excellence #1: dividing fractions/ mixed numbers
show all work & circle your final answer.
directions: use the algorithm to find the quotients below. be sure to rewrite each quotient that is an improper fraction as a mixed number. be sure to check each problem.

a. $\frac{5}{3} div \frac{3}{4}$
b. $\frac{8}{3} div 4$
c. $4 div \frac{8}{3}$
d. $1\frac{1}{3} div \frac{3}{4}$
e. $2\frac{1}{8} div 1\frac{2}{9}$
f. $\frac{1}{4} div 2\frac{2}{3}$
g. $\frac{2}{3} div \frac{3}{4}$
h. $2\frac{3}{5} div 2\frac{1}{2}$
i. $\frac{3}{4} div 3\frac{2}{5}$

Question

excellence #1: dividing fractions/ mixed numbers
show all work & circle your final answer.
directions: use the algorithm to find the quotients below. be sure to rewrite each quotient that is an improper fraction as a mixed number. be sure to check each problem.

a. $\frac{5}{3} div \frac{3}{4}$
b. $\frac{8}{3} div 4$
c. $4 div \frac{8}{3}$
d. $1\frac{1}{3} div \frac{3}{4}$
e. $2\frac{1}{8} div 1\frac{2}{9}$
f. $\frac{1}{4} div 2\frac{2}{3}$
g. $\frac{2}{3} div \frac{3}{4}$
h. $2\frac{3}{5} div 2\frac{1}{2}$
i. $\frac{3}{4} div 3\frac{2}{5}$

Accepted Answer

### Part a: $\boldsymbol{\frac{2}{3} \div \frac{3}{4}}$
# Explanation:
## Step1: Recall division of fractions rule
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. So, $\frac{2}{3} \div \frac{3}{4}=\frac{2}{3} 	imes \frac{4}{3}$.
## Step2: Multiply the numerators and denominators
Multiply the numerators: $2	imes4 = 8$. Multiply the denominators: $3	imes3=9$. So, $\frac{2}{3} 	imes \frac{4}{3}=\frac{8}{9}$.
# Answer: $\boxed{\frac{8}{9}}$

### Part b: $\boldsymbol{\frac{8}{3} \div 4}$
# Explanation:
## Step1: Rewrite the whole number as a fraction
The whole number $4$ can be written as $\frac{4}{1}$. The reciprocal of $\frac{4}{1}$ is $\frac{1}{4}$. So, $\frac{8}{3} \div 4=\frac{8}{3} 	imes \frac{1}{4}$.
## Step2: Multiply and simplify
Multiply the numerators: $8	imes1 = 8$. Multiply the denominators: $3	imes4 = 12$. Then simplify $\frac{8}{12}$ by dividing numerator and denominator by their greatest common divisor, which is $4$. $\frac{8\div4}{12\div4}=\frac{2}{3}$.
# Answer: $\boxed{\frac{2}{3}}$

### Part c: $\boldsymbol{4 \div \frac{8}{3}}$
# Explanation:
## Step1: Rewrite the whole number as a fraction and find reciprocal
Rewrite $4$ as $\frac{4}{1}$. The reciprocal of $\frac{8}{3}$ is $\frac{3}{8}$. So, $4\div\frac{8}{3}=\frac{4}{1} 	imes \frac{3}{8}$.
## Step2: Multiply and simplify
Multiply the numerators: $4	imes3 = 12$. Multiply the denominators: $1	imes8 = 8$. Then simplify $\frac{12}{8}$ by dividing numerator and denominator by their greatest common divisor, which is $4$. $\frac{12\div4}{8\div4}=\frac{3}{2}$. Convert the improper fraction $\frac{3}{2}$ to a mixed number: $\frac{3}{2}=1\frac{1}{2}$.
# Answer: $\boxed{1\frac{1}{2}}$

### Part d: $\boldsymbol{1\frac{1}{3} \div \frac{3}{4}}$
# Explanation:
## Step1: Convert mixed number to improper fraction
$1\frac{1}{3}=\frac{1	imes3 + 1}{3}=\frac{4}{3}$. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. So, $1\frac{1}{3} \div \frac{3}{4}=\frac{4}{3} 	imes \frac{4}{3}$.
## Step2: Multiply the numerators and denominators
Multiply the numerators: $4	imes4 = 16$. Multiply the denominators: $3	imes3 = 9$. Convert the improper fraction $\frac{16}{9}$ to a mixed number: $\frac{16}{9}=1\frac{7}{9}$.
# Answer: $\boxed{1\frac{7}{9}}$

