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HSPT Math : HSPT Mathematics

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

Example Questions

Example Question #216 : Fractions

$\frac{4}{5} - (-\frac{3}{5})$

Possible Answers:

$-\frac{1}{5}$

$1\frac{2}{5}$

$\frac{1}{5}$

$-1\frac{2}{5}$

Correct answer:

$1\frac{2}{5}$

Explanation:

$\frac{4}{5} - (-\frac{3}{5})$

When subtracting a negative, the subtraction and negative sign become an addition sign.

$\frac{4}{5} - (-\frac{3}{5}) = \frac{4}{5} + \frac{3}{5}$

$\frac{4}{5} + \frac{3}{5} = \frac{7}{5}$

$\frac{7}{5}$ is an improper fraction because the numerator is greater than the denominator. Therefore, it needs to be simplified. This is done by dividing the numerator by the denominator.

$7\div 5 = 1 \frac{2}{5}$

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Example Question #217 : Fractions

Find a-b if

$a = 6\frac{1}{3}$ and

$b=-1\frac{1}{3}$

Possible Answers:

$7\frac{2}{3}$

$-7\frac{2}{3}$

Correct answer:

$7\frac{2}{3}$

Explanation:

Find a-b if

$a = 6\frac{1}{3}$ and

$b=-1\frac{1}{3}$

$6\frac{1}{3} - (-1\frac{1}{3}) = 6\frac{1}{3} + 1\frac{1}{3}$

When subtracting a negative, the sign becomes a plus sign which indicates addition.

$6\frac{1}{3} + 1\frac{1}{3} = (6+1) + \frac{1+1}{3}$

$7\frac{2}{3}$

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Example Question #218 : Fractions

$8\frac{1}{10 } - 3\frac{7}{10}$

Possible Answers:

$4\frac{3}{5}$

$5\frac{3}{5}$

$4\frac{2}{5}$

$5\frac{2}{5}$

Correct answer:

$4\frac{2}{5}$

Explanation:

$8\frac{1}{10 } - 3\frac{7}{10}$

Because the numerator of the second mixed number (7) is greater than the numerator of the first mixed number (1) and the operation is subtraction, convert both mixed numbers into improper fractions.

$8\frac{1}{10} = \frac{(10\times 8)+1}{10} = \frac{81}{10}$

$3\frac{7}{10 } = \frac{(10\times 3)+7}{10} = \frac{37}{10}$

$\frac{81}{10} -\frac{37}{10} =\frac{81-37}{10}$

$\frac{44}{10} = 4\frac{4}{10} = 4\frac{2}{5}$

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Example Question #501 : Concepts

Find a + b if

a = 5/12 and

$b = -1\frac{1}{12}$

Possible Answers:

$-\frac{2}{3}$

$-\frac{3}{4}$

$1\frac{1}{3}$

$1\frac{1}{2}$

Correct answer:

$-\frac{2}{3}$

Explanation:

Find a + b if

a = 5/12 and

$b = -1\frac{1}{12}$

$\frac{5}{12} + (-1\frac{1}{12})$

Convert the mixed number to an improper fraction.

$\frac{5}{12} + (-\frac{13}{12}) =$

$\frac{5+ (-13)}{12} = \frac{-8}{12}$

Reduce to simplest form by dividing the numerator and the denominator by the GCF or the Greatest Common Factor which is 4.

$\frac{-8\div 4}{12\div 4} = -\frac{2}{3}$

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Example Question #511 : Arithmetic

$-1\frac{3}{7} - (-2\frac{2}{7})$

Possible Answers:

$-1\frac{1}{7}$

$\frac{5}{7}$

$\frac{6}{7}$

$1\frac{1}{7}$

Correct answer:

$\frac{6}{7}$

Explanation:

$-1\frac{3}{7} - (-2\frac{2}{7})$

The subtraction of a negative changes the subtraction and negative sign to a plus sign, indicating addition.

$-1\frac{3}{7} + 2\frac{2}{7}$

Because the numerator of the negative fraction is greater than the numerator of the positive fraction, convert both to a mixed number.

$- 1\frac{3}{7} = -\frac{10}{7}$

$2\frac{2}{7} = \frac{16}{7}$

$-\frac{10}{7} + \frac{16}{7} = \frac{6}{7}$

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Example Question #512 : Arithmetic

Find the perimeter of a rectangle wholes length is $4\frac{1}{4}$ inches and the width is $3\frac{3}{4}$ inches.

