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Chapter 2: Problem 2

Express the following improper fractions as mixed fractions: (a) \(\frac{5}{4}\) (b) \(\frac{6}{5}\) (c) \(\frac{12}{5}\) (d) \(\frac{47}{3}\) (e) \(-\frac{62}{7}\)

Short Answer

Expert verified
Question: Convert the following improper fractions to mixed fractions: a) \(\frac{5}{4}\) b) \(\frac{6}{5}\) c) \(\frac{12}{5}\) d) \(\frac{47}{3}\) e) \(-\frac{62}{7}\) Answer: a) \(1\frac{1}{4}\) b) \(1\frac{1}{5}\) c) \(2\frac{2}{5}\) d) \(15\frac{2}{3}\) e) \(-8\frac{6}{7}\)

Step by step solution

01

a) \(\frac{5}{4}\)

Divide the numerator (5) by the denominator (4): 5 ÷ 4 = 1 (quotient) with a remainder of 1 Express the result as a mixed fraction: \(1\frac{1}{4}\)
02

b) \(\frac{6}{5}\)

Divide the numerator (6) by the denominator (5): 6 ÷ 5 = 1 (quotient) with a remainder of 1 Express the result as a mixed fraction: \(1\frac{1}{5}\)
03

c) \(\frac{12}{5}\)

Divide the numerator (12) by the denominator (5): 12 ÷ 5 = 2 (quotient) with a remainder of 2 Express the result as a mixed fraction: \(2\frac{2}{5}\)
04

d) \(\frac{47}{3}\)

Divide the numerator (47) by the denominator (3): 47 ÷ 3 = 15 (quotient) with a remainder of 2 Express the result as a mixed fraction: \(15\frac{2}{3}\)
05

e) \(-\frac{62}{7}\)

Divide the numerator (62) by the denominator (7): Note: The result will be negative since the fraction is negative. 62 ÷ 7 = -8 (quotient) with a remainder of 6 Express the result as a mixed fraction: \(-8\frac{6}{7}\)

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Most popular questions from this chapter

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 the following, expressing your answer as a mixed fraction: (a) \(3 \frac{2}{3} \div 1 \frac{1}{2}\) (b) \(6 \frac{1}{4} \div 2 \frac{2}{3}\) (c) \(10 \frac{3}{4} \div 2 \frac{1}{5}\) (d) \(-12 \frac{2}{5} \div 3 \frac{1}{4}\) (e) \(10 \frac{5}{6} \div\left(-4 \frac{1}{2}\right)\)

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.

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

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) \(10 \frac{4}{7}\)
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