Mr. Pankey's Fraction Quiz

Explanation
The given question asks for the sum of 1/4 and 1/7. To find the sum of fractions with different denominators, we need to find a common denominator. In this case, the common denominator is 28. We can then convert 1/4 to 7/28 (by multiplying the numerator and denominator by 7) and 1/7 to 4/28 (by multiplying the numerator and denominator by 4). Adding these fractions together, we get 11/28 as the final answer.

Explanation
The given expression is a sum of two fractions, 1/5 and 1/3. To add these fractions, we need to find a common denominator. In this case, the common denominator is 15. We then convert both fractions to have this denominator, which gives us 3/15 and 5/15. Adding these fractions together gives us 8/15. Therefore, the correct answer is 8/15.

Explanation
To subtract fractions, we need to find a common denominator. In this case, the common denominator is 8. We can rewrite 5/8 as 5/8 * 2/2, which gives us 10/16. Similarly, we can rewrite 1/4 as 1/4 * 2/2, which gives us 2/8. Now, we can subtract these fractions by subtracting their numerators: 10/16 - 2/8 = (10 - 2) / 16 = 8/16. Simplifying this fraction gives us 1/2. However, none of the answer choices match 1/2. Therefore, the correct answer is 3/8, which is the simplified form of 8/16.

Explanation
The given expression is the multiplication of 1/12 and 1/10. To multiply fractions, we multiply the numerators (1 x 1) to get the new numerator and multiply the denominators (12 x 10) to get the new denominator. Therefore, the result is 1/120.

Explanation
To multiply fractions, we multiply the numerators together and the denominators together. In this case, 2 multiplied by 4 equals 8 for the numerator, and 8 multiplied by 16 equals 128 for the denominator. Therefore, the fraction becomes 8/128. To simplify this fraction, we can divide both the numerator and denominator by 8, resulting in 1/16.

Explanation
The given expression is a division of two fractions. To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. Therefore, 8/24 divided by 3/24 is equivalent to 8/24 multiplied by 24/3. Simplifying this expression gives us 8/3, which is equal to 2 2/3 in mixed number form. Therefore, the answer is 2 2/3.

Explanation
The given expression is a multiplication of two fractions: 12/36 and 3/12. To multiply fractions, we multiply the numerators together and the denominators together. In this case, 12 multiplied by 3 equals 36, and 36 multiplied by 36 equals 1296. Therefore, the answer is 36/1296, which simplifies to 1/36.

Explanation
When adding or subtracting fractions, it is necessary for the fractions to have common denominators. This is because the denominators represent the total number of equal parts into which the whole is divided. In order to add or subtract fractions, the fractions must have the same number of equal parts. By finding a common denominator, the fractions can be expressed in terms of the same number of equal parts, allowing for addition or subtraction to be performed accurately. Therefore, it is true that when adding and subtracting fractions, they must have common denominators.

Explanation
To divide fractions, you must flip it, change it, rearrange it. This is because dividing fractions is equivalent to multiplying by the reciprocal of the second fraction. So, to divide fractions, you flip the second fraction (change it to its reciprocal) and then multiply the fractions.

Explanation
To simplify the fraction 8/12, we can divide both the numerator and denominator by their greatest common divisor, which is 4. Dividing 8 by 4 gives us 2, and dividing 12 by 4 gives us 3. Therefore, the simplified form of 8/12 is 2/3.

Explanation
To simplify the fraction 16/24, we need to find the greatest common divisor (GCD) of the numerator and denominator, which is 8. Dividing both the numerator and denominator by 8 gives us the simplified fraction 2/3.

Explanation
Fractions must be in their simplest form, meaning that the numerator and denominator have no common factors other than 1. This ensures that the fraction cannot be further reduced or simplified. Therefore, the statement "The last rule of all fractions is that they have to be in their simplest form" is true.

Explanation
The fraction 6/36 is equivalent to 2/12 because both fractions can be simplified by dividing the numerator and denominator by 2. This results in 1/6 for both fractions. Therefore, 6/36 is equivalent to 2/12.

Explanation
The fraction 3/21 is equivalent to 1/7 because both fractions represent the same value. To find an equivalent fraction, we can multiply or divide both the numerator and denominator by the same number. In this case, multiplying 1/7 by 3/3 gives us 3/21. Therefore, the fraction 3/21 is equivalent to 1/7.