So, the result of [tex]\( 3 \cdot 3 \frac{1}{2} \times 3 \frac{2}{5} \)[/tex] is [tex]\( 35.7 \)[/tex].

### Expression 2: [tex]\( 4 \frac{3}{5} + 5 \frac{3}{4} \)[/tex]

1. Convert mixed numbers to improper fractions:
- [tex]\( 4 \frac{3}{5} = \frac{23}{5} \)[/tex]
- [tex]\( 5 \frac{3}{4} = \frac{23}{4} \)[/tex]

2. To add these fractions, find a common denominator:
- The common denominator of 5 and 4 is 20.

3. Convert each fraction to have the common denominator:
- [tex]\( \frac{23}{5} = \frac{23 \times 4}{5 \times 4} = \frac{92}{20} \)[/tex]
- [tex]\( \frac{23}{4} = \frac{23 \times 5}{4 \times 5} = \frac{115}{20} \)[/tex]

4. Add the fractions:
- [tex]\( \frac{92}{20} + \frac{115}{20} = \frac{207}{20} = 10.35 \)[/tex]

So, the result of [tex]\( 4 \frac{3}{5} + 5 \frac{3}{4} \)[/tex] is [tex]\( 10.35 \)[/tex].

### Expression 3: [tex]\( \frac{4}{2} \times 3 \frac{4}{7} \)[/tex]

1. Convert the mixed number to an improper fraction:
- [tex]\( 3 \frac{4}{7} = \frac{25}{7} \)[/tex]

2. Substitute into the expression:
- [tex]\( \frac{4}{2} \times \frac{25}{7} \)[/tex]

3. Simplify the expression:
- [tex]\( \frac{4}{2} = 2 \)[/tex]
- Then multiply: [tex]\( 2 \times \frac{25}{7} = \frac{50}{7} = 7.142857142857143 \)[/tex]

So, the result of [tex]\( \frac{4}{2} \times 3 \frac{4}{7} \)[/tex] is [tex]\( 7.142857142857143 \)[/tex].

### Summary

- [tex]\( 3 \cdot 3 \frac{1}{2} \times 3 \frac{2}{5} = 35.7 \)[/tex]
- [tex]\( 4 \frac{3}{5} + 5 \frac{3}{4} = 10.35 \)[/tex]
- [tex]\( \frac{4}{2} \times 3 \frac{4}{7} = 7.142857142857143 \)[/tex]

These are the results for the given expressions.
We appreciate every question and answer you provide. Keep engaging and finding the best solutions. This community is the perfect place to learn and grow together. Your questions find answers at IDNLearn.com. Thanks for visiting, and come back for more accurate and reliable solutions.