Operations with Fractions and Whole Numbers Quiz

To simplify the fraction 12/16, we need to find the greatest common divisor (GCD) of the numerator (12) and the denominator (16). The GCD of 12 and 16 is 4. Dividing both the numerator and the denominator by 4 gives us 12 ÷ 4 = 3 and 16 ÷ 4 = 4. Therefore, the simplified form of 12/16 is 3/4.

To find 1/4 of 20, you divide 20 by 4. This calculation represents taking one part out of four equal parts of the total. When you divide 20 by 4, you get 5, which means that one-quarter of 20 is equal to 5. This concept is fundamental in fractions, where the numerator indicates how many parts you have and the denominator indicates how many equal parts the whole is divided into.

To convert the improper fraction 9/4 into a mixed number, divide the numerator (9) by the denominator (4). This gives you 2 as the whole number (since 4 goes into 9 two times) and a remainder of 1 (9 - 8 = 1). The remainder becomes the numerator of the fractional part, while the denominator remains 4. Therefore, the mixed number is 2 1/4, which combines the whole number and the fraction.

To compare the fractions 3/5 and 2/3, it's helpful to find a common denominator. The least common multiple of 5 and 3 is 15. Converting both fractions, 3/5 becomes 9/15 and 2/3 becomes 10/15. Since 10/15 is greater than 9/15, it shows that 2/3 is larger than 3/5. Thus, 2/3 is the correct answer.

To simplify the fraction 15/45, we need to find the greatest common divisor (GCD) of the numerator (15) and the denominator (45). The GCD of 15 and 45 is 15. Dividing both the numerator and the denominator by their GCD gives us 15 ÷ 15 = 1 and 45 ÷ 15 = 3. Thus, the simplified form of 15/45 is 1/3.

To express 3/8 in its simplest form, we need to check if the numerator (3) and the denominator (8) have any common factors other than 1. The number 3 is a prime number and does not divide 8 evenly. Therefore, there are no common factors to simplify, and 3/8 is already in its simplest form. Thus, the fraction remains as 3/8.

To solve 5 + (-3), you are essentially subtracting 3 from 5. The negative sign indicates that you are taking away 3 from 5. When you perform the calculation, 5 - 3 equals 2. Therefore, the result of adding 5 and -3 is 2.

To calculate the square of a number, you multiply the number by itself. In this case, squaring 6 involves calculating 6 × 6. Performing this multiplication gives you 36. This result represents the area of a square with each side measuring 6 units, confirming that the square of 6 is indeed 36.

The square root of a number is a value that, when multiplied by itself, gives the original number. In this case, 7 multiplied by 7 equals 49. Therefore, the square root of 49 is 7, as it is the only positive integer that satisfies this condition.

To find the number, you start with the equation where 1/3 of the number equals 12. This can be expressed as \( x/3 = 12 \). To isolate \( x \), multiply both sides of the equation by 3, resulting in \( x = 12 \times 3 \). Calculating this gives \( x = 36 \). Therefore, the number is 36.