ISEE Middle Level Quantitative Reasoning - Fractions

Which is equivalent to $\frac{12}{60}$ ?

Explanation

Divide:

$12\div 60=.20$

Answer:

Multiply the following:

$\frac{4}{5} \cdot \frac{2}{3}$

$\frac{8}{15}$

$\frac{6}{8}$

$\frac{22}{15}$

$\frac{4}{5}$

$\frac{10}{12}$

Explanation

When multiplying fractions, we will multiply the numerators together, then multiply the denominators together. We do NOT have to find a common denominator. So,

$\frac{4}{5} \cdot \frac{2}{3}$

$\frac{4 \cdot 2}{5 \cdot 3}$

$\frac{8}{15}$

Add:

$\frac{6}{61}+\frac{11}{61}=$

$\frac{17}{61}$

$\frac{5}{61}$

$\frac{66}{61}$

$\frac{61}{17}$

Explanation

Add the numerators and leave the denominators the same:

$\frac{6}{61}+\frac{11}{61}=\frac{17}{61}$

Answer:

$\frac{17}{61}$

Find the equivalent of $\frac{96}{320}$

Explanation

To solve, divide: $96\div 320=.30$

Answer:

Which decimal is equivalent to $\frac{45}{180}$ ?

Explanation

Divide the numerator (top number) by the denominator (bottom number):

$45\div 180=.25$

Answer:

What is the equivalent of $\frac{15}{100}$ ?

Explanation

To solve, divide: $15\div 100=.15$

Answer:

$\tfrac{3}{4} \times 12 =$

$\frac{1}{4}$

$\frac{1}{3}$

$\frac{1}{12}$

Explanation

When dealing with problems that involve fractions and whole numbers, first convert your whole number into a fraction. You can easily do this by putting the whole number over 1.

$12 \rightarrow\tfrac{12}{1}$

$\tfrac{3}{4}\times12=\tfrac{3}{4}\times\tfrac{12}{1}$

When multiplying, multiply the numerators by each other and the denominators by each other.

$\tfrac{3}{4} \times\tfrac{12}{1} = \tfrac{3\times12}{4\times1}=\tfrac{36}{4}$

Always reduce a fraction when possible. In this case, the numerator and denominator of $\tfrac{36}{4}$ are both divisible by 4. So, it reduces to 9.

$\tfrac{36}{4}=\tfrac{36\div4}{4\div4}=\tfrac{9}{1}=9$

$\tfrac{36}{4} \rightarrow\tfrac{9}{1}\rightarrow9$

What is the decimal equivalent to $\frac{52}{130}$ ?

Explanation

To solve, divide the numerator (top half of the fraction) by the denominator (bottom half of the fraction):

$52\div 130=.40$

Answer:

How many of the following four numbers are elements of the set

$A = \left { x ; | ; \frac{1}{2}< x < \frac{2}{3}\right } ?$

(A)

(B)

(C)

(D)

Three

None

One

Two

Four

Explanation

$\frac{1}{2} = 1\div 2 = 0.5$ and $\frac{2}{3} = 2 \div 3= 0.666...$ , so we choose the numbers that fall between these two. Of the four choices, only 0.67 is not between these two numbers. The correct response is "three".