In 2/5 ÷ 4/7, the quotient will be

In 2/5 ÷ 4/7, the quotient will be . A. 7/8 B. 7/9 C. 7/10 D. 7/11 2. Corrected_text: 1/2 divided by 4/7 is equal to_. A. 4/9 B. 5/9 C. 7/8 D. 4/14 3. Corrected_text: Give the quotient in simplest form of 2 3/4 ÷ 1 1/4. A. 8/12 B. 1 13/27 C. 2 1/5 D. 3 2/3 4. Corrected_text: 1/2 divided by 2 is equal to__. A. 1/2 B. 1/3 C. 1/5 D. 1/4 5. Corrected_text: In 2 5/6 ÷ 2 2/4 = N, what is N? A. 1 8/60 B. 1 2/15 C. 1 68/60 D. 68/60 6. Corrected_text: What is the quotient of 1/3 ÷ 1/2? A. 2/3 B. 2/5 C. 2/6 D. 1/6

The Correct Answer and Explanation is:

Let’s work through each of these step-by-step:

1. 25÷47\frac{2}{5} \div \frac{4}{7}52​÷74​

To divide by a fraction, you multiply by its reciprocal. The reciprocal of 47\frac{4}{7}74​ is 74\frac{7}{4}47​. So: 25×74=2×75×4=1420\frac{2}{5} \times \frac{7}{4} = \frac{2 \times 7}{5 \times 4} = \frac{14}{20}52​×47​=5×42×7​=2014​

Now, simplify 1420\frac{14}{20}2014​ by dividing both the numerator and the denominator by 2: 1420=710\frac{14}{20} = \frac{7}{10}2014​=107​

So the correct answer is C. 710\frac{7}{10}107​.

2. 12÷47\frac{1}{2} \div \frac{4}{7}21​÷74​

Again, multiply by the reciprocal: 12×74=1×72×4=78\frac{1}{2} \times \frac{7}{4} = \frac{1 \times 7}{2 \times 4} = \frac{7}{8}21​×47​=2×41×7​=87​

The correct answer is C. 78\frac{7}{8}87​.

3. 234÷1142 \frac{3}{4} \div 1 \frac{1}{4}243​÷141​

First, convert the mixed numbers into improper fractions: 234=114and114=542 \frac{3}{4} = \frac{11}{4} \quad \text{and} \quad 1 \frac{1}{4} = \frac{5}{4}243​=411​and141​=45​

Now divide: 114÷54=114×45=11×44×5=4420\frac{11}{4} \div \frac{5}{4} = \frac{11}{4} \times \frac{4}{5} = \frac{11 \times 4}{4 \times 5} = \frac{44}{20}411​÷45​=411​×54​=4×511×4​=2044​

Simplify 4420\frac{44}{20}2044​: 4420=115\frac{44}{20} = \frac{11}{5}2044​=511​

Convert this back into a mixed number: 115=215\frac{11}{5} = 2 \frac{1}{5}511​=251​

So the correct answer is C. 2152 \frac{1}{5}251​.

4. 12÷2\frac{1}{2} \div 221​÷2

To divide by 2, multiply by 12\frac{1}{2}21​: 12÷2=12×12=14\frac{1}{2} \div 2 = \frac{1}{2} \times \frac{1}{2} = \frac{1}{4}21​÷2=21​×21​=41​

So the correct answer is D. 14\frac{1}{4}41​.

5. 256÷2242 \frac{5}{6} \div 2 \frac{2}{4}265​÷242​

Convert the mixed numbers into improper fractions: 256=176and224=104=522 \frac{5}{6} = \frac{17}{6} \quad \text{and} \quad 2 \frac{2}{4} = \frac{10}{4} = \frac{5}{2}265​=617​and242​=410​=25​

Now divide: 176÷52=176×25=17×26×5=3430\frac{17}{6} \div \frac{5}{2} = \frac{17}{6} \times \frac{2}{5} = \frac{17 \times 2}{6 \times 5} = \frac{34}{30}617​÷25​=617​×52​=6×517×2​=3034​

Simplify 3430\frac{34}{30}3034​: 3430=1715\frac{34}{30} = \frac{17}{15}3034​=1517​

Convert this to a mixed number: 1715=1215\frac{17}{15} = 1 \frac{2}{15}1517​=1152​

So the correct answer is B. 12151 \frac{2}{15}1152​.

6. 13÷12\frac{1}{3} \div \frac{1}{2}31​÷21​

To divide by 12\frac{1}{2}21​, multiply by its reciprocal: 13×21=1×23×1=23\frac{1}{3} \times \frac{2}{1} = \frac{1 \times 2}{3 \times 1} = \frac{2}{3}31​×12​=3×11×2​=32​

So the correct answer is A. 23\frac{2}{3}32​.

Summary of Answers:

1. C. 710\frac{7}{10}107​
2. C. 78\frac{7}{8}87​
3. C. 2152 \frac{1}{5}251​
4. D. 14\frac{1}{4}41​
5. B. 12151 \frac{2}{15}1152​
6. A. 23\frac{2}{3}32​