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HSPT Math : Fractions

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Example Questions

Example Question #31 : Fractions

Which of the following is the reciprocal of $-1 \frac {4}{5}$ $\displaystyle -1 \frac {4}{5}$ ?

Possible Answers:

$-\frac {5}{9}$ $\displaystyle -\frac {5}{9}$

$-5 \frac {1}{4}$ $\displaystyle -5 \frac {1}{4}$

$\frac {5}{9}$ $\displaystyle \frac {5}{9}$

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

Correct answer:

$-\frac {5}{9}$ $\displaystyle -\frac {5}{9}$

Explanation:

First, rewrite this as an improper fraction:

$-1 \frac {4}{5} =-\frac {5 \times 1+ 4}{5}= -\frac {9}{5}$ $\displaystyle -1 \frac {4}{5} =-\frac {5 \times 1+ 4}{5}= -\frac {9}{5}$

The reciprocal of an improper fraction can be found by switching its numerator and denominator, retaining the negative sign, so the reciprocal is $-\frac {5}{9}$ $\displaystyle -\frac {5}{9}$ .

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Example Question #32 : Fractions

Which of the following is the reciprocal of 2.8?

Possible Answers:

$\frac{5}{14}$ $\displaystyle \frac{5}{14}$

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

$2 \frac{4}{5}$ $\displaystyle 2 \frac{4}{5}$

$-2 \frac{4}{5}$ $\displaystyle -2 \frac{4}{5}$

Correct answer:

$\frac{5}{14}$ $\displaystyle \frac{5}{14}$

Explanation:

First, rewrite this as an improper fraction:

$2.8 = \frac{28}{10} = \frac{28\div 2}{10\div 2} = \frac{14}{5}$ $\displaystyle 2.8 = \frac{28}{10} = \frac{28\div 2}{10\div 2} = \frac{14}{5}$

The reciprocal of an improper fraction can be found by switching its numerator and denominator, so the reciprocal is $\frac{5}{14}$ $\displaystyle \frac{5}{14}$ .

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Example Question #21 : Fractions

Solve:

$\frac{3}{7}\div \frac{1}{5}$ $\displaystyle \frac{3}{7}\div \frac{1}{5}$

Possible Answers:

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

$\frac{1}{2}$ $\displaystyle \frac{1}{2}$

$\frac{3}{35}$ $\displaystyle \frac{3}{35}$

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

Correct answer:

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

Explanation:

$\frac{3}{7}\div \frac{1}{5}=\frac{3}{7}\times \frac{5}{1}=\frac{15}{7}$ $\displaystyle \frac{3}{7}\div \frac{1}{5}=\frac{3}{7}\times \frac{5}{1}=\frac{15}{7}$

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Example Question #33 : Fractions

Which of the following is the reciprocal of 31.25?

Possible Answers:

0.036 $\displaystyle 0.036$

0.028 $\displaystyle 0.028$

0.024 $\displaystyle 0.024$

0.032 $\displaystyle 0.032$

Correct answer:

0.032 $\displaystyle 0.032$

Explanation:

Rewrite 31.25 as a fraction:

$31.25 = \frac{3,125}{100} = \frac{3,125\div 25}{100\div 25} = \frac{125}{4}$ $\displaystyle 31.25 = \frac{3,125}{100} = \frac{3,125\div 25}{100\div 25} = \frac{125}{4}$

Exchange the positions of the numerator and the denominator to get $\frac{4}{125}$ $\displaystyle \frac{4}{125}$ . Now divide 4 by 125:

$\frac{4}{125} = 4 \div 125 = 0.032$ $\displaystyle \frac{4}{125} = 4 \div 125 = 0.032$

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Example Question #22 : Fractions

Solve:

$\frac{9}{10}\div \frac{3}{5}=$ $\displaystyle \frac{9}{10}\div \frac{3}{5}=$

Possible Answers:

$\frac{5}{6}$ $\displaystyle \frac{5}{6}$

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

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

$\small \frac{6}{5}$ $\displaystyle \small \frac{6}{5}$

Correct answer:

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

Explanation:

$\small \frac{9}{10}\div \frac{3}{5}=\frac{9}{10}\times\frac{5}{3}=\frac{45}{30}=\frac{3}{2}$ $\displaystyle \small \frac{9}{10}\div \frac{3}{5}=\frac{9}{10}\times\frac{5}{3}=\frac{45}{30}=\frac{3}{2}$

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Example Question #34 : Fractions

$\frac{7}{49}\div \frac{2}{14}=$ $\displaystyle \frac{7}{49}\div \frac{2}{14}=$

Possible Answers:

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

$\displaystyle 49$

$\frac{2}{94}$ $\displaystyle \frac{2}{94}$

196 $\displaystyle 196$

$\displaystyle 1$

Correct answer:

$\displaystyle 1$

Explanation:

Change division to multiplication by flipping the second fraction. Then, simplify and perform the multiplication.

$\frac{7}{49}\div \frac{2}{14}=$ $\displaystyle \frac{7}{49}\div \frac{2}{14}=$

$\frac{7}{49}\times \frac{14}{2}= \frac{1}{7}\times \frac{7}{1}=\frac{7}{7}=1$ $\displaystyle \frac{7}{49}\times \frac{14}{2}= \frac{1}{7}\times \frac{7}{1}=\frac{7}{7}=1$

The answer is 1.

