PSAT Math - Fractions | Practice Hub

Simplify:

$\frac{8x^3y^2z^2}{4xy^4z^3}$

$\frac{2x^2}{y^2z}$

$\frac{y^2z}{2x^2}$

Explanation

$\frac{8x^3y^2z^2}{4xy^4z^3}$

To simply a fraction with variables, subtract exponents of like bases:

This leaves us with the expression:

$2x^2y^{-2}z^{-1}$

Next, we know that to change negative exponents in the numerator into positive exponents, we place them in the denominator. Thus, our expression simplifies to:

$\frac{2x^2}{y^2z}$

Simplify the expression, $\left(\frac{x^2}{y^{-3}}\right)\left(\frac{x^{-1}}{y^3}\right)$ .

Can't be simplified

$\frac{x}{y^6}$

Explanation

The and variables with negative exponents can be rewritten with positive exponents by moving them from the denominator to the numerator, and vice versa. Therefore, the expression can be rewritten as

$\left(x^2y^3 \right) \left(\frac{1}{xy^3}\right) = \frac{x^2y^3}{xy^3}$ .

The exponents on the denominator can then be subtracted from the exponent in the numerator to give

$x^{2-1}y^{3-3} = x^1y^0 = x \cdot1 = x$

Which of the following fractions is between 0.2 and 0.3?

$\dpi{100} \small \frac{1}{4}$

$\dpi{100} \small \frac{1}{6}$

$\dpi{100} \small \frac{1}{3}$

$\dpi{100} \small \frac{1}{2}$

$\dpi{100} \small \frac{2}{3}$

Explanation

$\dpi{100} \small \frac{1}{4}=0.25$

$\dpi{100} \small 0.2<0.25<0.3$

$\dpi{100} \small \frac{1}{6}\approx 0.167<0.2$

The other three choices are larger than 0.3.

Which of the following fractions is between 0.2 and 0.3?

$\dpi{100} \small \frac{1}{4}$

$\dpi{100} \small \frac{1}{6}$

$\dpi{100} \small \frac{1}{3}$

$\dpi{100} \small \frac{1}{2}$

$\dpi{100} \small \frac{2}{3}$

Explanation

$\dpi{100} \small \frac{1}{4}=0.25$

$\dpi{100} \small 0.2<0.25<0.3$

$\dpi{100} \small \frac{1}{6}\approx 0.167<0.2$

The other three choices are larger than 0.3.

If a car travels at 30 mph, how many feet per second does travel?

44 ft/s

2,640 ft/s

4,400 ft/s

440 ft/s

264 ft/s

Explanation

30 miles / 1 hour * 5280 ft / 1 mile * 3600 seconds / 1 hour = 44 ft/sec

In a group of 20 children, 25% are girls. How many boys are there?

Explanation

Since $\dpi{100} \small \frac{1}{4}$ of the children are girls, this totals to $\dpi{100} \small 20 \times \frac{1}{4} = 5$ girls in the group.

$\dpi{100} \small 20-5=15$ boys.

The price of a computer is reduced by 1/8. The new price is then reduced by 1/6. What fraction of the original price is the current price?

1/48

1/24

35/48

23/24

13/48

Explanation

Let the original price = p.

After the first reduction, the price is (7/8)p

After the second reduction, the price is (5/6)(7/8)p = (35/48)p

There is a 5 to 3 ratio of red marbles to green marbles in a bucket. How many red marbles can be in a bucket of 40 marbles?

Explanation

In this problem, we use a proportion to solve for the number of red marbles in the bucket. Since the ratio is 5 to 3 we can set up a proportion of the red over total where the total is (red marbles + green marbles). We then set this proportion equal to over our new total, which is 40. Then we cross multiply and divide to get the number of red marbles in a bucket of 40 total marbles.

$\frac{red}{total}= \frac{x}{new\ total} ewline ewline \frac{5}{8}=\frac{x}{40} ewline ewline 5*40= 200 ewline ewline 200/8 = 25$

What is the reciprocal of the following fraction: 18/27

27/18

-18/27

9/27

Explanation

A fraction multiplied by its reciprocal will equal 1. To find the reciprocal of a fraction, switch the denominator and numerator. The reciprocal of 18/27 is 27/18.

What is the reciprocal of the following fraction: 18/27

27/18

-18/27

9/27

Explanation

A fraction multiplied by its reciprocal will equal 1. To find the reciprocal of a fraction, switch the denominator and numerator. The reciprocal of 18/27 is 27/18.

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