General Fractions - PSAT Math

$\frac{0}{6}$=0, which is an integer (a number with no fraction or decimal part). All the other choices reduce to non-integers.

$$\frac{4x^{5}$$$y^{3}$$z}{12x^{3}$$y^{6}$$z^{2}$$}=\frac{x^{2}$$$}{3y^{3}$z}

First, let's simplify $\frac{4}{12}$. The greatest common factor of 4 and 12 is 4. 4 divided by 4 is 1 and 12 divided by 4 is 3. Therefore $\frac{4}{12}$=\frac{1}{3}$.

To simply fractions with exponents, subtract the exponent in the numerator from the exponent in the denominator. That leaves us with $$\frac{1}{3}$x^{2}$$y^{-3}$$z^{-1}$ or $$\frac{x^{2}$$$}{3y^{3}$z}

Let us simplify $\frac{6}{45}$:

$\frac{6}{45}$=\frac{3times 2}{3times 15}$=\frac{2}{15}$

We can get alternate forms of the same fraction by multiplying the denominator and the numerator by the same number:

$\frac{2times 2}{15times 2}$=\frac{4}{30}$

$\frac{2times 1.5}{15times 1.5}$=\frac{3}{22.5}$

Now let's look at $\frac{12}{89}$:

, but .

Therefore, $\frac{12}{89}$ is the correct answer, as it is not equivalent to $\frac{6}{45}$.

24/32 = 1.33

16/12 =1.33

224/168 =1.33

4/3 = 1.33

96/72 = 1.33

160/96 = 1.67

The root occurs where . So we substitute 0 for .

This means that the root is at .

To solve this problem, you must do three things: find out how many students selected a pink OR brown marker, make that a fraction with the total number of students in the class as the denominator, then simplify that fraction. Shown below:

Students who chose pink OR brown:

Pink: , Brown:

Total students:

Total students in the class:

Make it a fraction:

Simplify. To simplify a fraction, you must find the greatest common factor (GCF), then divide both the numerator and the denominator by the GCF. For and , the GCF is , because it is the largest number that goes into both numbers.

The answer is .

There are two ways to deal with fractions. One way is to convert them all to decimals. (By using your calculator, divide the numerator by the denominator). Using this method all you would need to do is to see which is greater than 0.5. Otherwise to see which is greater than 1/2, double the numerator and see if the result is greater than the denominator. In B, the correct answer, doubling the numerator gives us 12, which is bigger than 11.

If all are converted to decimals, 0.65 is the biggest.

The easiest method is to put each of these fractions into a calculator, and then place them in order on a number line to see which value falls in between 1/2 = 0.5 and ¾ = 0.75. Without a calculator you must do long division to find the value of the numerator (top number) divided by the denominator (bottom number) for each fraction. You can actually eliminate answers b. and d. because they are equal to 1/2 and ¾ respectively. 4/5= 0.80, 3/6 = 0.5, 5/8= 0.625, 6/8 = 0.75.

Using math symbols to dictate height we find that Ben>Jaime, Mary>Ben, Chris>Mary. Putting these in order we have Chris>Mary, Mary>Ben, Ben>Jaime. This shows that Mary is the second tallest.

Method 1:

Find the common denominator (420) and convert each fraction to this denominator:

1/2 = 210/420

2/3 = 280/420

2/5 = 168/420

3/4 = 315/420

4/7 = 240/420

Now sort by numerator, largest to smallest.

Method 2:

Divide each fraction to obtain a decimal. Sort the decimals, largest to smallest.

$\frac{1}{4}$=0.25

0.2<0.25<0.3

$\frac{1}{6}$approx 0.167<0.2

The other three choices are larger than 0.3.

The trick to this problem is to see that three of the choices have the numerator and denominator 3 units apart. The other two choices can be made three units apart as well- multiply both and by to get them to be and , respectively.

The trick is that once all fractions are the same units apart in denominator and numerator, the biggest number is the largest fraction.

We need to order: three fifths, seven eights, 0.5, sixteen eighteenths, 97%, seventeen fifths.

Let us re-write each as a fraction: , , , , , and . We can now easily order these:

becomes

Going from 48 cookies to 12 cookies is a scaling factor of 1/4, so all the ingredients get multiplied by 1/4. In order to make 12 cookies you will need 1/4 c white sugar, 1/4 c packed brown sugar, and 3/4 c flour. Added all together you get 5/4 or 1 1/4 c.

How many times does 12 go into 17? Once with a remainder of 5.

So becomes

First, you must solve the equation for . Then, you must convert the answer's improper fraction to a mixed fraction.

Solve for .

Now, to convert an improper fraction, you must see how many times the denominator goes into the numerator, and then leave the remainder as a fraction. Example below:

Find out how many times the denominator goes into the numerator:

Therefore,