Find the quotient of 2/8 and 3/4. 2. What is 3 1/3 divided by 2/3? 3. What will be the result if 2 2/4 is divided by 2/5? 4. What is the quotient of 4 2/3 and 1 2/4?
The Correct Answer and Explanation is:
Let’s go through each of these questions step by step:
1. Find the quotient of 2/8 and 3/4.
To divide fractions, you multiply the first fraction by the reciprocal (inverse) of the second fraction. 28÷34=28×43\frac{2}{8} \div \frac{3}{4} = \frac{2}{8} \times \frac{4}{3}82÷43=82×34
First, simplify the fractions: 28=14\frac{2}{8} = \frac{1}{4}82=41
Now multiply: 14×43=1×44×3=412=13\frac{1}{4} \times \frac{4}{3} = \frac{1 \times 4}{4 \times 3} = \frac{4}{12} = \frac{1}{3}41×34=4×31×4=124=31
Answer: The quotient is 13\frac{1}{3}31.
2. What is 3 1/3 divided by 2/3?
To divide mixed numbers, first convert the mixed number to an improper fraction. 313=1033 \frac{1}{3} = \frac{10}{3}331=310
Now, divide by 23\frac{2}{3}32: 103÷23=103×32\frac{10}{3} \div \frac{2}{3} = \frac{10}{3} \times \frac{3}{2}310÷32=310×23
Multiply the fractions: 10×33×2=306=5\frac{10 \times 3}{3 \times 2} = \frac{30}{6} = 53×210×3=630=5
Answer: The result is 555.
3. What will be the result if 2 2/4 is divided by 2/5?
First, convert the mixed number 2242 \frac{2}{4}242 to an improper fraction: 224=104=522 \frac{2}{4} = \frac{10}{4} = \frac{5}{2}242=410=25
Now divide by 25\frac{2}{5}52: 52÷25=52×52\frac{5}{2} \div \frac{2}{5} = \frac{5}{2} \times \frac{5}{2}25÷52=25×25
Multiply the fractions: 5×52×2=254\frac{5 \times 5}{2 \times 2} = \frac{25}{4}2×25×5=425
Convert this back to a mixed number: 254=614\frac{25}{4} = 6 \frac{1}{4}425=641
Answer: The result is 6146 \frac{1}{4}641.
4. What is the quotient of 4 2/3 and 1 2/4?
Convert both mixed numbers to improper fractions. For 4234 \frac{2}{3}432: 423=1434 \frac{2}{3} = \frac{14}{3}432=314
For 1241 \frac{2}{4}142: 124=64=321 \frac{2}{4} = \frac{6}{4} = \frac{3}{2}142=46=23
Now divide 143\frac{14}{3}314 by 32\frac{3}{2}23: 143÷32=143×23\frac{14}{3} \div \frac{3}{2} = \frac{14}{3} \times \frac{2}{3}314÷23=314×32
Multiply the fractions: 14×23×3=289\frac{14 \times 2}{3 \times 3} = \frac{28}{9}3×314×2=928
Convert 289\frac{28}{9}928 to a mixed number: 289=319\frac{28}{9} = 3 \frac{1}{9}928=391
Answer: The quotient is 3193 \frac{1}{9}391.
Summary of answers:
- The quotient of 28\frac{2}{8}82 and 34\frac{3}{4}43 is 13\frac{1}{3}31.
- 313÷23=53 \frac{1}{3} \div \frac{2}{3} = 5331÷32=5.
- 224÷25=6142 \frac{2}{4} \div \frac{2}{5} = 6 \frac{1}{4}242÷52=641.
- The quotient of 4234 \frac{2}{3}432 and 1241 \frac{2}{4}142 is 3193 \frac{1}{9}391.
