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HSPT Math : Arithmetic

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Example Questions

Example Question #471 : Arithmetic

Subtract:

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

Possible Answers:

$\frac{23}{45}$ $\displaystyle \frac{23}{45}$

$\displaystyle 45$

$\frac{43}{45}$ $\displaystyle \frac{43}{45}$

$\displaystyle 43$

Correct answer:

$\frac{23}{45}$ $\displaystyle \frac{23}{45}$

Explanation:

Subtract the numerators and keep the denominator the same:

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

Answer: $\frac{23}{45}$ $\displaystyle \frac{23}{45}$

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Example Question #472 : Arithmetic

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

Possible Answers:

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

$\frac{13}{4}$ $\displaystyle \frac{13}{4}$

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

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

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

Correct answer:

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

Explanation:

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

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

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

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Example Question #1064 : Hspt Mathematics

Solve the equation:

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

Possible Answers:

$\displaystyle 4$

$\frac{60}{67}$ $\displaystyle \frac{60}{67}$

$\frac{63}{67}$ $\displaystyle \frac{63}{67}$

$\displaystyle 67$

$\displaystyle 63$

Correct answer:

$\frac{63}{67}$ $\displaystyle \frac{63}{67}$

Explanation:

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

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

Answer: $\frac{63}{67}$ $\displaystyle \frac{63}{67}$

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Example Question #1065 : Hspt Mathematics

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

Possible Answers:

$\frac{7}{15}$ $\displaystyle \frac{7}{15}$

$\displaystyle 42$

$\frac{42}{0}$ $\displaystyle \frac{42}{0}$

$\frac{62}{90}$ $\displaystyle \frac{62}{90}$

$\displaystyle 90$

Correct answer:

$\frac{7}{15}$ $\displaystyle \frac{7}{15}$

Explanation:

Subtract the numerators and keep the denominators the same:

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

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

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

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Example Question #471 : Arithmetic

Solve:

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

Possible Answers:

$\frac{3}{5}$ $\displaystyle \frac{3}{5}$

$-\frac{3}{5}$ $\displaystyle -\frac{3}{5}$

$\frac{1}{14}$ $\displaystyle \frac{1}{14}$

$\frac{1}{7}$ $\displaystyle \frac{1}{7}$

$-\frac{1}{14}$ $\displaystyle -\frac{1}{14}$

Correct answer:

$\frac{1}{14}$ $\displaystyle \frac{1}{14}$

Explanation:

The lowest common denominator of 2 and 7 is 14.

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

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

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

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Example Question #23 : How To Subtract Fractions

Subtract:

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

Possible Answers:

$\frac{3}{15}$ $\displaystyle \frac{3}{15}$

$\frac{7}{15}$ $\displaystyle \frac{7}{15}$

$\frac{6}{15}$ $\displaystyle \frac{6}{15}$

$\frac{1}{30}$ $\displaystyle \frac{1}{30}$

$\frac{1}{15}$ $\displaystyle \frac{1}{15}$

Correct answer:

$\frac{3}{15}$ $\displaystyle \frac{3}{15}$

Explanation:

Subtract the numerators and leave the denominators the same:

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

Answer: $\frac{3}{15}$ $\displaystyle \frac{3}{15}$

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Example Question #24 : How To Subtract Fractions

Subtract:

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

Possible Answers:

$\frac{1}{24}$ $\displaystyle \frac{1}{24}$

$\frac{1}{12}$ $\displaystyle \frac{1}{12}$

$\displaystyle 1$

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

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

Correct answer:

$\frac{1}{12}$ $\displaystyle \frac{1}{12}$

Explanation:

Subtract the numerators and leave the denominators the same:

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

Answer: $\frac{1}{12}$ $\displaystyle \frac{1}{12}$

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Example Question #472 : Arithmetic

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

Possible Answers:

$\frac{10}{21}$ $\displaystyle \frac{10}{21}$

$\frac{20}{21}$ $\displaystyle \frac{20}{21}$

$\frac{3}{21}$ $\displaystyle \frac{3}{21}$

$\frac{6}{21}$ $\displaystyle \frac{6}{21}$

Correct answer:

$\frac{6}{21}$ $\displaystyle \frac{6}{21}$

Explanation:

Subtract the numerators and keep the denominator as is:

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

Answer: $\frac{6}{21}$ $\displaystyle \frac{6}{21}$

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Example Question #471 : Arithmetic

Evaluate: $8 \tfrac{1}{4} - 5 \tfrac{7}{8}$

Possible Answers:

$3\tfrac{1}{2}$ $\displaystyle 3\tfrac{1}{2}$

$2\tfrac{3}{8}$ $\displaystyle 2\tfrac{3}{8}$

$3\tfrac{1}{8}$ $\displaystyle 3\tfrac{1}{8}$

$3\tfrac{5}{8}$ $\displaystyle 3\tfrac{5}{8}$

$3\tfrac{7}{32}$ $\displaystyle 3\tfrac{7}{32}$

Correct answer:

$2\tfrac{3}{8}$ $\displaystyle 2\tfrac{3}{8}$

Explanation:

Rewrite as fractions with a common denominator:

$8 \tfrac{1}{4} - 5 \tfrac{7}{8}$

$8 \tfrac{2}{8} - 5 \tfrac{7}{8}$

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

$7 \tfrac{8+2}{8} - 5 \tfrac{7}{8}$

$7 \tfrac{10}{8} - 5 \tfrac{7}{8}$

Subtract fractions by subtracting denominators, then subtract integers.

$7 \tfrac{10}{8}$ $\displaystyle 7 \tfrac{10}{8}$

$\underline{5 \tfrac{7}{8}}$

$2 \tfrac{3}{8}$ $\displaystyle 2 \tfrac{3}{8}$

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Example Question #1 : How To Add Fractions

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

Possible Answers:

4.25 $\displaystyle 4.25$

3.75 $\displaystyle 3.75$

4.7 $\displaystyle 4.7$

4.5 $\displaystyle 4.5$

3.25 $\displaystyle 3.25$

Correct answer:

4.25 $\displaystyle 4.25$

Explanation:

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

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

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

$\frac{17}{4}$ $\displaystyle \frac{17}{4}$ reduces to $4 \frac{1}{4}}$ $\displaystyle 4 \frac{1}{4}}$ and is equivalent to 4.25 $\displaystyle 4.25$ .

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HSPT Math : Arithmetic

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #471 : Arithmetic

Example Question #472 : Arithmetic

Example Question #1064 : Hspt Mathematics

Example Question #1065 : Hspt Mathematics

Example Question #471 : Arithmetic

Example Question #23 : How To Subtract Fractions

Example Question #24 : How To Subtract Fractions

Example Question #472 : Arithmetic

Example Question #471 : Arithmetic

Example Question #1 : How To Add Fractions

All HSPT Math Resources

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