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HSPT Math : Fractions

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Example Question #221 : Fractions

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

Possible Answers:

$\frac{5}{7}$

$1\frac{1}{7}$

$\frac{6}{7}$

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

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 #222 : Fractions

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:

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

8 inches

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

16 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 #223 : Fractions

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

Possible Answers:

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

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

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

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 #221 : Fractions

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.

lbs.

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

$11\frac{1}{2}$ 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 #221 : 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:

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

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

cups

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

$-\frac{1}{4}$

$\frac{1}{4}$

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

$1\frac{1}{2}$

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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Example Question #227 : Fractions

$5\frac{5}{9} + 3 \frac{7}{9}$

Possible Answers:

$8 \frac{1}{3}$

$9\frac{1}{2}$

$9\frac{2}{3}$

$9\frac{1}{3}$

Correct answer:

$9\frac{1}{3}$

Explanation:

$5\frac{5}{9} + 3 \frac{7}{9}$

Add the whole numbers and fractions separately.

$(5 + 3) + \frac{5+7}{9}$

$8 + \frac{12}{9}$

$8 + 1\frac{3}{9} = 9 \frac{3}{9}$

Reduce to simplest form by dividing the numerator and the denominator by the greatest common factor of 3 and 9, which is 3.

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

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Example Question #228 : Fractions

$\frac{3x-1}{4x-1} + \frac{x-2}{x+3}$

Possible Answers:

$\frac{7x^{2}+x+1}{(4x-1) (x+3)}$

$\frac{7x^{2}+x-1}{(4x-1) (x+3)}$

$\frac{8x^{3}-1}{(4x-1)(x+3)}$

$\frac{7x^{2}-x-1}{(4x-1) (x+3)}$

Correct answer:

$\frac{7x^{2}-x-1}{(4x-1) (x+3)}$

Explanation:

$\frac{3x-1}{4x-1} + \frac{x-2}{x+3}$

The method for solving the addition of an algebraic fraction with unlike denominators is the same as the method for fractions with unlike denominators; find the common denominator.

The common denominator is (4x-1) (x+3)

Using the FOIL Method, cross multiply:

$(3x-1) (x+3) = 3x^{2} +8x-3$ .

Using the FOIL Method, cross multiply: $(x-2) (4x-1) = 4x^{2} -9x +2$ .

$\frac{3x^{2}+ 8x-3}{(4x-1) (x+3)} + \frac{4x^{2}-9x +2}{ (4x-1)(x+3)} =$ $\frac{7x^{2}-x-1}{(4x-1) (x+3)}$

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Example Question #221 : Fractions

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

Possible Answers:

$-\frac{8x +1}{x-3}$

$\frac{4x^{2}-12x-1}{x-3}$

$\frac{4x^{2}-12x+1}{x-3}$

$\frac{4x^{2}+12x+1}{x-3}$

Correct answer:

$\frac{4x^{2}-12x+1}{x-3}$

Explanation:

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

The method for solving the addition of an algebraic fraction with unlike denominators is the same as the method for fractions with unlike denominators; find the common denominator.

The common denominator is (x-3)

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

$4x (x-3) = 4x^{2} - 12x+1$

$\frac{4x}{1} +\frac{1}{(x-3)} =$

$\frac{4x^{2}-12x+1}{x-3}$

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Example Question #230 : Fractions

The measurement of the base of an isosceles triangles is $1\frac{5}{6} cm$ . The sides measure $1\frac{2}{3}cm$ each. What is the perimeter of this triangle?

Possible Answers:

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

$5\frac{1}{3}cm$

$5\frac{1}{6}cm$

$3\frac{1}{6}cm$

Correct answer:

$5\frac{1}{6}cm$

Explanation:

The formula for the perimeter of a triangle is P = a +b+c where each of the variables represents one of the measurements for each side of the triangle.

$1\frac{5}{6} + 1\frac{2}{3} + 1\frac{2}{3}$ Two sides of an isosceles triangle are equal.

Convert all mixed number (whole number and fraction), to improper fractions.

$1\frac{5}{6} = \frac{(6\times 1)+5}{6} = \frac{11}{6}$

$1\frac{2}{3} = \frac{(3\times 1)+2}{3} =\frac{5}{3}$

$\frac{11}{6} +\frac{5}{3} +\frac{5}{3}$

Because the denominators are not the same, create equivalent fractions with the same denominator. Find the least common multiple of LCM of 3 and 6.

Multiples of 3 are 3,6,9, and 12.

Multiples of 6 are 6,12, 18, 24, and 30.

The LCM which becomes the LCD or least common denominator of 3 and 6 is 6.

$\frac{5}{3} =\frac{10}{6}$

$\frac{11}{6} +\frac{10}{6} +\frac{10}{6} = \frac{11+10=10}{6} = \frac{31}{6}$

$\frac{31}{6} = 5\frac{1}{6}$

The perimeter of this isosceles triangle is $5\frac{1}{6}cm$ .

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HSPT Math : Fractions

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #221 : Fractions

Example Question #222 : Fractions

Example Question #223 : Fractions

Example Question #221 : Fractions

Example Question #221 : Fractions

Example Question #221 : Fractions

Example Question #227 : Fractions

Example Question #228 : Fractions

Example Question #221 : Fractions

Example Question #230 : Fractions

All HSPT Math Resources

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