Question

example 1 multiply fractions
find $\frac{5}{6} \times \frac{2}{3}$. write the product as a fraction in simplest form.
method 1 use a visual model
divide a rectangle into 3 rows to represent thirds and 6 columns to represent sixths.
shade a section that is $\frac{2}{3}$ unit wide by $\frac{5}{6}$ unit long.
the section that is shaded both blue and yellow represents the product. there are 18 total sections in the rectangle and ten are shaded twice. so, $\frac{5}{6} \times \frac{2}{3} = \frac{10}{18}$.
to write the product in simplest form, divide the numerator and denominator by their gcf, 2.
$\frac{10}{18} = \frac{10 \div 2}{18 \div 2}$ or $\frac{5}{9}$
method 2 use an equation.
$\frac{5}{6} \times \frac{2}{3} = \square$ write the equation.
$\frac{5}{6} \times \frac{2}{3} = \frac{5 \times 2}{6 \times 3}$ multiply the numerators and denominators.
$= \frac{10}{18}$ or $\frac{5}{9}$ divide by the gcf of the numerator and denominator, 2, to simplify.
so, $\frac{5}{6} \times \frac{2}{3}$ is ________.
check
find $\frac{3}{4} \times \frac{4}{9}$. write the product as a fraction in simplest form.

Explanation:

Step1: Multiply numerators and denominators

To multiply the fractions $\frac{3}{4}$ and $\frac{4}{9}$, we multiply the numerators together and the denominators together. So, we have $\frac{3\times4}{4\times9}$.

Step2: Simplify the fraction

First, calculate the numerator and denominator: $3\times4 = 12$ and $4\times9 = 36$. So the fraction is $\frac{12}{36}$. Now, we find the greatest common factor (GCF) of 12 and 36, which is 12. Divide both the numerator and the denominator by 12: $\frac{12\div12}{36\div12}=\frac{1}{3}$. We can also simplify before multiplying by canceling out the common factor of 4 in the numerator of the second fraction and the denominator of the first fraction: $\frac{3}{\cancel{4}}\times\frac{\cancel{4}}{9}=\frac{3}{9}$, and then simplify $\frac{3}{9}$ by dividing numerator and denominator by 3 to get $\frac{1}{3}$.

Answer:

$\frac{1}{3}$