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SAT Math : Mixed / Improper Fractions

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Example Questions

Example Question #1 : How To Find Out An Improper Fraction From A Mixed Fraction

What is $3\frac{2}{5}$ as an improper fraction?

Possible Answers:

$\frac{21}{5}$

$\frac{11}{5}$

$\frac{10}{2}$

$\frac{17}{5}$

$\frac{6}{2}$

Correct answer:

$\frac{17}{5}$

Explanation:

$3\frac{2}{5}$ becomes $3 + \frac{2}{5} = \frac{15}{5} + \frac{2}{5} = \frac{17}{5}$

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Example Question #1522 : Act Math

Write $71\frac{5}{7}$ as an improper fraction.

Possible Answers:

$\frac{355}{7}$

$\frac{76}{8}$

$\frac{76}{7}$

$\frac{360}{7}$

$\frac{502}{7}$

Correct answer:

$\frac{502}{7}$

Explanation:

To find the improper fraction value, we must effectively add together 71 and ⁵/₇. To do this, we will give 71 a denominator of 7; therefore, we are transforming ⁷¹/₁ to ^x/₇. The shortest way to do this is to multiply by ⁷/₇ (which really is 1); therefore, 71 = 71 * (⁷/₇) = ⁴⁹⁷/₇.

Now add them: ^{(497 + 5)}/₇ = ⁵⁰²/₇

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Example Question #1523 : Act Math

Which of the following improper fractions is equivalent to $14\frac{2}{5}$ ?

Possible Answers:

$\frac{70}{5}$

$\frac{72}{5}$

$\frac{24}{5}$

$\frac{84}{3}$

$\frac{16}{5}$

Correct answer:

$\frac{72}{5}$

Explanation:

To find an improper fraction, you need to multiply the whole number that you have by the denominator of the associated fraction. For our problem, this means that you will multiply by , getting . Next, you add this to the numerator of your fraction, giving you 70+2 , or . Finally, you place this over your original denominator, giving you:

$\frac{72}{5}$

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Example Question #1 : How To Find Out An Improper Fraction From A Mixed Fraction

Which of the following improper fractions is equivalent to $27\frac{4}{19}$ ?

Possible Answers:

$\frac{517}{19}$

$\frac{49}{19}$

$\frac{481}{19}$

$\frac{31}{19}$

$\frac{813}{17}$

Correct answer:

$\frac{517}{19}$

Explanation:

To find an improper fraction, you need to multiply the whole number that you have by the denominator of the associated fraction. For our problem, this means that you will multiply by , getting 513 . Next, you add this to the numerator of your fraction, giving you 513+4 , or 517 . Finally, you place this over your original denominator, giving you:

$\frac{517}{19}$

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Example Question #1 : How To Find Out A Mixed Fraction From An Improper Fraction

To make 48 cookies you need 1 cup white sugar, 1 cup packed brown sugar and 3 cups of flour. You want to make 12 cookies, so you adjust the ingredients accordingly. After the adjustment, how many total cups of dry ingredients do you have?

Possible Answers:

¹/₄ c

1 ¹/₂ c

1 ¹/₄ c

³/₄ c

1 ³/₄ c

Correct answer:

1 ¹/₄ c

Explanation:

Going from 48 cookies to 12 cookies is a scaling factor of ¹/₄, so all the ingredients get multiplied by ¹/₄. In order to make 12 cookies you will need ¹/₄ c white sugar, 1/4 c packed brown sugar, and ³/₄ c flour. Added all together you get ⁵/₄ or 1 ¹/₄ c.

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Example Question #2 : How To Find Out A Mixed Fraction From An Improper Fraction

What is $\frac{17}{12}$ written as a mixed number?

Possible Answers:

$2\frac{1}{6}$

$\frac{7}{12}$

$1\frac{1}{3}$

$1\frac{5}{12}$

$3\frac{1}{2}$

Correct answer:

$1\frac{5}{12}$

Explanation:

How many times does 12 go into 17? Once with a remainder of 5.

So $\frac{17}{12}$ becomes $1\frac{5}{12}$

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Example Question #2 : Mixed / Improper Fractions

Which of the following is the mixed fraction equivalent to $\frac{19}{3}$ ?

Possible Answers:

$6\frac{3}{5}$

$6\frac{1}{3}$

$\frac{13}{3}$

$8\frac{2}{3}$

$\frac{3}{19}$

Correct answer:

$6\frac{1}{3}$

Explanation:

To begin, notice that using your calculator, you can find:

$\frac{19}{3} = 6.33333...$

Now, the closest even multiple of that is less than is . Therefore, you know that your number is:

$\frac{19}{3}=\frac{18}{3}+\frac{1}{3}$

This is the same as:

$6+\frac{1}{3}$ , or simply, $6\frac{1}{3}$ . This is your mixed fraction.

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Example Question #4 : Mixed / Improper Fractions

Which of the following is equivalent to $\frac{82}{4}$ ?

Possible Answers:

$15\frac{1}{2}$

$20\frac{1}{4}$

$15\frac{3}{4}$

$20\frac{3}{8}$

$20\frac{1}{2}$

Correct answer:

$20\frac{1}{2}$

Explanation:

Although there are many ways to convert improper fractions into mixed fractions, the easiest way is to use your calculator to your advantage. Begin by dividing by . This gives you 20.5 . Therefore, you can eliminate all the options that have do not have for their first portion. Next, multiply 0.5 by the denominator (), and get . This means that you have and $\frac{2}{4}$ , or $\frac{1}{2}$ . Thus, your answer is $20\frac{1}{2}$ .

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Example Question #1 : How To Find Out A Mixed Fraction From An Improper Fraction

Convert $3\frac{3}{5}$ to an improper fraction.

Possible Answers:

$\frac{5}{18}$

$\frac{18}{5}$

$\frac{13}{5}$

$\frac{11}{5}$

$\frac{5}{13}$

Correct answer:

$\frac{18}{5}$

Explanation:

The denominator will stay the same. The new numerator of the improper fraction can be determined by multiplying the denominator with the whole number coefficient, and then adding the numerator.

$3\frac{3}{5}=\frac{(5\times3)+3}{5}=\frac{18}{5}$

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Example Question #4 : Mixed / Improper Fractions

Change $\frac{12}{7}$ into a mixed fraction.

Possible Answers:

$1\frac{6}{7}$

$1\frac{2}{7}$

$1\frac{7}{12}$

$1\frac{5}{12}$

$1\frac{5}{7}$

Correct answer:

$1\frac{5}{7}$

Explanation:

Divide 12 by 7. This means that seven goes into twelve one time. One times seven gives you seven. From here we subtract seven from twelve which give us our remainder of five.

$12\div7 = 1 \textup{ Remainder }5$

The remainder of five is a fraction of seven.

Write the mixed fraction.

The answer is:

$1\frac{5}{7}$

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SAT Math : Mixed / Improper Fractions

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Find Out An Improper Fraction From A Mixed Fraction

Example Question #1522 : Act Math

Example Question #1523 : Act Math

Example Question #1 : How To Find Out An Improper Fraction From A Mixed Fraction

Example Question #1 : How To Find Out A Mixed Fraction From An Improper Fraction

Example Question #2 : How To Find Out A Mixed Fraction From An Improper Fraction

Example Question #2 : Mixed / Improper Fractions

Example Question #4 : Mixed / Improper Fractions

Example Question #1 : How To Find Out A Mixed Fraction From An Improper Fraction

Example Question #4 : Mixed / Improper Fractions

All SAT Math Resources

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