Question

1. estimate the following quantities:

a. what is $\frac{1}{3}$ of 7?

b. what is $\frac{4}{5}$ of $9\frac{2}{3}$?

c. what is $2\frac{4}{7}$ of $10\frac{1}{9}$?

Explanation:

Part a:

Step1: Understand the operation

To find $\frac{1}{3}$ of 7, we use the multiplication operation: $\frac{1}{3} \times 7$.

Step2: Calculate the value

$\frac{1}{3} \times 7=\frac{7}{3}\approx2.33$ (or we can keep it as a fraction $\frac{7}{3}$)

Part b:

Step1: Convert the mixed number to improper fraction

First, convert $9\frac{2}{3}$ to an improper fraction. $9\frac{2}{3}=\frac{9\times3 + 2}{3}=\frac{29}{3}$

Step2: Multiply by the fraction

Now, find $\frac{4}{5}$ of $\frac{29}{3}$, which is $\frac{4}{5}\times\frac{29}{3}=\frac{116}{15}\approx7.73$ (or as a mixed number $7\frac{11}{15}$)

Part c:

Step1: Convert mixed numbers to improper fractions

Convert $2\frac{4}{7}$ to $\frac{2\times7 + 4}{7}=\frac{18}{7}$ and $10\frac{1}{9}$ to $\frac{10\times9+1}{9}=\frac{91}{9}$

Step2: Multiply the fractions

Now, multiply $\frac{18}{7}\times\frac{91}{9}$. Simplify first: $\frac{18}{9}=2$ and $\frac{91}{7} = 13$. Then $2\times13 = 26$

Answer:

a. $\frac{7}{3}$ (or approximately $2.33$)
b. $\frac{116}{15}$ (or approximately $7.73$ or $7\frac{11}{15}$)
c. $26$