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HSPT Math : Concepts

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

Example Questions

Example Question #41 : How To Subtract Variables

Simplify:

(3x+2)-(4x-7)

Possible Answers:

-x+9

x-9

x+9

-x-5

x-5

Correct answer:

-x+9

Explanation:

When solving this problem we need to remember our order of operations, or PEMDAS.

PEMDAS stands for parentheses, exponents, multiplication/division, and addition/subtraction. When you have a problem with several different operations, you need to solve the problem in this order and you work from left to right for multiplication/division and addition/subtraction.

Parentheses: We are not able to add a variable to a number, so we move on to the next step

Multiplication: We can distribute the negative sign to the and

(3x+2)-(4x-7)

=3x+2-4x-(-7)

Remember, a negative times a negative will equal a positive, so we have a

=3x+2-4x+7

Finally we can combine like terms

3x-4x=-x

2+7=9

=-x+9

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Example Question #821 : Concepts

Solve for :

$\frac{3}{4} t = \frac{4}{3}$

Possible Answers:

$\frac{4}{9}$

$\frac{4}{3}$

$\frac{16}{9}$

$\frac{16}{3}$

Correct answer:

$\frac{16}{9}$

Explanation:

Divide both sides by $\frac{3}{4}$ :

$\frac{3}{4} t = \frac{4}{3}$

$\frac{3}{4} t \div \frac{3}{4}= \frac{4}{3} \div \frac{3}{4}$

$t = \frac{4}{3} \cdot \frac{4}{3} = \frac{4\cdot 4}{3\cdot 3} = \frac{16}{9}$

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Example Question #1 : How To Find The Solution To An Equation

$3a+8+7=14\times 3=$

Possible Answers:

Correct answer:

Explanation:

To solve:

First, solve both equations on each end, keeping the variable.

$\small 3a+ 8+ 7 = 14\cdot 3$

3a + 15= 42

Then, subtract 15 from each side of the equation.

3a +15-15=42-15

3a =27

Finally, divide each side by 3 so that only the variable remains.

$\small 3a\div 3=27\div 3$

$\small \small a=9$

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Example Question #3 : How To Find The Solution To An Equation

Solve for :

7n + 19 = 82

Possible Answers:

n=6

n = 7

n = 9

n = 10

n = 8

Correct answer:

n = 9

Explanation:

Subtract 19, then divide by 7:

7n + 19 = 82

7n + 19-19 = 82-19

7n = 63

$7n \div 7= 63 \div 7$

n = 9

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Example Question #2 : How To Find The Solution To An Equation

A bicycle originally costs $120.00. If it is on sale for 30% off, what is the sale price of the bicycle?

Possible Answers:

$\$84.00$

$\$156.00$

$\$90.00$

$\$117.00$

Correct answer:

$\$84.00$

Explanation:

First multiply the original price by 30%.

$120\ast .30=36$

Then subtract that amount from the original price.

120-36=84

The sale price is $84.00

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Example Question #212 : Algebra

$8\cdot \left ( 2\cdot 5 \right ) \div \left ( 4\cdot 1 \right )=$

Possible Answers:

Correct answer:

Explanation:

First solve the parentheses.

$8 * 10 \div 4=$

Then solve from left to right since multiplication and division are interchangeable:

$80\div 4=20$

The answer is 20.

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Example Question #213 : Algebra

$3 \frac{2}{6} \ast 2\frac{3}{4}=$

Possible Answers:

$9 \frac{1}{6}$

$22\frac{1}{6}$

Correct answer:

$9 \frac{1}{6}$

Explanation:

First, convert each mixed number into an improper fraction.

$\frac{20}{6}\ast \frac{11}{4}$

Then, reduce where possible and multiply.

Finally, convert your answer into a mixed-number fraction.

$\frac{55}{6}=9 {\frac{1}{6}}$

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Example Question #827 : Concepts

$11 \frac{1}{4} \div 5\frac{2}{5}=$

Possible Answers:

$2 \frac{1}{12}$

$2\frac{1}{18}$

Correct answer:

$2 \frac{1}{12}$

Explanation:

First, convert each mixed number into an improper fraction and flip the second fraction. Then, change the operation to multiplication:

$\frac{45}{4} \ast \frac{5}{27}=$

Reduce where possible and multiply. Convert your answer into a mixed fraction.

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Example Question #211 : Algebraic Concepts

$8^{3}\div 2^{2}=$

Possible Answers:

128

Correct answer:

128

Explanation:

First find the exponent value for each number:

$8^{3}\div 2^{2}=512 \div 4=$

Then divide accordingly. The answer is 128.

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Example Question #3 : Equations

11+39=12+28+2a

Possible Answers:

2.5

Correct answer:

Explanation:

First follow order of operations and solve on each side.

11+39=12+28+2a

50=40+2a

Then, subtract 40 from each side to leave only the variable:

50-40=40+2a-40

10=2a

Finally, divide both sides by 2.

$10\div 2=2a\div 2$

The answer is 5=a

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HSPT Math : Concepts

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #41 : How To Subtract Variables

Example Question #821 : Concepts

Example Question #1 : How To Find The Solution To An Equation

Example Question #3 : How To Find The Solution To An Equation

Example Question #2 : How To Find The Solution To An Equation

Example Question #212 : Algebra

Example Question #213 : Algebra

Example Question #827 : Concepts

Example Question #211 : Algebraic Concepts

Example Question #3 : Equations

All HSPT Math Resources

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