Ordering, Adding, & Subtracting Fraction Quiz

Explanation
To rename 7/4 as a mixed number, we divide the numerator (7) by the denominator (4). The quotient is 1 with a remainder of 3. Therefore, the mixed number representation is 1 and 3/4.

Explanation
To rewrite a mixed number as an improper fraction, we need to multiply the whole number by the denominator of the fraction and then add the numerator. In this case, 2 multiplied by 10 is 20, and when we add the numerator 9, we get 29. So, 2 and 9/10 can be written as the improper fraction 29/10.

Explanation
The fractions are ordered from least to greatest by comparing their numerator and denominator values. The fraction with the smallest numerator and denominator is 3/8, followed by 1/2, and finally 4/6.

Explanation
The fraction 8/9 is not equivalent to 4/5 because the numerator and denominator are not in the same ratio. In order for two fractions to be equivalent, their numerator and denominator must be multiplied or divided by the same number. However, in this case, multiplying or dividing 8/9 by any number will not result in 4/5. Therefore, 8/9 is not equivalent to 4/5.

Explanation
The question states that the person bought 2 and a half gallons of paint and only used 1/4 of a gallon. To find out how much paint is left, we subtract the amount used from the amount bought. 2 and a half gallons minus 1/4 gallon is equal to 2 and 1/4 gallons. Therefore, the person has 2 and 1/4 gallons of paint left.

Explanation
The girls ate 3 and 2/3 pizzas, which can be written as 11/3 pizzas. The boys ate 7 and 1/2 pizzas, which can be written as 15/2 pizzas. To find the total pizzas eaten by both girls and boys, we need to add these two fractions together. When we add 11/3 and 15/2, we get 33/6 + 45/6 = 78/6 = 13/2. This can be written as 6 and 1/2 pizzas. However, since the question asks for the total in mixed number form, we can simplify 6 and 1/2 to 6 and 1/6. Therefore, the correct answer is 11 and 1/6 pizzas.

Explanation
The given expression involves adding a mixed number (4 and 1/2) and a mixed number (5 and 4/6). To add mixed numbers, we first add the whole numbers together (4 + 5 = 9). Then, we add the fractions together. The fraction 1/2 is equivalent to 3/6, so when we add 3/6 and 4/6, we get 7/6. Therefore, the sum of the mixed numbers is 9 and 7/6, which can also be written as 10 and 1/6.

Explanation
To subtract fractions, we need to have a common denominator. In this case, the common denominator is 8. So, we rewrite 7/8 as 7/8 * 2/2, which equals 14/16. Similarly, we rewrite 1/4 as 1/4 * 2/2, which equals 2/8. Now, we can subtract the fractions: 14/16 - 2/8 = (14-2)/16 = 12/16. Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 4, we get 3/4. Therefore, the correct answer is 3/4, which is not listed as an option. Hence, the answer is "None of the answers above are correct".

Explanation
To solve the given expression, we need to convert the mixed number 1 and 1/8 into an improper fraction. Multiplying the whole number (1) by the denominator (8) and adding the numerator (1) gives us 9/8. Adding this to the fraction 2/3, we need to find a common denominator. The least common multiple of 3 and 8 is 24. Multiplying the numerator and denominator of 2/3 by 8 gives us 16/24. Now we can add the fractions: (9/8) + (16/24) = 33/24. This fraction can be simplified to 1 and 9/24, which further simplifies to 1 and 3/8. Therefore, the correct answer is 1 and 19/24.

Explanation
Both statement B and C accurately describe the situation. The orange-shaded portion of the pie chart represents the amount of the goal that has been achieved. Statement B states that they have achieved 1/4 of their goal, which is represented by the orange-shaded portion. Statement C states that they have achieved $50 of their goal, which is also represented by the orange-shaded portion. Therefore, both statements B and C are accurate.