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Example Question #504 : Numbers And Operations

$12 \frac{4}{6} \div 4\frac{2}{4}=$ $\displaystyle 12 \frac{4}{6} \div 4\frac{2}{4}=$

Possible Answers:

$2\frac{20}{27}$ $\displaystyle 2\frac{20}{27}$

$3\frac{1}{3}$ $\displaystyle 3\frac{1}{3}$

$2\frac{22}{27}$ $\displaystyle 2\frac{22}{27}$

$2\frac{7}{9}$ $\displaystyle 2\frac{7}{9}$

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

Correct answer:

$2\frac{22}{27}$ $\displaystyle 2\frac{22}{27}$

Explanation:

First convert each fraction into an improper fraction.

$\frac{76}{6}\div \frac{18}{4}=$ $\displaystyle \frac{76}{6}\div \frac{18}{4}=$

Then flip the second fraction, reduce and multiply:

$\frac{76}{6}\ast \frac{4}{18}=$ $\displaystyle \frac{76}{6}\ast \frac{4}{18}=$

The answer is $2\frac{22}{27}$ $\displaystyle 2\frac{22}{27}$ .

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Example Question #921 : Hspt Mathematics

Divide:

$\frac{4}{9}\div \frac{2}{3}$ $\displaystyle \frac{4}{9}\div \frac{2}{3}$

Possible Answers:

$\frac{1}{}3$ $\displaystyle \frac{1}{}3$

$\frac{7}{}9$ $\displaystyle \frac{7}{}9$

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

$\frac{4}{}9$ $\displaystyle \frac{4}{}9$

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

Correct answer:

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

Explanation:

The first step in dividing fractions is to make the second fraction a reciprocal (flip it) and then rewrite the problem as a multiplication problem: $\left(\frac{4}{9}\times \frac{3}{2}\right)$ $\displaystyle \left(\frac{4}{9}\times \frac{3}{2}\right)$ .

You can cross-reduce so that the problem now becomes $\left(\frac{2}{3}\times \frac{1}{1}\right)$ $\displaystyle \left(\frac{2}{3}\times \frac{1}{1}\right)$ . Then, mulitply straight across so that your answer is $\frac{2}{3}$ $\displaystyle \frac{2}{3}$ .

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Example Question #534 : Numbers And Operations

What is the value of $\displaystyle x$ in this equation?

$\frac{9}{5}\div \frac{5}{7}=x$ $\displaystyle \frac{9}{5}\div \frac{5}{7}=x$

Possible Answers:

$\frac{25}{63}$ $\displaystyle \frac{25}{63}$

$\frac{63}{25}$ $\displaystyle \frac{63}{25}$

$\frac{9}{7}$ $\displaystyle \frac{9}{7}$

$\frac{7}{9}$ $\displaystyle \frac{7}{9}$

Correct answer:

$\frac{63}{25}$ $\displaystyle \frac{63}{25}$

Explanation:

In order to solve $\frac{9}{5}\div \frac{5}{7}$ $\displaystyle \frac{9}{5}\div \frac{5}{7}$ , the latter fraction must be inverted and then multiplied by the first fraction, as shown below:

$\frac{9}{5}\cdot \frac{7}{5} = \frac{63}{25}$ $\displaystyle \frac{9}{5}\cdot \frac{7}{5} = \frac{63}{25}$

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Example Question #31 : Fractions

$\frac{7}{16}*\frac{8}{3}=?$ $\displaystyle \frac{7}{16}*\frac{8}{3}=?$

Possible Answers:

$\frac{15}{19}$ $\displaystyle \frac{15}{19}$

$\frac{6}{7}$ $\displaystyle \frac{6}{7}$

$\frac{7}{6}$ $\displaystyle \frac{7}{6}$

$\frac{56}{19}$ $\displaystyle \frac{56}{19}$

Correct answer:

$\frac{7}{6}$ $\displaystyle \frac{7}{6}$

Explanation:

To multiply a fraction you multiply the top number of the first fraction by the top number of the second fraction and the bottom number of the first fraction by the bottom number of the second fraction.

So $\frac{(7*8)}{(16*3)}$ $\displaystyle \frac{(7*8)}{(16*3)}$

Then simplify the answer by dividing by the greatest common factor. $\frac{(56/8)}{(48/8)}$ $\displaystyle \frac{(56/8)}{(48/8)}$

After performing this the answer is $\frac{7}{6}$ $\displaystyle \frac{7}{6}$ .

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HSPT Math : Fractions

Study concepts, example questions & explanations for HSPT Math

All HSPT Math Resources

Example Questions

Example Question #31 : Fractions

Example Question #32 : Fractions

Example Question #21 : Fractions

Example Question #33 : Fractions

Example Question #22 : Fractions

Example Question #34 : Fractions

Example Question #504 : Numbers And Operations

Example Question #921 : Hspt Mathematics

Example Question #534 : Numbers And Operations

Example Question #31 : Fractions

All HSPT Math Resources

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