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HSPT Math : Fractions

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Example Questions

Example Question #231 : Fractions

Two line segments have lengths of $2\frac{3}{4} inches$ $\displaystyle 2\frac{3}{4} inches$ and $2\frac{5}{6} inches.$ $\displaystyle 2\frac{5}{6} inches.$ What is the total measurement of these two line segments?

Possible Answers:

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

$5\frac{7}{12} inches$ $\displaystyle 5\frac{7}{12} inches$

$4\frac{11}{12} inches$ $\displaystyle 4\frac{11}{12} inches$

$4\frac{2}{3} inches$ $\displaystyle 4\frac{2}{3} inches$

Correct answer:

$5\frac{7}{12} inches$ $\displaystyle 5\frac{7}{12} inches$

Explanation:

$2\frac{3}{4} +2\frac{5}{6}$ $\displaystyle 2\frac{3}{4} +2\frac{5}{6}$

Convert all mixed numbers to improper fractions.

$2\frac{3}{4} = \frac{(4\times 2)+3}{4} = \frac{11}{4}$ $\displaystyle 2\frac{3}{4} = \frac{(4\times 2)+3}{4} = \frac{11}{4}$

$2\frac{5}{6} = \frac{(6\times 2)+5}{6} = \frac{17}{6}$ $\displaystyle 2\frac{5}{6} = \frac{(6\times 2)+5}{6} = \frac{17}{6}$

$\frac{11}{4} +\frac{17}{6}$ $\displaystyle \frac{11}{4} +\frac{17}{6}$

Because the denominators are not the same, find the LCD of 4 and 6.

Multiples of 4 are 4,8,12, 16.

Multiples of 6 are 6 and 12.

The LCM or the LCD of 4 and 6 is 12. Then, create equivalent fractions.

$\frac{11}{4} = \frac{33}{12}$ $\displaystyle \frac{11}{4} = \frac{33}{12}$ Both numerator and denominator were multiplied by 3.

$\frac{17}{6} =\frac{34}{12}$ $\displaystyle \frac{17}{6} =\frac{34}{12}$ Both numerator and denominator were multiplied by 2.

$\frac{33}{12} +\frac{34}{12} = \frac{33+34}{12} =\frac{67}{12}$ $\displaystyle \frac{33}{12} +\frac{34}{12} = \frac{33+34}{12} =\frac{67}{12}$

$\frac{67}{12} = 5\frac{7}{12}$ $\displaystyle \frac{67}{12} = 5\frac{7}{12}$

The sum of the two line segments is $5\frac{7}{12} inches.$ $\displaystyle 5\frac{7}{12} inches.$

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Example Question #521 : Concepts

What is a fraction form of .036?

Possible Answers:

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

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

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

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

Correct answer:

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

Explanation:

The fraction form of .036 is $\dpi{100} \frac{36}{1000}$ $\displaystyle \dpi{100} \frac{36}{1000}$. 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.

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

We can divide by 2 again:

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

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

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Example Question #522 : Concepts

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

Possible Answers:

$\dpi{100} 8$ $\displaystyle \dpi{100} 8$

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

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

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

Correct answer:

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

Explanation:

First add the whole numbers.

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

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 $\dpi{100} 4\times 5$ $\displaystyle \dpi{100} 4\times 5$ to get 20, and $\dpi{100} 5\times 4$ $\displaystyle \dpi{100} 5\times 4$ to get 20.

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

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

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HSPT Math : Fractions

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #231 : Fractions

Example Question #521 : Concepts

Example Question #522 : Concepts

All HSPT Math Resources

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