ISEE Middle Level Quantitative Reasoning - ISEE Middle Level (grades 7-8) Quantitative Reasoning

Find the decimal equivalent of $\frac{72}{90}$ .

Explanation

To solve, divide:

$72\div 90=0.80$

Another way to solve is to reduce the fraction by removing the greatest common factor.

$\frac{72}{90}=\frac{72\div9}{90\div9}=\frac{8}{10}$

Eight over ten, or eight-tenths, is equal to .

Answer:

Annie has a piece of wallpaper that is by . How much of a wall can be covered by this piece of wallpaper?

Explanation

This problem asks us to calculate the amount of space that the wallpaper will cover. The amount of space that something covers can be described as its area. In this case area is calculated by using the formula $A=l \times w$

$A=3\times2$

Solve:

$\sqrt{225}\cdot 5=$

Explanation

First, find the square root:

$\sqrt{225}=15$

Then, solve:

$15\cdot 5=75$

Answer:

Which is greater?

(A)

(B)

(B) is greater

(A) is greater

(A) and (B) are equal

It is impossible to determine which is greater from the information given

Explanation

$-7K\div (-7) = 91 \div (-7)$

$-6M \div (-6) = 72 \div (-6)$

, so .

Therefore , so (B) is greater.

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The square and the triangle in the above diagram are both equally divided. Which is the greater quantity?

(a) The fraction of the square that is shaded

(b) The fraction of the triangle that is shaded

(a) and (b) are equal

(b) is the greater quantity

(a) is the greater quantity

It is impossible to determine which is greater from the information given

Explanation

The square is divided into eighteen triangles of equal size and shape; nine are shaded, so the fraction of the square that is shaded is

$\frac{9}{18} = \frac{9 \div 9 }{18\div 9 } = \frac{1}{2}$

The triangle is divided into sixteen triangles of equal size and shape; eight are shaded, so the fraction of the square that is shaded is

$\frac{8}{16} = \frac{8 \div 8 }{16 \div 8 } = \frac{1}{2}$ .

The fractions are equal.

What is the area of the figure below?

Explanation

To find the area of the figure above, we need to slip the figure into two rectangles.

6.5

Using our area formula, $A=l\times w$ , we can solve for the area of both of our rectangles

$A=7\times 12$ $A=7\times 5$

To find our final answer, we need to add the areas together.

The ratio of the perimeter of one square to that of another square is . What is the ratio of the area of the first square to that of the second square?

Explanation

For the sake of simplicity, we will assume that the second square has sidelength 1; Then its perimeter is $4 \times 1 = 4$ , and its area is $1^{2} = 1$ .

The perimeter of the first square is $\frac{7}{4} \times 4 = 7$ , and its sidelength is $7 \div 4 = \frac{7}{4}$ . The area of this square is therefore $\left (\frac{7}{4} \right )^{2} =\frac{49}{16}$ .

The ratio of the areas is therefore $\frac{49}{16} : 1 = 49:16$ .

A rectangular postage stamp has a width of 3 cm and a height of 12 cm. Find the area of the stamp.

Explanation

A rectangular postage stamp has a width of 3 cm and a height of 12 cm. Find the area of the stamp.

To find the area of a rectangle, we must perform the following:

$A_{Rectangle}=l*w$

Where l and w are our length and width.

This means we need to multiply the given measurements. Be sure to use the right units!

And we have our answer. It must be centimeters squared, because we are dealing with area.

Multiply the following:

$\frac{2}{3} \cdot 18$

Explanation

To multiply fractions, we will multiply the numerators together, then we will multiply the denominators together. Note that we do NOT need to find a common denominator.

So, in the problem

$\frac{2}{3} \cdot 18$