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Chapter 2: Problem 3

Express each of the following improper fractions as mixed fractions: (a) \(\frac{20}{3}\) (b) \(\frac{32}{7}\) (c) \(\frac{60}{9}\) (d) \(\frac{102}{50}\) (e) \(\frac{120}{11}\)

Short Answer

Expert verified
Question: Convert the following improper fractions to mixed fractions: (a) \(\frac{20}{3}\) (b) \(\frac{32}{7}\) (c) \(\frac{60}{9}\) (d) \(\frac{102}{50}\) (e) \(\frac{120}{11}\) Answer: (a) \(6\frac{2}{3}\) (b) \(4\frac{4}{7}\) (c) \(6\frac{2}{3}\) (d) \(2\frac{1}{25}\) (e) \(10\frac{10}{11}\)

Step by step solution

01

Identify the improper fraction

An improper fraction is a fraction in which the numerator is greater than the denominator.
02

Divide the numerator by the denominator

For each given improper fraction, perform the division to find the quotient as the whole number part and the remainder as a new numerator over the original denominator.
03

(a) Convert \(\frac{20}{3}\)

Divide 20 by 3 to get the quotient (6) and remainder (2). So, the mixed fraction is \(6\frac{2}{3}\).
04

(b) Convert \(\frac{32}{7}\)

Divide 32 by 7 to get the quotient (4) and remainder (4). So, the mixed fraction is \(4\frac{4}{7}\).
05

(c) Convert \(\frac{60}{9}\)

First simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD) which is 3. So, \(\frac{60}{9} = \frac{20}{3}\), now divide 20 by 3 to get the quotient (6) and remainder (2). So, the mixed fraction is \(6\frac{2}{3}\).
06

(d) Convert \(\frac{102}{50}\)

First simplify the fraction by dividing both the numerator and the denominator by their greatest common divisor (GCD) which is 2. So, \(\frac{102}{50} = \frac{51}{25}\), now divide 51 by 25 to get the quotient (2) and remainder (1). So, the mixed fraction is \(2\frac{1}{25}\).
07

(e) Convert \(\frac{120}{11}\)

Divide 120 by 11 to get the quotient (10) and remainder (10). So, the mixed fraction is \(10\frac{10}{11}\).

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Most popular questions from this chapter

Express each of the following mixed fractions as an improper fraction: (a) \(3 \frac{2}{3}\) (b) \(5 \frac{2}{5}\) (c) \(7 \frac{1}{2}\) (d) \(-9 \frac{3}{4}\) (e) \(10 \frac{4}{7}\)

Express each of the following fractions in their simplest form: (a) \(\frac{12}{60}\) (c) \(\frac{27}{81}\) (d) \(\frac{6}{92}\) (e) \(\frac{377}{390}\)

Calculate (a) \(\frac{6}{7} \times \frac{14}{27}\) (b) \(\frac{7}{10} \times \frac{4}{5} \times \frac{30}{49}\) (c) \(\frac{8}{9} \times \frac{18}{25}\) (d) \(\left(-\frac{4}{5}\right) \times\left(-\frac{3}{4}\right)\) (e) \(\frac{16}{21} \times\left(-\frac{3}{4}\right)\)

(a) Express \(\frac{3}{5}\) as an equivalent fraction with a denominator of 40 . (b) Express \(\frac{9}{30}\) as an equivalent fraction with a denominator of 10 . (c) Express 6 as an equivalent fraction with a denominator of 4 .

Thermodynamics - Cooling of a liquid. The temperature of a liquid is measured every 20 minutes and the results recorded in the table below. \begin{tabular}{lrllllrr} \hline Time \((\min )\) & 0 & 20 & 40 & 60 & 80 & 100 & 120 \\ Temp \(\left({ }^{\circ} \mathrm{C}\right)\) & 96 & 88 & 81 & 76 & 72 & 70 & 68 \\\ \hline \end{tabular} Calculate the rate of decrease of temperature. in units of \({ }^{\circ} \mathrm{C}\) per minute: (a) in the first 20 minutes (b) in the first 40 minutes (c) in the first 60 minutes (d) in the last 60 minutes (e) in the last 20 minutes In each case express your answer as a fraction in its simplest form.
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