### Part e: $\boldsymbol{2\frac{1}{8} \div 1\frac{2}{9}}$
# Explanation:
## Step1: Convert mixed numbers to improper fractions
$2\frac{1}{8}=\frac{2	imes8+1}{8}=\frac{17}{8}$. $1\frac{2}{9}=\frac{1	imes9 + 2}{9}=\frac{11}{9}$. The reciprocal of $\frac{11}{9}$ is $\frac{9}{11}$. So, $2\frac{1}{8} \div 1\frac{2}{9}=\frac{17}{8} 	imes \frac{9}{11}$.
## Step2: Multiply the numerators and denominators
Multiply the numerators: $17	imes9=153$. Multiply the denominators: $8	imes11 = 88$. Convert the improper fraction $\frac{153}{88}$ to a mixed number: $\frac{153}{88}=1\frac{65}{88}$.
# Answer: $\boxed{1\frac{65}{88}}$

### Part f: $\boldsymbol{\frac{1}{4} \div 2\frac{2}{3}}$
# Explanation:
## Step1: Convert mixed number to improper fraction
$2\frac{2}{3}=\frac{2	imes3+2}{3}=\frac{8}{3}$. The reciprocal of $\frac{8}{3}$ is $\frac{3}{8}$. So, $\frac{1}{4} \div 2\frac{2}{3}=\frac{1}{4} 	imes \frac{3}{8}$.
## Step2: Multiply the numerators and denominators
Multiply the numerators: $1	imes3 = 3$. Multiply the denominators: $4	imes8 = 32$. So, $\frac{1}{4} 	imes \frac{3}{8}=\frac{3}{32}$.
# Answer: $\boxed{\frac{3}{32}}$

### Part g: $\boldsymbol{\frac{2}{3} \div \frac{3}{4}}$ (Wait, this is same as part a? Maybe a typo, assuming it's a different problem, let's re - check. If it's $\frac{2}{3}\div\frac{3}{4}$, we already solved it. If it's a different fraction, but as per the image, let's assume it's $\frac{2}{3}\div\frac{3}{4}$ again. But maybe it's a typo, if we consider it as $\frac{2}{3}\div\frac{3}{4}$, the answer is $\frac{8}{9}$ as in part a. But if it's a different problem, please re - check the original problem. For now, assuming it's $\frac{2}{3}\div\frac{3}{4}$)
# Explanation:
## Step1: Recall division of fractions rule
To divide fractions, multiply the first fraction by the reciprocal of the second fraction. The reciprocal of $\frac{3}{4}$ is $\frac{4}{3}$. So, $\frac{2}{3} \div \frac{3}{4}=\frac{2}{3} 	imes \frac{4}{3}$.
## Step2: Multiply the numerators and denominators
Multiply the numerators: $2	imes4 = 8$. Multiply the denominators: $3	imes3 = 9$. So, $\frac{2}{3} 	imes \frac{4}{3}=\frac{8}{9}$.
# Answer: $\boxed{\frac{8}{9}}$ (If it's a different problem, please provide the correct fraction)

### Part h: $\boldsymbol{2\frac{3}{5} \div 2\frac{1}{2}}$
# Explanation:
## Step1: Convert mixed numbers to improper fractions
$2\frac{3}{5}=\frac{2	imes5 + 3}{5}=\frac{13}{5}$. $2\frac{1}{2}=\frac{2	imes2+1}{2}=\frac{5}{2}$. The reciprocal of $\frac{5}{2}$ is $\frac{2}{5}$. So, $2\frac{3}{5} \div 2\frac{1}{2}=\frac{13}{5} 	imes \frac{2}{5}$.
## Step2: Multiply the numerators and denominators
Multiply the numerators: $13	imes2 = 26$. Multiply the denominators: $5	imes5 = 25$. Convert the improper fraction $\frac{26}{25}$ to a mixed number: $\frac{26}{25}=1\frac{1}{25}$.
# Answer: $\boxed{1\frac{1}{25}}$

### Part i: $\boldsymbol{\frac{3}{4} \div 3\frac{3}{5}}$
# Explanation:
## Step1: Convert mixed number to improper fraction
$3\frac{3}{5}=\frac{3	imes5+3}{5}=\frac{18}{5}$. The reciprocal of $\frac{18}{5}$ is $\frac{5}{18}$. So, $\frac{3}{4} \div 3\frac{3}{5}=\frac{3}{4} 	imes \frac{5}{18}$.
## Step2: Multiply and simplify
Multiply the numerators: $3	imes5 = 15$. Multiply the denominators: $4	imes18 = 72$. Simplify $\frac{15}{72}$ by dividing numerator and denominator by their greatest common divisor, which is $3$. $\frac{15\div3}{72\div3}=\frac{5}{24}$.
# Answer: $\boxed{\frac{5}{24}}$

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QUESTION IMAGE

Question

Explanation:

Part a: $\boldsymbol{\frac{2}{3} \div \frac{3}{4}}$

Step1: Recall division of fractions rule

Step2: Multiply the numerators and denominators

Step1: Rewrite the whole number as a fraction

Step2: Multiply and simplify

Step1: Rewrite the whole number as a fraction and find reciprocal

Step2: Multiply and simplify

Answer:

Part b: $\boldsymbol{\frac{8}{3} \div 4}$