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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

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6 Diagnostic Tests 130 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #4 : How To Find The Solution To An Equation

13 + 27=12+3+ 5a

Possible Answers:

5.5

Correct answer:

Explanation:

First solve with order of operations on each side:

13 + 27=12+3+ 5a

40 = 15+5a

Then subtract 15 from each side:

40-15=15+ 5a-15

25=5a

Finally, divide each side by 5:

$25\div 5=5a\div 5$

5=a

The answer is 5.

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Example Question #11 : Equations

$7 \ast \left ( 3\ast 5 \right )\div \left ( 25\div 5 \right )=$

Possible Answers:

Correct answer:

Explanation:

Solve inside the parentheses first:

$7 \ast (15) \div (5)=$

Follow order of operations to solve:

$105 \div 5=21$

The answer is 21.

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Example Question #831 : Concepts

Melissa is going on a road trip to her mother's house in another state. On a full tank of gas, she can travel 230 miles. At least how many times will she need to fill up her gas tank if her mother lives 950 miles away?

Possible Answers:

Correct answer:

Explanation:

Divide the total distance (950) by the number of miles per full tank of gas (230).

$950\div 230=4.1$

Therefore, she will have to fill up her tank with gas at least 5 times.

Answer is at least 5 times.

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Example Question #832 : Concepts

$12a + 2a -18= 3(6) + 2(5\ast 2)$

Possible Answers:

Correct answer:

Explanation:

First solve what is inside parentheses and follow the order of operations:

$12a + 2a -18= 3(6) + 2(5\ast 2)$

14a-18= 18+ 2(10)

14a -18= 18+20

14a-18=38

Then, add 18 to each side:

14a=56

Finally, divide each side my 14:

$14a \div 14= 56\div 14$

a=4

The answer is 4.

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Example Question #833 : Concepts

$3\frac{3}{9} \div 5\frac{1}{5}=$

Possible Answers:

$\frac{117}{75}$

$1\frac{3}{4}$

$\frac{25}{39}$

$1\frac{1}{2}$

Correct answer:

$\frac{25}{39}$

Explanation:

First, convert each fraction into an improper fraction.

$\frac{30}{9} \div \frac{26}{5}=$

Then, change the operation to multiplication and flip the second fraction.

$\frac{30}{9} \ast \frac{5}{26}=$

Reduce and multiply.

$\frac{30}{9}\ast \frac{5}{26}=\frac{10}{3}\ast \frac{5}{26}=\frac{5}{3}\ast \frac{5}{13}=\frac{25}{39}$

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Example Question #834 : Concepts

$7\frac{3}{6}\div 11\frac{2}{3}=$

Possible Answers:

$\frac{9}{14}$

$\frac{9}{16}$

Correct answer:

$\frac{9}{14}$

Explanation:

First, convert each mixed number into an improper fraction:

$\frac{45}{6}\div \frac{35}{3}=$

Then, change the operation to multiplication and flip the second fraction:

$\frac{45}{6}\ast \frac{3}{35}=$

Reduce and multiply:

$\frac{45}{6}\ast \frac{3}{35}=\frac{9}{2}\ast \frac{1}{7}=\frac{9}{14}$

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Example Question #835 : Concepts

$14\frac{2}{7}\div 2\frac{4}{14}=$

Possible Answers:

$6\frac{3}{6}$

$6\frac{1}{4}$

Correct answer:

$6\frac{1}{4}$

Explanation:

First, convert each fraction into an improper fraction. Then, change the operation to multiplication and flip the second fraction. Reduce and multiply.

$14\frac{2}{7}\div 2\frac{4}{14}=\frac{100}{7}\div \frac{32}{14}=\frac{100}{7}\cdot \frac{14}{32}=\frac{25}{1}\cdot \frac{2}{8}=\frac{50}{8}=\frac{25}{4}=6\frac{1}{4}$

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Example Question #836 : Concepts

Nelson received $64.00 in holiday gifts. If he would like to buy a baseball bat for $16.00, a glove for $34.00, and a cap for $11.00, how much money will he have left over?

Possible Answers:

$3.00

5.00

4.00

2.00

Correct answer:

$3.00

Explanation:

First, add up all the items on his wish list:

16+34+11=61

Then, subtract that amount from the original amount:

$64-61=\$ 3$

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Example Question #837 : Concepts

Angelina leaves her home at 6 AM. If she drives 65 miles per hour, what time will she arrive to her grandfather's home, 195 miles away?

Possible Answers:

11:00am

9:00pm

9:00am

10:00am

Correct answer:

9:00am

Explanation:

First, divide $195\div 65=3$ .

Then, calculate what time Angelina will arrive by adding 3 hours to 6:00.

6+3=9

The answer is 9:00 AM.

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Example Question #838 : Concepts

$\frac{\sqrt{36} \div \sqrt{4}}{2}=$

Possible Answers:

$1\frac{1}{2}$

$4\frac{1}{2}$

Correct answer:

$1\frac{1}{2}$

Explanation:

First, find the square root for each number:

$\sqrt{36}=6$

$\sqrt{4}=2$

Solve the equation accordingly:

$\frac{6\div 2}{2}=$

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

The answer is $1\frac{1}{2}$ .

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #4 : How To Find The Solution To An Equation

Example Question #11 : Equations

Example Question #831 : Concepts

Example Question #832 : Concepts

Example Question #833 : Concepts

Example Question #834 : Concepts

Example Question #835 : Concepts

Example Question #836 : Concepts

Example Question #837 : Concepts

Example Question #838 : Concepts

All HSPT Math Resources

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