FREE IAAT Pre-Algebraic Number Skills and Concepts Questions and Answers
Which of the following expressions represents the sum of 5 and twice x?
Explanation:
The sum of 5 and twice x is represented by the expression x + 5, as "twice x" is equivalent to 2x, and the sum of 5 and 2x is x + 5.
Tiffany walked 1 mile from home to school. After school, she walked to her friend Joan’s house to wait for her dad to pick her up. Joan’s home is twice the distance from Tiffany’s home to school. How many miles did Tiffany walk by the time her dad picked her up?
Explanation:
Tiffany walked 1 mile from home to school. Joan's house is twice the distance from Tiffany's home to school, so it is 2 miles from Tiffany's home. Therefore, the distance from the school to Joan's house is also 2 miles. Adding these distances together, Tiffany walked a total of 1 mile+2 miles=3 miles.
There are 49 boys and 28 girls in a school auditorium. Express the ratio of the number of boys to that of girls.
Explanation:
Given, the number of boys = 49; and the number of girls = 28. The GCF of 49 and 28 is 7. Now, to simplify, divide the two terms by their GCF which is 7. This means, (49 ÷ 7)/(28 ÷ 7) = 7/4.
Therefore, the ratio of the number of boys to that of girls = 7:4.
If 14 cups of yogurt and 4 cups of strawberry crystals are needed to make a strawberry pie, what is the ratio of yogurt and strawberry crystals that is used for the recipe?
Explanation:
The ratio of yogurt to strawberry crystals used for the recipe is found by dividing the number of cups of yogurt by the number of cups of strawberry crystals. In this case, there are 14 cups of yogurt and 4 cups of strawberry crystals. So, the ratio of yogurt to strawberry crystals is 14:4, which simplifies to 7:2.
Sophia baked cookies for her class. Every student had one cookie, including Sophia. At the end of the school day, 3 cookies were left. How many kids were in the class?
Explanation:
Let's denote the total number of cookies Sophia baked as 𝑛. Since every student, including Sophia, had one cookie, and 3 cookies were left at the end of the school day, the number of cookies eaten was n − 3. This number of cookies eaten is equal to the number of kids in the class since each student had one cookie.
Therefore, the number of kids in the class is represented by the expression 𝑛 − 3.
James sells ice cream on weekends. If he sells cones with two scoops, he gets a bonus of 10 cents per scoop. On Saturday, he sold 12 cones with two scoops. On Sunday, he sold only 4 cones with double scoops. What was his bonus?
Explanation:
James gets a bonus of 10 cents per scoop. Each cone with two scoops will earn him a bonus for two scoops. On Saturday, he sold 12 cones with two scoops, and on Sunday, he sold 4 cones with two scoops. The total number of cones with two scoops sold is 12 + 4 = 16 cones.
Since each cone has two scoops, the total number of scoops is 2 × (12 + 4).
To calculate the total bonus:
0.10 (per scoop) × 2 × (12 + 4) = 0.10 × 2 × 16 = 0.10 × 32 = 3.20
Which one is the best answer? 2/5 + 5/8 =
Explanation:
To find the sum of 2/5 and 5/8, we need to find a common denominator and then add the fractions.
The common denominator for 5 and 8 is 40.
Converting 2/5 to have a denominator of 40, we get 16/40.
Converting 5/8 to have a denominator of 40, we get 25/40.
Adding the fractions, we have:
16/40 + 25/40 = 41/40
In a class of 50 students, 23 are girls and the remaining are boys. Find the ratio of the number of boys to the number of girls.
Explanation:
Total number of students = 50; Number of girls = 23.
Total number of boys = Total number of students - Total number of girls
= 50 - 23
= 27
Therefore, the desired ratio is, (Number of boys: Number of girls), which is 27:23.
There were 46 kids in the tram, in which 26 were boys and 20 were girls. What is the ratio of the boys to the total number of girls?
Explanation:
The ratio of boys to the total number of girls is found by dividing the number of boys by the number of girls. In this case, there are 26 boys and 20 girls. So, the ratio of boys to girls is 26:20, which simplifies to 13:10.
The perimeter of a stop sign is 48 inches. If each side is equal to one another, what is the length of each side?
Explanation:
A stop sign has 8 sides, and since each side is equal, the length of each side can be represented as 𝑛. The perimeter of the stop sign is the sum of the lengths of all 8 sides. Therefore, the equation to represent this is 8n = 48. Solving for 𝑛:
n = 48/8 = 6 inches
Thus, each side of the stop sign is 6 inches long.
Which carton of yogurt is the best value?
Explanation:
16 oz for 1.60 is the best value because it has the lowest price per ounce, making it the most cost-effective choice.