Question

1. convert to improper fraction: 2 1/5 =
2. multiply the improper fration:
3. simplify the fraction!!!

math nation - unit 2, lesson 7 - multiplying positive fractions - volume 1, page 80

Explanation:

Step1: Convert mixed - number to improper fraction

To convert $2\frac{1}{5}$ to an improper fraction, we use the formula $a\frac{b}{c}=\frac{a\times c + b}{c}$. Here, $a = 2$, $b = 1$, and $c = 5$. So $2\frac{1}{5}=\frac{2\times5 + 1}{5}=\frac{10 + 1}{5}=\frac{11}{5}$.

Step2: Multiply the improper fraction

Let's assume we are multiplying $\frac{11}{5}$ by $\frac{3}{21}$ (from the partially visible text). The rule for multiplying fractions is $\frac{a}{b}\times\frac{c}{d}=\frac{a\times c}{b\times d}$. So $\frac{11}{5}\times\frac{3}{21}=\frac{11\times3}{5\times21}=\frac{33}{105}$.

Step3: Simplify the fraction

Find the greatest common divisor (GCD) of 33 and 105. The factors of 33 are 1, 3, 11, 33 and the factors of 105 are 1, 3, 5, 7, 15, 21, 35, 105. The GCD of 33 and 105 is 3. Divide both the numerator and denominator by 3: $\frac{33\div3}{105\div3}=\frac{11}{35}$.

Answer:

$\frac{11}{35}$