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 break down each of these problems step by step:
1. Find the quotient of 2/8 and 3/4.
To divide fractions, you multiply the first fraction by the reciprocal (or inverse) of the second fraction.
So, for 28÷34\frac{2}{8} \div \frac{3}{4}82÷43, we first rewrite the division as multiplication:28×43\frac{2}{8} \times \frac{4}{3}82×34
Now, multiply the numerators and denominators:2×48×3=824\frac{2 \times 4}{8 \times 3} = \frac{8}{24}8×32×4=248
Simplify the fraction by dividing both the numerator and denominator by 8:824=13\frac{8}{24} = \frac{1}{3}248=31
Thus, the quotient of 28\frac{2}{8}82 and 34\frac{3}{4}43 is 13\frac{1}{3}31.
2. What is 313÷233 \frac{1}{3} \div \frac{2}{3}331÷32?
First, convert the mixed number 3133 \frac{1}{3}331 into an improper fraction:313=1033 \frac{1}{3} = \frac{10}{3}331=310
Now, divide 103\frac{10}{3}310 by 23\frac{2}{3}32. This becomes:103÷23=103×32\frac{10}{3} \div \frac{2}{3} = \frac{10}{3} \times \frac{3}{2}310÷32=310×23
Now, multiply the numerators and denominators:10×33×2=306\frac{10 \times 3}{3 \times 2} = \frac{30}{6}3×210×3=630
Simplify the fraction:306=5\frac{30}{6} = 5630=5
Thus, the result of 313÷233 \frac{1}{3} \div \frac{2}{3}331÷32 is 5.
3. What will be the result if 2242 \frac{2}{4}242 is divided by 25\frac{2}{5}52?
First, convert 2242 \frac{2}{4}242 into an improper fraction:224=1042 \frac{2}{4} = \frac{10}{4}242=410
Now, divide 104\frac{10}{4}410 by 25\frac{2}{5}52:104÷25=104×52\frac{10}{4} \div \frac{2}{5} = \frac{10}{4} \times \frac{5}{2}410÷52=410×25
Now, multiply the numerators and denominators:10×54×2=508\frac{10 \times 5}{4 \times 2} = \frac{50}{8}4×210×5=850
Simplify the fraction by dividing both the numerator and denominator by 2:508=254\frac{50}{8} = \frac{25}{4}850=425
Convert the improper fraction 254\frac{25}{4}425 back to a mixed number:254=614\frac{25}{4} = 6 \frac{1}{4}425=641
Thus, the result of 224÷252 \frac{2}{4} \div \frac{2}{5}242÷52 is 6146 \frac{1}{4}641.
4. What is the quotient of 4234 \frac{2}{3}432 and 1241 \frac{2}{4}142?
Convert the mixed numbers into improper fractions:423=143,124=64=324 \frac{2}{3} = \frac{14}{3}, \quad 1 \frac{2}{4} = \frac{6}{4} = \frac{3}{2}432=314,142=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
Now, multiply the numerators and denominators:14×23×3=289\frac{14 \times 2}{3 \times 3} = \frac{28}{9}3×314×2=928
Convert the improper fraction 289\frac{28}{9}928 back to a mixed number:289=319\frac{28}{9} = 3 \frac{1}{9}928=391
Thus, the quotient of 4234 \frac{2}{3}432 and 1241 \frac{2}{4}142 is 3193 \frac{1}{9}391.
Summary of Answers:
- 28÷34=13\frac{2}{8} \div \frac{3}{4} = \frac{1}{3}82÷43=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
- 423÷124=3194 \frac{2}{3} \div 1 \frac{2}{4} = 3 \frac{1}{9}432÷142=391
These steps involve converting mixed numbers into improper fractions, multiplying by the reciprocal, and simplifying the result.
