SSAT Upper Level Quantitative - Number Concepts and Operations

Convert into a fraction in simplest form.

$\frac{19}{50}$

$\frac{19}{25}$

$\frac{38}{50}$

$\frac{5}{19}$

Explanation

Think of the decimal as the fraction $\frac{0.38}{1}$ .

Now, multiply the numerator and denominator by for every digit after the decimal. In this case, because there are digits after the decimal, we will be multiplying by twice, or by .

$\frac{0.38}{1}\times 100=\frac{38}{100}$

Now, simplify this fraction.

$\frac{38}{100}=\frac{19}{50}$

Define an operation $\forall$ as follows:

For all real numbers :

$a \forall b = a^{4} + \frac{1}{b^{4}}$ .

Evaluate $\frac{1}{2} \forall (-2 )$ .

$\frac{1}{8}$

$16\frac{1}{16}$

$-15\frac{15}{16}$

The correct answer is not among the other responses.

Explanation

$a \forall b = a^{4} + \frac{1}{b^{4}}$

$\frac{1}{2} \forall (-2 ) = \left (\frac{1}{2} \right )^{4} + \frac{1}{(-2)^{4}}= \frac{1}{16} + \frac{1}{16} = \frac{2}{16} = \frac{1}{8}$

$\dpi{100} 4.8-\frac{9}{2}$

$\dpi{100} 0.3$

$\dpi{100} -5.2$

$\dpi{100} \frac{5}{2}$

$\dpi{100} 2$

Explanation

First convert $\dpi{100} \frac{9}{2}$ into a decimal.

$\dpi{100} 9\div 2=4\ remainder\ of\ 1$

So we are left with $\dpi{100} 4\frac{1}{2}$ , which is 4.5 in decimal form.

Now subtract:

$\dpi{100} 4.8-4.5=0.3$

Define an operation $\bigtriangleup$ on the real numbers as follows:

For all real numbers :

$a \bigtriangleup b = \sqrt[3]{a} - \sqrt[4]{b}$ .

Evaluate $(-1) \bigtriangleup (-1)$ .

The expression is undefined on the real numbers.

Explanation

$a \bigtriangleup b = \sqrt[3]{a} - \sqrt[4]{b}$

$(-1) \bigtriangleup (-1) = \sqrt[3]{-1} - \sqrt[4]{-1}$

However, $\sqrt[4]{-1}$ is undefined in the real numbers; subsequently, so is $(-1) \bigtriangleup (-1)$ .

Convert into a fraction in simplest form.

$\frac{19}{50}$

$\frac{19}{25}$

$\frac{38}{50}$

$\frac{5}{19}$

Explanation

Think of the decimal as the fraction $\frac{0.38}{1}$ .

Now, multiply the numerator and denominator by for every digit after the decimal. In this case, because there are digits after the decimal, we will be multiplying by twice, or by .

$\frac{0.38}{1}\times 100=\frac{38}{100}$

Now, simplify this fraction.

$\frac{38}{100}=\frac{19}{50}$

Put the fraction in simplest form.

$\frac{224}{400}$

$\frac{14}{25}$

$\frac{28}{50}$

$\frac{25}{14}$

$\frac{56}{100}$

Explanation

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

$\frac{224\div4}{400\div4}=\frac{56\div2}{100\div2}=\frac{28\div2}{50\div2}=\frac{14}{25}$

Convert $\frac{7}{9}$ to a percent.

Explanation

Percent also means out of one hundred. Set up the following ratio to find the percent value.

$\frac{7}{9}=\frac{x}{100}$

Now, solve for , which will be the percent value because in the ratio we set up, is the numerator of a fraction with a denominator of .

$x=\frac{700}{9}=77.8$

Multiply these fractions:

$\frac{1}{4}\cdot \frac{2}{5}$

$\frac{1}{10}$

$\frac{1}{5}$

$\frac{1}{20}$

$\frac{2}{9}$

Explanation

To multiply the fractions, simply multiply the numerators together and the denominators together.

$\frac{1}{4}\cdot \frac{2}{5}=\frac{1\cdot 2}{4\cdot 5}=\frac{2}{20}$

Then simplify the fraction accordingly:

$\frac{2\div 2}{20\div 2}=\frac{1}{10}$

Simplify:

$\frac{1+\frac{1}{x}}{3+\frac{3}{x}}$

$\frac{1}{3}$

$\frac{X+1}{X+3}$

Explanation

Simplify into a complex fraction for the numerator and denominator.

For the numerator, we need to multiply $1\cdot \left(\frac{x}{x}\right)$ then the top should read $\frac{x+1}{x}$ .

For the bottom, we need to multiply $3 \cdot \left(\frac{x}{x} \right )$ in order to add the components. Thus the bottom should read $\frac{3x+3}{x}$ .