Grade 9 Quiz (Advanced)

Explanation
To find 2/7 of 21, we divide 21 by 7 to get 3. Then, we multiply 3 by 2 to get the result of 6. Therefore, the correct answer is 6.

Explanation
To find the area of a rectangle, we multiply its length by its width. In this case, the length is given as 4 1/2 cm, which can be written as 9/2 cm. The width is given as 1 1/4 cm, which can be written as 5/4 cm. Multiplying these values together, we get (9/2) * (5/4) = 45/8. Therefore, the area of the rectangle is 45/8.

Explanation
Joseph weighed 8 11/16 pounds and Jerri weighed 8 3/4 pounds when they were born. To compare their weights, we need to convert the mixed numbers to improper fractions. 8 11/16 can be written as 139/16 and 8 3/4 can be written as 35/4. Comparing the fractions, we can see that 139/16 is greater than 35/4. Therefore, Joseph weighed more than Jerri. To find out how much more, we subtract 35/4 from 139/16, which equals 17 7/16. So, Jerri weighed 1/16 pound less than Joseph.

Explanation
After Lobna eats 1/3 of the pizza, there is 2/3 of the pizza remaining. Then, when she eats 1/2 of the pizza, she is eating half of the remaining 2/3. This can be represented as 1/2 * 2/3 = 1/3. Therefore, the fraction of the remaining part of the pizza is 1/3, which is equal to 1/6 of the original pizza.

Explanation
The given ratio 3:6:9 can be simplified by dividing all the numbers by the greatest common divisor, which is 3. This results in the simplified ratio of 1:2:3. Therefore, the correct answer is 1:2:3.

Explanation
The given expression "500 m : 2 km" can be simplified by converting both measurements to the same unit. Since 1 km is equal to 1000 m, we can convert 2 km to 2000 m. Now, we have 500 m : 2000 m. Simplifying this ratio by dividing both values by 500, we get 1 : 4. Therefore, the simplified ratio is 1:4.

Explanation
The ratio of the number of minutes that you do homework to the number of minutes that you are in school is 3:16. This means that for every 3 minutes you spend doing homework, you spend 16 minutes in school.

Explanation
Since the ratio of girls to boys is 4:5, we can assume that the total ratio of girls and boys in the club is 4+5=9. To find the number of girls, we need to divide the total number of children in the club (144) by the total ratio (9) and then multiply it by the ratio of girls (4). Therefore, the number of girls in the club is (144/9) * 4 = 64.

Explanation
To find the number of gallons of gasoline used on a trip of 468 miles, we can set up a proportion using the given information. We know that the car uses 20 gallons of gasoline for a trip of 360 miles. So, the ratio of gallons of gasoline to miles traveled is 20/360. We can use this ratio to find the number of gallons of gasoline used on a trip of 468 miles. By cross-multiplying, we get (20/360) = (x/468), where x represents the unknown number of gallons. Solving for x, we find that x is approximately 26 gallons. Therefore, 26 gallons of gasoline would be used on a trip of 468 miles.

Explanation
The pump takes 90 minutes to fill a 750 gallon tank. Since the size of the tank is proportional to the time it takes to fill it, we can use this information to find the time it takes to fill a 1000 gallon tank. We can set up a proportion: 750/90 = 1000/x, where x represents the time it takes to fill the 1000 gallon tank. Cross-multiplying and solving for x, we get x = (90 * 1000) / 750 = 120 minutes. Therefore, it will take 120 minutes for the pump to fill a 1000 gallon tank.

Explanation
Aisha uses 4 ounces of cream to 10 ounces of chocolate. To find the proportion of cream, we divide the amount of cream by the amount of chocolate. So, 4 divided by 10 is equal to 0.4. This can be simplified to 2 divided by 5. Therefore, the proportion of cream is 2:5.

Explanation
To find 15% of 120, we can multiply 120 by 0.15. This calculation gives us 18, which is the correct answer.

Explanation
35% of 120 inches is equal to 42 inches.

Explanation
To calculate an increase of 15% on $68, we can multiply $68 by 0.15 to find the amount of increase. 0.15 multiplied by $68 equals $10.2. Adding the increase to the original amount gives us $68 + $10.2 = $78.2. Therefore, the correct answer is $78.2.

Explanation
The selling price of the refrigerator is $697. This can be calculated by subtracting the discount of 18% from the marked price of $850. To find the discount amount, we multiply 18% by $850, which gives us $153. Subtracting $153 from $850 gives us $697, which is the selling price of the refrigerator after the discount.

Explanation
The marked price of the gloves can be calculated by dividing the selling price by (100% - discount percentage) and then multiplying it by 100. In this case, the selling price is $44 and the discount percentage is 45%. So, the marked price would be $44 / (100% - 45%) * 100 = $44 / 55% * 100 = $80.

Explanation
An Egyptian fraction is a fraction where the numerator is always 1. In this case, the fraction 1/5 is an Egyptian fraction because the numerator is 1. The other fractions listed have numerators that are not equal to 1, therefore they are not Egyptian fractions.

Explanation
To change 2/5 to an Egyptian fraction, we need to express it as a sum of unit fractions. The given answer, 1/3 + 1/15, is the correct representation of 2/5 as an Egyptian fraction. By adding these two fractions, we get 5/15 + 1/15, which simplifies to 6/15. Further simplifying, we get 2/5, which matches the original fraction. Therefore, 1/3 + 1/15 is the correct answer.

Explanation
The given sequence is a Fibonacci sequence, where each number is the sum of the two preceding numbers. Starting with 1 and 1, the next number is 2, then 3, then 5, and so on. Therefore, the next number in the sequence would be the sum of 8 and 5, which is 13.