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HSPT Math : Concepts

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Example Questions

Example Question #391 : Arithmetic

What is a fraction form of .036?

Possible Answers:

$\dpi{100} \frac{36}{100}$

$\dpi{100} \frac{9}{250}$

$\dpi{100} \frac{1}{36}$

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

Correct answer:

$\dpi{100} \frac{9}{250}$

Explanation:

The fraction form of .036 is $\dpi{100} \frac{36}{1000}$ . None of our answers match this fraction, so we must reduce it. The easiest way to do so is to divide the top and bottom by 2.

$\dpi{100} \frac{36}{1000}=\frac{18}{500}$

We can divide by 2 again:

$\dpi{100} \frac{18}{500}=\frac{9}{250}$

This is one of our answers (and also the fraction in its most reduced form).

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Example Question #392 : Arithmetic

$\dpi{100} 2\frac{1}{4}+5\frac{4}{5}=$

Possible Answers:

$\dpi{100} 7\frac{4}{9}$

$\dpi{100} 8\frac{1}{20}$

$\dpi{100} 7\frac{4}{5}$

$\dpi{100} 8$

Correct answer:

$\dpi{100} 8\frac{1}{20}$

Explanation:

First add the whole numbers.

$\dpi{100} 2+5=7$

Then add the fractions. In order to this, the fractions need to have a common denominator. The denominators are 4 and 5, so we need to find the least common multiple of 4 and 5. We can do this by finding all the multiples of the larger number (5) and try to divide each of them by 4.

5: No

10: No

15: No

20: Yes

So the least common multiple is 20. We can multiply $\dpi{100} 4\times 5$ to get 20, and $\dpi{100} 5\times 4$ to get 20.

$\dpi{100} \frac{1}{4}+\frac{4}{5}=\frac{5\times 1}{5\times 4}+\frac{4\times 4}{4\times 5}=\frac{5}{20}+\frac{16}{20}=\frac{21}{20}$

We convert $\dpi{100} \frac{21}{20}$ to $\dpi{100} 1\frac{1}{20}$ and add it to 7 to get $\dpi{100} 8\frac{1}{20}$ .

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Example Question #393 : Arithmetic

What is $\frac{5}{12}-\frac{3}8{}=?$

Possible Answers:

$\frac{2}4{}$

$\frac{6}{8}$

$\frac{1}{24}$

$\frac{5}{6}$

Correct answer:

$\frac{1}{24}$

Explanation:

To subtract fractions we must first ensure that we have the same denominator which is the bottom part of the fraction.

To do this we must find the least common multiple of the denominators.

The least common multiple is the smallest number that multiples of both of the denominators multiply to. For example, for 2 and 6 it would be 6, for 2 and 5 it would be 10, for 3 and 8 it would be 24.

In this case the LCM is $8*3=24\:\:\:12*2=24$ .

We then multiply the numerator and denominator of the fractions by the numbers it takes to reach the LCM $\frac{5}{12}*\frac{2}{2}$ and $\frac{3}{8}*\frac{3}{3}$ to get the same denominator because anything divided by itself is one so the fractions maintain their same value as the numbers change into the format we need to determine the answer.

To multiply a fraction you multiply the top number of the first fraction by the top number of the second fraction and the bottom number of the first fraction by the bottom number of the second fraction.

After doing this we then subtract the first numerator (top part of the fraction) from the second numerator and place the result over the new denominator

$\frac{10}{24}-\frac{9}{24}=\frac{1}{24}$

The final answer is $\frac{1}{24}$

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Example Question #394 : Arithmetic

$\frac{4}{9}-\frac{1}{12}=$

Possible Answers:

$\frac{3}{9}$

$\frac{13}{36}$

$\frac{1}{4}$

Correct answer:

$\frac{13}{36}$

Explanation:

First, find a common denominator (36). Then, subtract the numerators.

The answer is $\frac{13}{36}$

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Example Question #395 : Arithmetic

Find the arithmetic mean of the following five numbers.

$\frac{2}{5}, \frac{1}{5},\frac{1}{2},\frac{3}{10}, \frac{2}{5}$

Possible Answers:

$\frac{3}{5}$

$\frac{9}{25}$

$\frac{7}{25}$

$\frac{2}{5}$

$\frac{6}{25}$

Correct answer:

$\frac{9}{25}$

Explanation:

Add the numbers, then divide by or, equivalently, multiply by $\frac{1}{5}$ .

