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question 32
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solve the following \\(\frac{6}{8} \times \frac{4}{15} = \frac{x}{y}\\)
\\(x = \square\\)
\\(y = \square\\)
question 33
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solve the following \\(3 \frac{1}{4} \times \frac{12}{26} = a \frac{x}{y}\\)
\\(a = \square\\)
\\(x = \square\\)
\\(y = \square\\)
question 34
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solve the following \\(1 \frac{1}{2} \times 2 \frac{2}{3} = a\\)
\\(a = \square\\)

Explanation:

Question 32

Step1: Multiply numerators and denominators

To solve \(\frac{6}{8} \times \frac{4}{15}\), we multiply the numerators \(6\times4 = 24\) and the denominators \(8\times15=120\). So we have \(\frac{24}{120}\).

Step2: Simplify the fraction

Simplify \(\frac{24}{120}\) by dividing both numerator and denominator by their greatest common divisor, which is 24. \(\frac{24\div24}{120\div24}=\frac{1}{5}\).

Step1: Convert mixed number to improper fraction

First, convert \(3\frac{1}{4}\) to an improper fraction. \(3\frac{1}{4}=\frac{3\times4 + 1}{4}=\frac{13}{4}\).

Step2: Multiply the fractions

Now multiply \(\frac{13}{4}\times\frac{12}{26}\). Multiply numerators \(13\times12 = 156\) and denominators \(4\times26 = 104\). So we have \(\frac{156}{104}\).

Step3: Simplify the fraction

Simplify \(\frac{156}{104}\). The greatest common divisor of 156 and 104 is 52. Divide numerator and denominator by 52: \(\frac{156\div52}{104\div52}=\frac{3}{2}\). Here, \(A = 1\) (since \(\frac{3}{2}=1\frac{1}{2}\), but in the form \(A\frac{x}{y}\), \(A = 1\), \(x = 1\), \(y = 2\)).

Step1: Convert mixed numbers to improper fractions

Convert \(1\frac{1}{2}\) to \(\frac{3}{2}\) and \(2\frac{2}{3}\) to \(\frac{8}{3}\).

Step2: Multiply the fractions

Multiply \(\frac{3}{2}\times\frac{8}{3}\). The 3 in the numerator and denominator cancels out, and \(8\div2 = 4\). So \(\frac{3\times8}{2\times3}=\frac{24}{6}=4\).

Answer:

\(x = 1\)
\(y = 5\)

Question 33