https://r2.erweima.ai/mathbot/image/17269251426947y64yb1r.jpg

https://r2.erweima.ai/mathbot/image/17269251426955w437dyt.jpg

Let's start by addressing the first image with multiple fraction multiplications:

### First Image: Fraction Operations
I'll break down the operations row by row:

#### First Row:
1. \(\frac{1}{4} \times \frac{1}{2} = \frac{1 \times 1}{4 \times 2} = \frac{1}{8}\)
2. \(\frac{1}{4} \times \frac{3}{2} = \frac{1 \times 3}{4 \times 2} = \frac{3}{8}\)
3. \(\frac{1}{4} \times \frac{4}{5} = \frac{1 \times 4}{4 \times 5} = \frac{4}{20} = \frac{1}{5}\)

#### Second Row:
1. \(\frac{1}{6} \times \frac{1}{3} = \frac{1 \times 1}{6 \times 3} = \frac{1}{18}\)
2. \(\frac{2}{3} \times \frac{5}{7} = \frac{2 \times 5}{3 \times 7} = \frac{10}{21}\)
3. \(\frac{3}{4} \times \frac{1}{2} = \frac{3 \times 1}{4 \times 2} = \frac{3}{8}\)

#### Third Row:
1. \(\frac{2}{3} \times \frac{5}{4} = \frac{2 \times 5}{3 \times 4} = \frac{10}{12} = \frac{5}{6}\)
2. \(5 \cdot \frac{3}{4} = \frac{5 \times 3}{4} = \frac{15}{4}\)
3. \(-20 \cdot \frac{1}{2} = -\frac{20 \times 1}{2} = -10\)

#### Fourth Row:
1. \(\frac{12}{4} \times \frac{27}{3} = 3 \times 9 = 27\)
2. \(\frac{42}{81} \times \frac{9}{12} = \frac{42 \times 9}{81 \times 12} = \frac{378}{972} = \frac{7}{18}\)
3. \(\frac{12}{8} \times \frac{64}{48} = \frac{3}{2} \times \frac{4}{3} = 2\)

#### Fifth Row:
1. \(1 \cdot \frac{2}{9} \cdot \frac{5}{4} = \frac{2 \times 5}{9 \times 4} = \frac{10}{36} = \frac{5}{18}\)
2. \(\frac{4}{5} \cdot 2 \cdot \frac{10}{7} = \frac{4 \times 10}{5 \times 7} = \frac{40}{35} = \frac{8}{7}\)
3. \(\frac{7}{9} \cdot 12 \cdot \frac{6}{3} = \frac{7 \times 12 \times 2}{9} = \frac{168}{9} = 18 \frac{6}{9}\)

#### Sixth Row:
1. \(\frac{52}{60} \cdot \frac{3}{2} \cdot \frac{4}{5} = \frac{13}{15} \cdot \frac{3}{2} \cdot \frac{4}{5} = \frac{156}{150} = 1 \frac{3}{25}\)
2. \(\frac{22}{2} \cdot \frac{39}{2} \cdot \frac{2}{2} = \frac{11 \times 39 \times 1}{2} = 214.5\)
3. \(7^{\frac{21}{12}} \cdot 3^{\frac{1}{2}} \cdot 9^{10/5} = (solve exponents separately)\)

### Now, for the Second Image:

#### Problema 2:
You are asked to find "half of a third quarter" of a total.
1. The fraction representing the third quarter of a total is \(\frac{3}{4}\).
2. To find half of this, multiply \(\frac{3}{4}\) by \(\frac{1}{2}\):
   \[
   \frac{3}{4} \times \frac{1}{2} = \frac{3}{8}
   \]
Thus, half of a third quarter is \(\frac{3}{8}\) of the total.

#### Problema 3:
You are asked to calculate how much "two-thirds of three-fifths" is.
1. The expression for this is \(\frac{2}{3} \times \frac{3}{5}\):
   \[
   \frac{2 \times 3}{3 \times 5} = \frac{6}{15} = \frac{2}{5}
   \]
So, two-thirds of three-fifths is \(\frac{2}{5}\).

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Would you like more details on any specific operations? Here are five related questions for further understanding:

1. How do you simplify a product of fractions?
2. How do negative numbers affect multiplication of fractions?
3. What happens when you multiply a whole number by a fraction?
4. How do you handle fraction multiplication with larger denominators?
5. How does multiplying by a unit fraction (like \(\frac{1}{2}\)) affect a number?

**Tip:** When multiplying fractions, always simplify the numerators and denominators before performing the multiplication to avoid large numbers.

¿Qué fracción del total es la mitad de una tercera cuarta parte? y Calcular cuánto son dos tercios de tres quintas partes.

Learn how to multiply fractions and simplify results through a step-by-step guide. Explore examples such as calculating two-thirds of three-fifths and finding half of a third quarter. This resource is perfect for students in Grades 5-7.

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