$\frac{\frac{2}{5}+ \frac{1}{5}+\frac{1}{2}+\frac{3}{10}+ \frac{2}{5}}{5}$

$\frac{1}{5} \left(\frac{2}{5}+ \frac{1}{5}+\frac{1}{2}+\frac{3}{10}+ \frac{2}{5}\right )$

Find the common denominator of the terms we are adding.

$\frac{1}{5} \left(\frac{4}{10}+ \frac{2}{10}+\frac{5}{10}+\frac{3}{10}+ \frac{4}{10}\right )$

$\frac{1}{5} \left(\frac{4+2+5+3+4}{10} \right)$

Multiply and simplify.

$\frac{1}{5} \left(\frac{18}{10} \right)= \frac{1}{5} \left(\frac{9}{5} \right) = \frac{9}{25}$

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Example Question #396 : Arithmetic

Add:

$\frac{1}{9}+\frac{7}{3}$

Possible Answers:

$\frac{8}{3}$

$\frac{20}{9}$

$\frac{22}{9}$

$\frac{22}{3}$

$\frac{2}{3}$

Correct answer:

$\frac{22}{9}$

Explanation:

Rewrite using the lowest comon denominator. Since LCM (9, 3) = 9 :

$\frac{1}{9}+\frac{7}{3}=\frac{1}{9}+\frac{7\times 3}{3\times 3}=\frac{1}{9}+\frac{21}{9}=\frac{1+21}{9}=\frac{22}{9}$

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Example Question #6 : Addition With Fractions

Solve:

$\frac{3}{2}+\frac{7}{9}=$

Possible Answers:

$\frac{10}{11}$

$\frac{41}{18}$

$\frac{10}{9}$

Correct answer:

$\frac{41}{18}$

Explanation:

The least common multiple of 2 and 9 is 18.

$\frac{3}{2}=\frac{27}{18}$

$\frac{7}{9}=\frac{14}{18}$

$\frac{27}{18}+\frac{14}{18}=\frac{27+14}{18}=\frac{41}{18}$

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Example Question #397 : Arithmetic

$\frac{2}{5}+\frac{1}{5}=$

Possible Answers:

$\frac{3}{5}$

$\frac{2}{5}$

$\frac{5}{5}$

$\frac{1}{5}$

Correct answer:

$\frac{3}{5}$

Explanation:

Add the numerators:

$\frac{2}{5}+\frac{1}{5}=$ $\frac{3}{5}$

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Example Question #398 : Arithmetic

Which of the following expressions is equal to $6\frac{4}{5} + 4 \frac{2}{5}$ ?

Possible Answers:

10.4

10.8

11.2

10.2

Correct answer:

11.2

Explanation:

Rewrite both numbers as decimals:

$\frac{4}{5} = 4 \div 5 = 0.8$ , so $6\frac{4}{5} = 6.8$

$\frac{2}{5} = 2\div 5 = 0.4$ , so $4 \frac{2}{5} = 4.4$

Add the decimals vertically, lining up the decimal points:

6.8

$\underline{+4.4}$

11.2

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Example Question #399 : Arithmetic

Add the fractions below:

$\frac{3}{4}+\frac{5}{6}$

Possible Answers:

$1\frac{17}{24}$

$2\frac{7}{12}$

$1\frac{7}{24}$

$1\frac{5}{12}$

$1\frac{7}{12}$

Correct answer:

$1\frac{7}{12}$

Explanation:

To add fractions with different denominators, first the fractions should be rewritten as equivalent fractions with the same denominators. The simplest common denominator to get is the product of the denominators (i.e. $6\cdot 4=24$ , in this question). However, the best denominator to use is the least common denominator, which is the least common multiple of the denominators (which is 12 in this case).

$\frac{3}{4}+\frac{5}{6}= \left ( \frac{3}{4}\cdot \frac{3}{3} +\frac{5}{6}\cdot \frac{2}{2} \right )$

$=\frac{9}{12}+\frac{10}{12}$

Now the denominators are equal and we can add the numerators:

$\frac{9}{12}+\frac{10}{12}=\frac{19}{12}$

which can be written as:

$1\frac{7}{12}$

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #391 : Arithmetic

Example Question #392 : Arithmetic

Example Question #393 : Arithmetic

Example Question #394 : Arithmetic

Example Question #395 : Arithmetic

Example Question #396 : Arithmetic

Example Question #6 : Addition With Fractions

Example Question #397 : Arithmetic

Example Question #398 : Arithmetic

Example Question #399 : Arithmetic

All HSPT Math Resources

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