General Fractions - PSAT Math

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Question

Simplify x/2 – x/5

Answer

Simplifying this expression is similar to 1/2 – 1/5. The denominators are relatively prime (have no common factors) so the least common denominator (LCD) is 2 * 5 = 10. So the problem becomes 1/2 – 1/5 = 5/10 – 2/10 = 3/10.

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Question

If $\dpi{100} \small \frac{p}{6}$ is an integer, which of the following is a possible value of $\dpi{100} \small p$ ?

Answer

$\dpi{100} \small \frac{0}{6}=0$ , which is an integer (a number with no fraction or decimal part). All the other choices reduce to non-integers.

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Question

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

Answer

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

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 $\frac{x^{2}}{3y^{3}z}$

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Question

Which of the following fractions is not equivalent to $\frac{6}{45}$ ?

Answer

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

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

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

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

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

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

$6 \times 2 = 12$ , but $45 \times 2 = 90$ .

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

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Question

Which of the following is not equal to 32/24?

Answer

24/32 = 1.33

16/12 =1.33

224/168 =1.33

4/3 = 1.33

96/72 = 1.33

160/96 = 1.67

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Question

Find the root of

$y=\frac{x^2-\sqrt3x+\sqrt5x-\sqrt{15}}{x-\sqrt3}$

Answer

$y=\frac{x^2-\sqrt3x+\sqrt5x-\sqrt{15}}{x-\sqrt3}=\frac{(x-\sqrt3)(x+\sqrt5)}{x-\sqrt3}=x+\sqrt5$

The root occurs where . So we substitute 0 for .

$y=x+\sqrt{5}$

$0=x+\sqrt{5}$

This means that the root is at $x=-\sqrt5$ .

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Question

Marker Colors Students
Blue 13
Pink 10
Orange 5
Brown 5
Green 7

The above chart shows the number of students in a class who chose each of the five marker colors available.

What fraction of the class selected a pink marker OR a brown marker?

Marker Colors	Students
Blue	13
Pink	10
Orange	5
Brown	5
Green	7

Answer

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:

$\frac{15}{40}$

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.

$\frac{15}{40}\div \frac{5}{5} = \frac{3}{8}$

The answer is $\frac{3}{8}$ .

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Question

Which of the following is greater than 1/2 ?

Answer

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.

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Question

Which of the following has the greatest value?

Answer

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

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Question

Which fraction falls between ½ and 3/4?

Answer

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.

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Question

If Ben is taller than Jaime, Mary is taller than Ben, and Chris is taller than Mary. Who is the second tallest?

Answer

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.

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Question

Order the following fractions in descending order.

1/2, 2/3, 2/5, 3/4, 4/7

Answer

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.

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Question

Answer

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Question

Which of the following fractions is between 0.2 and 0.3?

Answer

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

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

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

The other three choices are larger than 0.3.

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Question

Which of the following fractions is the greatest?

Answer

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 $\frac{3}{4}$ and $\frac{2}{3}$ by $\frac{3}{3}$ to get them to be $\frac{9}{12}$ and $\frac{6}{9}$ , respectively.

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

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Question

Order the following from least to greatest: three-fifths, seven-eighths, 0.5, sixteen-eighteenths, 97%, 17-fifths.

Answer

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

Let us re-write each as a fraction: $\frac{3}{5}$ , $\frac{7}{8}$ , $\frac{1}{2}$ , $\frac{16}{18}=\frac{8}{9}$ , $\frac{97}{100}$ , and $\frac{17}{5}$ . We can now easily order these:

$\frac{1}{2},\frac{3}{5},\frac{7}{8},\frac{8}{9},\frac{97}{100},\frac{17}{5}$

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Question

What is $3\frac{2}{5}$ as an improper fraction?

Answer

$3\frac{2}{5}$ becomes $3 + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5}$

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Question

To make 48 cookies you need 1 cup white sugar, 1 cup packed brown sugar and 3 cups of flour. You want to make 12 cookies, so you adjust the ingredients accordingly. After the adjustment, how many total cups of dry ingredients do you have?

Answer

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.

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Question

What is $\frac{17}{12}$ written as a mixed number?

