ISEE Middle Level Quantitative : ISEE Middle Level (grades 7-8) Quantitative Reasoning
Study concepts, example questions & explanations for ISEE Middle Level Quantitative
All ISEE Middle Level Quantitative Resources
Example Questions
Example Question #11 : How To Find The Decimal Equivalent Of A Fraction
Write the result as a decimal:
First, evaluate the term in parenthesis:
Apply the exponent by sparing the numerator and the denominator.
To subtract, convert the terms to a common denominator.
Divide to convert the fraction to a decimal.
Example Question #12 : How To Find The Decimal Equivalent Of A Fraction
Which is the greater quantity?
(a)
(b)
(b) is the greater quantity
(a) is the greater quantity
It is impossible to determine which is greater from the information given
(a) and (b) are equal
(a) and (b) are equal
Multiply both sides by 8, and the following is revealed:
On the left side, the division is cancelled by the multiplication. On the right, 
Example Question #13 : How To Find The Decimal Equivalent Of A Fraction
Which is the greater quantity?
(a)
(b)
It is impossible to determine which is greater from the information given
(b) is the greater quantity
(a) is the greater quantity
(a) and (b) are equal
(a) is the greater quantity
This can be solved by noting that, converting the decimal to a fraction, 
The equation can be rewritten as
Multiply both sides by 
Example Question #11 : How To Find The Decimal Equivalent Of A Fraction
Express 
The last nonzero digit is in the ten-thousandths place, so write the number, without decimal point or leading zeroes, over 10,000. Then reduce.
Example Question #1 : How To Find A Ratio
On Katy's facebook page, she has 
Katy has 
Example Question #2 : How To Find A Ratio
Mike drove 120 miles to his mother's house. He finished the trip in two hours and 15 minutes. It took him one hour to drive the first 50 miles.
Which is the greater quantity?
(a) Mike's average speed over the first 50 miles
(b) Mike's average speed over the last 70 miles
It is impossible to tell from the information given
(a) is greater
(a) and (b) are equal
(b) is greater
(b) is greater
We can compare miles per hour.
(a) 50 miles over a one-hour period is 50 miles per hour.
(b) 70 miles over a one-and-one-fourth-hour period is
Mike drove an average of 56 miles per hour over the last 70 miles, making (b) greater.
Example Question #1 : How To Find A Ratio
Travis took 45 minutes to drive a total of 40 miles.
Which is the greater quantity?
(a) 55 miles per hour
(b) The average rate at which Travis drove
(a) and (b) are equal
(b) is greater
(a) is greater
It is impossible to tell from the information given
(a) is greater
Travis drove 40 miles in three-fourths of an hour, so we can divide:
which is less than 55.
Example Question #2 : Ratio And Proportion
The distance between Wilsonville and Coleman is 320 miles and is represented by six inches on a map. The distance between Wilsonville and Garrett is 120 miles.
Which is the greater quantity?
(a) The distance between Coleman and Garrett on the map
(b)
(a) is greater
(b) is greater
(a) and (b) are equal
It is impossible to tell from the information given
It is impossible to tell from the information given
The closest that Coleman and Garrett can be to each other is 200 miles (if Garrett is between Wilsonville and Coleman); the farthest is 440 miles (if Wilsonville is between Coleman and Garrett).
Call the map distance between Coleman and Garrett 
The two extremes of 
The minimum:
The maximum:
It is therefore unclear whether the map distance is greater than or less than 5 inches.
Example Question #191 : Numbers And Operations
There are fifteen boys in a room and twelve girls. Five more girls enter. What is the ratio of girls to total students in the room after this change occurs?
After the new girls enter the room, you have 
Example Question #192 : Numbers And Operations
In a bowl of 
We know that 
Thus far, we know that we must have:
and
Now, if we double the apples, we will have:
and
This means that the proportion of kiwis to total fruit will be:
All ISEE Middle Level Quantitative Resources
