ATI TEAS 7 Math Version 4 Questions

Explanation

<h2>20/24 and 21/24 are equivalent to 5/6 and 7/8, respectively.</h2> To determine equivalence, we can simplify or convert the given fractions. The fractions 20/24 and 21/24 can be simplified to 5/6 and 7/8, confirming that they are indeed equivalent. <b>A) 20/48 and 42/48</b> The fraction 20/48 simplifies to 5/12, not 5/6, since both the numerator and denominator can be divided by 4. Similarly, 42/48 simplifies to 7/8, but since one fraction is incorrect, this pair cannot be equivalent to 5/6 and 7/8. <b>B) 10/12 and 14/12</b> 10/12 simplifies to 5/6, but 14/12 simplifies to 7/6, which exceeds 1 and does not match 7/8. Therefore, while one fraction is correct, the other does not correspond with the required equivalence. <b>C) 20/24 and 21/24</b> Both fractions can be simplified: 20/24 simplifies to 5/6 and 21/24 simplifies to 7/8. This pair is equivalent to the original fractions, making it the correct choice. <b>D) 10/16 and 14/16</b> 10/16 simplifies to 5/8, which is not equivalent to 5/6, and 14/16 simplifies to 7/8. Since only one of the fractions matches, this pair cannot be equivalent to the given fractions. <b>Conclusion</b> To find equivalent fractions, one must check if the simplified forms match the original fractions. The pair 20/24 and 21/24 effectively simplifies to 5/6 and 7/8, respectively, confirming their equivalence. Other options either simplify incorrectly or contain one fraction that does not match, disqualifying them as answers.

Explanation

<h2>2/3 and 10/15 are equivalent fractions.</h2> Both fractions represent the same value when simplified. The fraction 10/15 can be reduced by dividing both the numerator and the denominator by their greatest common divisor, which is 5, resulting in 2/3. Therefore, these two fractions are indeed equivalent. <b>A) 5/9 and 45/72</b> To determine if these fractions are equivalent, we can simplify 45/72 by dividing both the numerator and denominator by their greatest common divisor, which is 9. This results in 5/8, not 5/9; hence, they are not equivalent. <b>B) 4/5 and 7/4</b> These fractions are not equivalent as they represent different values. The fraction 4/5 is less than 1, while 7/4 is greater than 1. Their different values indicate that they cannot be equivalent fractions. <b>D) 3/8 and 8/13</b> Similar to the previous choices, these fractions are not equivalent. When evaluated, 3/8 is approximately 0.375, while 8/13 is approximately 0.615. Since the values differ, they do not represent the same fraction. <b>Conclusion</b> The equivalence of fractions is determined by whether they simplify to the same value. Among the options provided, 2/3 and 10/15 are equivalent, as shown by the simplification process. The other pairs do not yield the same values upon evaluation, confirming that they are not equivalent fractions. Understanding how to simplify fractions is crucial for identifying equivalencies accurately.

Explanation

<h2>The probability that a randomly selected marble is not red is 7/10.</h2> In the jar, there are a total of 20 marbles (6 red, 4 blue, and 10 green). To find the probability of not selecting a red marble, we can calculate the number of non-red marbles (4 blue + 10 green = 14) and divide that by the total number of marbles, resulting in a probability of 14/20, which simplifies to 7/10. <b>A) {3/10}</b> This choice represents the probability of selecting a red marble instead. It is calculated by taking the number of red marbles (6) and dividing it by the total number of marbles (20), resulting in 6/20, which simplifies to 3/10. Thus, this option is not relevant to the probability of selecting a non-red marble. <b>B) {7/10}</b> This is the correct answer, calculated by determining the number of non-red marbles (14) divided by the total number of marbles (20). The probability of not selecting a red marble is therefore 14/20, which simplifies to 7/10, confirming this as the right choice. <b>C) {1/5}</b> This choice represents a probability that is too low for the given scenario. It would imply that out of 5 total events, only 1 is successful in terms of selecting a non-red marble, which does not align with the actual count of non-red marbles (14 out of 20). <b>D) {1/2}</b> This option suggests that there is an equal chance of selecting a red or non-red marble, which is incorrect. Given that there are 14 non-red marbles compared to 6 red marbles, the likelihood of selecting a non-red marble is actually greater than 1/2. <b>Conclusion</b> The probability of randomly selecting a marble that is not red from the jar is accurately represented by 7/10. This result is derived from the ratio of non-red marbles to the total number of marbles, highlighting the importance of understanding total outcomes in probability. The other choices fail to reflect the correct relationship between the counts of red and non-red marbles in the jar.

Explanation

<h2>Each of the other three friends received 1/6 of the pizza.</h2> After one friend eats half of the pizza, there is half left for the remaining three friends to share. Dividing this half equally among the three friends results in each receiving one-sixth of the entire pizza. <b>A) 1/3</b> If each of the three friends received 1/3 of the pizza, that would total 1 (3/3) when combined with the half already eaten. However, since only half of the pizza remains after one friend consumes their portion, this option is incorrect. <b>B) 1/5</b> If each friend received 1/5 of the pizza, then three friends would collectively receive 3/5 of the pizza. Adding the half consumed by the first friend would total 1.1 (5/5), which is more than one whole pizza, making this option impossible. <b>C) 1/6</b> This choice is correct because after one friend eats half, the remaining half is divided by three, resulting in each friend receiving 1/6 of the entire pizza (1/2 divided by 3 equals 1/6). <b>D) 1/4</b> If each friend received 1/4 of the pizza, then three friends would total 3/4 of the pizza. Adding the eaten half would again exceed one whole pizza (3/4 + 1/2 = 5/4), which is not feasible. <b>Conclusion</b> The division of the pizza illustrates how to correctly allocate portions among friends. After one eats half, the remaining half is split among three friends, leading each to receive 1/6 of the total pizza. The other options suggest incorrect distributions that exceed the available pizza or miscalculate the portions, reinforcing the arithmetic behind equitable sharing.

Explanation

<h2>The perimeter of the garden is 24.7 meters.</h2> To find the perimeter of the garden, we sum the lengths of all four sides. The three sides measuring 5.5 meters contribute a total of 16.5 meters, and when we add the fourth side measuring 8.2 meters, the total perimeter becomes 24.7 meters. <b>A) 16.5 meters</b> This choice only accounts for the three sides measuring 5.5 meters each, resulting in a total of 16.5 meters. It neglects the additional side measuring 8.2 meters, which is essential for calculating the full perimeter of the garden. <b>B) 24.7 meters</b> This is the correct answer as it accurately represents the total perimeter calculated by adding all the sides together: 5.5 + 5.5 + 5.5 + 8.2 = 24.7 meters. <b>C) 13.7 meters</b> This option does not correctly reflect the measurements of the garden sides. It underestimates the total perimeter significantly, suggesting a miscalculation or misunderstanding of the side lengths provided. <b>D) 27.4 meters</b> This choice incorrectly suggests that the perimeter exceeds the actual sum of the side lengths. It appears to result from a possible mathematical error, such as incorrectly calculating one or more of the side lengths, leading to an inflated total. <b>Conclusion</b> The perimeter of a shape is determined by the sum of all its sides. For the garden in this question, the accurate calculation yields a perimeter of 24.7 meters, confirming that option B is correct. The other choices either result from miscalculations or fail to incorporate all the side measurements, highlighting the importance of careful addition in perimeter computations.