Answer

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

So $\frac{17}{12}$ becomes $1\frac{5}{12}$

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Question

If , what does equal?

Answer

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

Solve for .

$x = \frac{20}{3}$

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:

$20\div3 = 6, remainder 2$

Therefore,

$x = 6\tfrac{2}{3}$

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General Fractions - PSAT Math

Simplify x/2 – x/5

Simplifying this expression is similar to 1/2 – 1/5. The denominators are relatively prime (have no common factors) so the least common denominator (LCD) is 2 * 5 = 10. So the problem becomes 1/2 – 1/5 = 5/10 – 2/10 = 3/10.

If is an integer, which of the following is a possible value of ?

, which is an integer (a number with no fraction or decimal part). All the other choices reduce to non-integers.

Simplify:

First, let's simplify . The greatest common factor of 4 and 12 is 4. 4 divided by 4 is 1 and 12 divided by 4 is 3. Therefore . To simply fractions with exponents, subtract the exponent in the numerator from the exponent in the denominator. That leaves us with or

Which of the following fractions is not equivalent to ?

Let us simplify : We can get alternate forms of the same fraction by multiplying the denominator and the numerator by the same number: Now let's look at : , but . Therefore, is the correct answer, as it is not equivalent to .

Which of the following is not equal to 32/24?

24/32 = 1.33 16/12 =1.33 224/168 =1.33 4/3 = 1.33 96/72 = 1.33 160/96 = 1.67

Find the root of

The root occurs where . So we substitute 0 for . This means that the root is at .

Marker ColorsStudentsBlue13Pink10Orange5Brown5Green7 The above chart shows the number of students in a class who chose each of the five marker colors available. What fraction of the class selected a pink marker OR a brown marker?

Which of the following is greater than 1/2 ?

Which of the following has the greatest value?

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

Which fraction falls between ½ and 3/4?

If Ben is taller than Jaime, Mary is taller than Ben, and Chris is taller than Mary. Who is the second tallest?

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.

Order the following fractions in descending order. 1/2, 2/3, 2/5, 3/4, 4/7

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.

Which of the following fractions is between 0.2 and 0.3?

The other three choices are larger than 0.3.

Which of the following fractions is the greatest?

Order the following from least to greatest: three-fifths, seven-eighths, 0.5, sixteen-eighteenths, 97%, 17-fifths.

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:

What is as an improper fraction?

becomes

To make 48 cookies you need 1 cup white sugar, 1 cup packed brown sugar and 3 cups of flour. You want to make 12 cookies, so you adjust the ingredients accordingly. After the adjustment, how many total cups of dry ingredients do you have?

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.

What is written as a mixed number?

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

If , what does equal?

If $\dpi{100} \small \frac{p}{6}$ is an integer, which of the following is a possible value of $\dpi{100} \small p$ ?

$\dpi{100} \small \frac{0}{6}=0$ , which is an integer (a number with no fraction or decimal part). All the other choices reduce to non-integers.

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

Which of the following fractions 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

Find the root of

$y=\frac{x^2-\sqrt3x+\sqrt5x-\sqrt{15}}{x-\sqrt3}$

$y=\frac{x^2-\sqrt3x+\sqrt5x-\sqrt{15}}{x-\sqrt3}=\frac{(x-\sqrt3)(x+\sqrt5)}{x-\sqrt3}=x+\sqrt5$

The root occurs where . So we substitute 0 for .

$y=x+\sqrt{5}$

$0=x+\sqrt{5}$

This means that the root is at $x=-\sqrt5$ .

Marker Colors Students
Blue 13
Pink 10
Orange 5
Brown 5
Green 7

The above chart shows the number of students in a class who chose each of the five marker colors available.

What fraction of the class selected a pink marker OR a brown marker?

Order the following fractions in descending order.

1/2, 2/3, 2/5, 3/4, 4/7

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

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

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

The other three choices are larger than 0.3.

What is $3\frac{2}{5}$ as an improper fraction?

$3\frac{2}{5}$ becomes $3 + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5}$

What is $\frac{17}{12}$ written as a mixed number?

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

So $\frac{17}{12}$ becomes $1\frac{5}{12}$