HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

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Example Questions

Example Question #471 : Arithmetic

Subtract:

\displaystyle \frac{33}{45}-\frac{10}{45}=

Possible Answers:

\displaystyle \frac{23}{45}

\displaystyle 45

\displaystyle \frac{43}{45}

\displaystyle 43

Correct answer:

\displaystyle \frac{23}{45}

Explanation:

Subtract the numerators and keep the denominator the same:

\displaystyle \frac{33}{45}-\frac{10}{45}=\frac{23}{45}

Answer: \displaystyle \frac{23}{45}

Example Question #472 : Arithmetic

Solve:
\displaystyle \small \frac{17}{4}-\frac{6}{8}=

Possible Answers:

\displaystyle \small \frac{11}{4}

\displaystyle \frac{13}{4}

\displaystyle \small \frac{7}{2}

\displaystyle \small \frac{11}{8}

\displaystyle \small \frac{9}{2}

Correct answer:

\displaystyle \small \frac{7}{2}

Explanation:

The least common denominator between \displaystyle \small 4 and \displaystyle \small 8 is \displaystyle \small 8.

\displaystyle \small \frac{17}{4}=\frac{34}{8}

\displaystyle \small \frac{34}{8}-\frac{6}{8}=\frac{28}{8}=\frac{7}{2}

Example Question #1064 : Hspt Mathematics

Solve the equation:

\displaystyle \frac{65}{67}-\frac{2}{67}=

Possible Answers:

\displaystyle 4

\displaystyle \frac{60}{67}

\displaystyle \frac{63}{67}

\displaystyle 67

\displaystyle 63

Correct answer:

\displaystyle \frac{63}{67}

Explanation:

When subtracting fractions that have the same denominator, only the top numbers are subtracted. Subtract the numerators and leave the denominators the same:

\displaystyle \frac{65}{67}-\frac{2}{67}=\frac{63}{67}

Answer: \displaystyle \frac{63}{67}

Example Question #1065 : Hspt Mathematics

Subtract:\displaystyle \frac{52}{90}-\frac{10}{90}=

Possible Answers:

\displaystyle \frac{7}{15}

\displaystyle 42

\displaystyle \frac{42}{0}

\displaystyle \frac{62}{90}

\displaystyle 90

Correct answer:

\displaystyle \frac{7}{15}

Explanation:

Subtract the numerators and keep the denominators the same:

\displaystyle \frac{52}{90}-\frac{10}{90}=\frac{42}{90}

Reduce the fraction: \displaystyle \frac{42\div 2}{90 \div 2}=\frac{21}{45}

Reduce again: \displaystyle \frac{21\div 3}{45 \div 3}=\frac{7}{15}

Example Question #471 : Arithmetic

Solve:

\displaystyle \frac{1}{2}-\frac{3}{7}

Possible Answers:

\displaystyle \frac{3}{5}

\displaystyle -\frac{3}{5}

\displaystyle \frac{1}{14}

\displaystyle \frac{1}{7}

\displaystyle -\frac{1}{14}

Correct answer:

\displaystyle \frac{1}{14}

Explanation:

The lowest common denominator of 2 and 7 is 14.

\displaystyle \frac{1}{2}=\frac{7}{14}

\displaystyle \frac{3}{7}=\frac{6}{14}

\displaystyle \frac{7}{14}-\frac{6}{14}=\frac{1}{14}

Example Question #23 : How To Subtract Fractions

Subtract:

\displaystyle \frac{5}{15}-\frac{2}{15}=

Possible Answers:

\displaystyle \frac{3}{15}

\displaystyle \frac{7}{15}

\displaystyle \frac{6}{15}

\displaystyle \frac{1}{30}

\displaystyle \frac{1}{15}

Correct answer:

\displaystyle \frac{3}{15}

Explanation:

Subtract the numerators and leave the denominators the same:

\displaystyle \frac{5}{15}-\frac{2}{15}=\frac{3}{15}

Answer: \displaystyle \frac{3}{15}

Example Question #24 : How To Subtract Fractions

Subtract:

\displaystyle \frac{3}{12}-\frac{2}{12}=

Possible Answers:

\displaystyle \frac{1}{24}

\displaystyle \frac{1}{12}

\displaystyle 1

\displaystyle \frac{5}{12}

\displaystyle \frac{11}{12}

Correct answer:

\displaystyle \frac{1}{12}

Explanation:

Subtract the numerators and leave the denominators the same:

\displaystyle \frac{3}{12}-\frac{2}{12}=\frac{1}{12}

Answer: \displaystyle \frac{1}{12}

Example Question #472 : Arithmetic

\displaystyle \frac{20}{21}-\frac{14}{21}=

Possible Answers:

\displaystyle \frac{10}{21}

\displaystyle \frac{20}{21}

\displaystyle \frac{3}{21}

 

\displaystyle \frac{6}{21}

Correct answer:

\displaystyle \frac{6}{21}

Explanation:

Subtract the numerators and keep the denominator as is:

\displaystyle \frac{20}{21}-\frac{14}{21}=\frac{6}{21}

Answer: \displaystyle \frac{6}{21}

Example Question #471 : Arithmetic

Evaluate: 

Possible Answers:

Correct answer:

Explanation:

Rewrite as fractions with a common denominator:

Now, in the first number, "borrow" eight eighths from the units column:

Subtract fractions by subtracting denominators, then subtract integers.

Example Question #1 : How To Add Fractions

\displaystyle 1 \frac{1}{2} + 2 \frac{3}{4} =

Possible Answers:

\displaystyle 4.25

\displaystyle 3.75

\displaystyle 4.7

\displaystyle 4.5

\displaystyle 3.25

Correct answer:

\displaystyle 4.25

Explanation:

I think the easiest way to do this problem is to make a common denominator.  4 is the smallest common denominator.  

\displaystyle 2 \frac{3}{4} is equivalent to \displaystyle \frac{11}{4}.  

When you add \displaystyle \frac{6}{4} and \displaystyle \frac{11}{4} you get \displaystyle \frac{17}{4}.  

\displaystyle \frac{17}{4} reduces to and is equivalent to \displaystyle 4.25.

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