Question

$\frac{9}{8}×\frac{4}{5}=$ (d) $\frac{4}{9}×\frac{3}{4}=$

Explanation:

First Problem: $\boldsymbol{\frac{9}{8} \times \frac{4}{5}}$

Step1: Multiply numerators and denominators

To multiply fractions, we multiply the numerators together and the denominators together. So, $\frac{9}{8} \times \frac{4}{5} = \frac{9 \times 4}{8 \times 5}$.

Step2: Simplify the fraction

First, calculate the numerator: $9 \times 4 = 36$. Then the denominator: $8 \times 5 = 40$. Now we have $\frac{36}{40}$. We can simplify this fraction by dividing both the numerator and the denominator by their greatest common divisor, which is 4. So, $\frac{36 \div 4}{40 \div 4} = \frac{9}{10}$.

Step1: Multiply numerators and denominators (or simplify first)

We can either multiply first: $\frac{4}{9} \times \frac{3}{4} = \frac{4 \times 3}{9 \times 4}$, or we can simplify before multiplying. Let's simplify first. The 4 in the numerator of the first fraction and the 4 in the denominator of the second fraction can cancel out. Also, the 3 in the numerator of the second fraction and the 9 in the denominator of the first fraction have a common factor of 3. So, $\frac{4}{9} \times \frac{3}{4} = \frac{\cancel{4}^1}{9} \times \frac{3}{\cancel{4}^1} = \frac{1 \times 3}{9 \times 1}$ (after canceling 4s), and then $\frac{1 \times 3}{9 \times 1} = \frac{3}{9}$, which simplifies to $\frac{1}{3}$ (dividing numerator and denominator by 3).
Alternatively, multiplying first: $4 \times 3 = 12$ and $9 \times 4 = 36$, so $\frac{12}{36}$, which simplifies to $\frac{1}{3}$ (dividing numerator and denominator by 12).

Answer:

$\frac{9}{10}$

Second Problem: $\boldsymbol{\frac{4}{9} \times \frac{3}{4}}$