Possible Answers:

$7 \frac{3}{4} inches$

16 inches

$15 \frac{1}{2} inches$

8 inches

Correct answer:

16 inches

Explanation:

The formula for the perimeter of a rectangle is P = 2(l+w).

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

$(4+3) + (\frac{1+3}{4})$

$7 + \frac{4}{4} = 7 + 1 = 8$

2 (8) = 16

The perimeter of the rectangle is 16 inches.

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Example Question #222 : Fractions

Mary is $58\frac{1}{4}$ inches tall. Jane is $56\frac{3}{4}$ inches tall. How much taller is Mary?

Possible Answers:

$1\frac{1}{2}$ inches

$1\frac{1}{4}$ inches

inches

$1\frac{3}{4}$ inches

Correct answer:

$1\frac{1}{2}$ inches

Explanation:

$58\frac{1}{4} -56\frac{3}{4} =$

Convert both mixed numbers to improper fractions.

$58 \frac{1}{4} = \frac{(4\times58)+1 }{4} = \frac{233}{4}$

$56\frac{3}{4} = \frac{(4\times 56)+3}{4} = \frac{227}{4}$

$\frac{233}{4} - \frac{227}{4} = \frac{233-227}{4}$

$\frac{6}{4} = 1\frac{2}{4} = 1\frac{1}{2}$

Mary is $1\frac{1}{2}$ inches taller than Jane.

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Example Question #513 : Arithmetic

John weighs $125 \frac{5}{8}$ lbs. The total combined weight for John and his pet dog is $136\frac{3}{8}$ lbs. How much does John's dog weigh?

Possible Answers:

$11\frac{3}{8}$ lbs.

$11\frac{1}{2}$ lbs.

$10\frac{3}{4}$ lbs.

lbs.

Correct answer:

$10\frac{3}{4}$ lbs.

Explanation:

$136\frac{3}{8} - 125\frac{5}{8}=$

Convert both mixed numbers to improper fractions.

$136\frac{3}{8} =\frac{(8\times136) +3}{8} =\frac{1091}{8}$

$125\frac{5}{8} = \frac{(8\times 125)+5}{8} =\frac{1005}{8}$

$\frac{1091-1005}{8} = \frac{86}{8}$

$\frac{86}{8} = 10\frac{6}{8} = 10\frac{3}{4}$

The weight of John's dog is $10 \frac{3}{4}$ lbs.

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Example Question #223 : Fractions

Donna poured $1\frac{3}{4}$ cups of chocolate chips into a mixing bowl. Then she added $3\frac{3}{4}$ cups of of pancake mix. What is the total amount of ingredients in the bowl?

Possible Answers:

cups

$5\frac{1}{4}$ cups

$5\frac{1}{2}$ cups

$5\frac{3}{4}$ cups

Correct answer:

$5\frac{1}{2}$ cups

Explanation:

$1\frac{3}{4} +3\frac{3}{4} =$

Add the whole numbers and fractions separately:

$(1+3) + \frac{3+3}{4}$

$4 + \frac{6}{4} = 4 + 1\frac{2}{4} = 5\frac{2}{4}$

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

There was a total of $5\frac{1}{2}$ cups of ingredients in the mixing bowl.

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Example Question #221 : Fractions

Solve.

$\frac{5}{8} + (-\frac{7}{8})$

Possible Answers:

$-1\frac{1}{2}$

$\frac{1}{4}$

$-\frac{1}{4}$

$1\frac{1}{2}$

Correct answer:

$-\frac{1}{4}$

Explanation:

$\frac{5}{8} + (-\frac{7}{8}) =$

These fractions are like fractions because the denominators are the same.

When the denominator is the same, just add the numerators.

5 + (-7) = -2

$\frac{-2}{8} = -\frac{1}{4}$

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HSPT Math : HSPT Mathematics

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #216 : Fractions

Example Question #217 : Fractions

Example Question #218 : Fractions

Example Question #501 : Concepts

Example Question #511 : Arithmetic

Example Question #512 : Arithmetic

Example Question #222 : Fractions

Example Question #513 : Arithmetic

Example Question #223 : Fractions

Example Question #221 : Fractions

All HSPT Math Resources

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