Simplifying Fractions - SSAT Upper Level Quantitative (Math)

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Question

Reduce $\frac{16}{60}$ to lowest terms, call the sum of the numerator and the denominator. Which statement is true of ?

Answer

$\frac{16}{60} = \frac{16 \div 4}{60 \div 4} = \frac{4}{15}$

Add the numerator and the denominator:

The correct response is therefore $15 < N \le 20$ .

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Question

Reduce the fraction $\frac{39}{111}$ to lowest terms, and call the product of the numerator and the denominator of the simplified fraction. Give the value of .

Answer

$\frac{39 \div 3}{111 \div 3} = \frac{13}{37}$

Multiply the numerator and the denominator: $13 \times 37 = 481$

The product is a three-digit number.

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Question

Rewrite the mixed fraction $6\frac{12}{15}$ as an improper fraction in lowest terms, and call the product of the numerator and the denominator of the simplified improper fraction. How many digits does have?

Answer

$\frac{12}{15} = \frac{12 \div 3}{15 \div 3} = \frac{4}{5}$ , so $6\frac{12}{15}$ simplifies to $6\frac{4}{5}$ .

The numerator of the improper form of a mixed fraction is the original numerator added to the product of the integer and the original denominator. The new denominator is the same as the old one. Therefore,

$6\frac{4}{5} = \frac{6 \times 5 + 4}{5} = \frac{30+4}{5} = \frac{34}{5}$

Multiply the numerator and the denominator: $34 \times 5 = 170$ ,

a three-digit number.

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Question

Consider a fraction $\frac{N}{65}$ , where the numerator is unknown. How many of the following values of would yield a fraction not in lowest terms?

I)

II)

III)

IV)

Answer

The prime factorization of is $5 \times 13$ , so the fraction $\frac{N}{65}$ is reducible if and only if is a multiple of 5 or 13.

We can immediately tell that 115 is the only multiple of 5, so we test the other numbers to see if there is a multiple of 13. We soon see that

$117 \div 13 = 9$ , so 116 and 118 cannot be multples of 13.

115 and 117 are the only values of that yield reducible fractions, so the correct response is two.

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Question

Put the fraction in the simplest form.

$\frac{24}{36}$

Answer

To put a fraction in simplest form, keep dividing the numerator and denominator by the same number until you cannot go any further.

$\frac{24\div2}{36\div2}=\frac{12}{18}$

$\frac{12\div2}{18\div2}=\frac{6}{9}$

$\frac{6\div3}{9\div3}=\frac{2}{3}$

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Question

Put the fraction in simplest form.

$\frac{224}{400}$

Answer

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

$\frac{224\div4}{400\div4}=\frac{56\div2}{100\div2}=\frac{28\div2}{50\div2}=\frac{14}{25}$

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Question

Put the fraction in simplest form.

$\frac{48}{120}$

Answer

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

$\frac{48\div12}{120\div12}=\frac{4\div2}{10\div2}=\frac{2}{5}$

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Question

Put the fraction in simplest form.

$\frac{36}{120}$

Answer

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

$\frac{36 \div 12}{120 \div 12}=\frac{3}{10}$

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Question

Put the fraction in simplest form.

$\frac{20}{36}$

Answer

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

$\frac{20\div4}{36\div4}=\frac{5}{9}$

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Question

Put the fraction in simplest form.

$\frac{24}{100}$

Answer

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

$\frac{24\div4}{100\div4}=\frac{6}{25}$

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Question

Put the fraction in simplest form.

$\frac{36}{84}$

Answer

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder.

$\frac{36\div12}{84\div12}=\frac{3}{7}$

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Question

Put the fraction in simplest form.

$\frac{12x}{30}$

Answer

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder. Since only the numerator has , leave the variable alone.

$\frac{12x\div6}{30\div6}=\frac{2x}{5}$

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Question

Put the fraction in simplest form.

$\frac{30x}{75x}$

Answer

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder. Since both the numerator and the denominator have in them, consider the fraction like this:

$\frac{30x}{75x}=\frac{30}{75}\times\frac{x}{x}$

$\frac{x}{x}=1$

$\frac{30x}{75x}=\frac{30}{75}\times\frac{x}{x}=\frac{30}{75}\cdot 1=\frac{30}{75}$

$\frac{30\div15}{75\div15}=\frac{2}{5}$

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Question

Put the fraction in simplest form.

$\frac{48t}{60s}$

Answer

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder. Since we have different variables in the numerator and the denominator, leave the variables alone.

$\frac{48t\div12}{60s\div12}=\frac{4t}{5s}$

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Question

Put the fraction in simplest form.

$\frac{96x}{224y}$

Answer

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder. Since the variables in the numerator and denominator are not the same, leave them alone.

$\frac{96x\div2}{224y\div2}=\frac{48x\div4}{112y\div4}=\frac{12x\div4}{28y\div4}=\frac{3x}{7y}$

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Question

Put the fraction in simplest form.

$\frac{57a}{300q}$

Answer

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder. Since the variables in the numerator and denominator are different, leave the variables alone.

$\frac{57a\div3}{300q\div3}=\frac{19a}{100q}$

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Question

Put the fraction in simplest form.

$\frac{96m}{220h}$

Answer

To simplify a fraction, divide both the numerator and the denominator by the same numbers until there is no number that can divide them both without resulting in a remainder. Since the variables in the numerator and denominator are different, leave them alone.

$\frac{96m\div4}{220h\div4}=\frac{24m}{55h}$

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Question

Fill in the blank with the missing fraction.

$\frac{1}{7}\times\frac{?}{?}=\frac{3}{21}$

Answer

In this problem we are making equivalent fractions. In order to make equivalent fractions you have to multiply the numerator and the denominator by the same number.

$1\times3=3$

$7\times3=21$

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Question

Fill in the blank with the missing fraction.

$\frac{2}{5}\times\frac{?}{?}=\frac{4}{10}$

Answer

In this problem we are making equivalent fractions. In order to make equivalent fractions you have to multiply the numerator and the denominator by the same number.

$2\times2=4$

$5\times2=10$

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Question

Fill in the blank with the missing fraction.

$\frac{3}{4}\times\frac{?}{?}=\frac{9}{12}$

Answer

In this problem we are making equivalent fractions. In order to make equivalent fractions you have to multiply the numerator and the denominator by the same number.

$3\times3=9$

$4\times3=12$

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