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

Short Answer

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Question: Convert the following mixed fractions to improper fractions: a) \(3 \frac{2}{3}\) b) \(5 \frac{2}{5}\) c) \(7 \frac{1}{2}\) d) \(-9 \frac{3}{4}\) e) \(10 \frac{4}{7}\) Answer: a) \(\frac{11}{3}\) b) \(\frac{27}{5}\) c) \(\frac{15}{2}\) d) \(\frac{-33}{4}\) e) \(\frac{74}{7}\)

Step by step solution

01

(a) Convert \(3 \frac{2}{3}\) to an improper fraction

First, multiply the whole number (3) by the denominator (3): \(3 \times 3 = 9\). Then add the numerator (2) to the result: \(9 + 2 = 11\). The improper fraction is \(\frac{11}{3}\).
02

(b) Convert \(5 \frac{2}{5}\) to an improper fraction

First, multiply the whole number (5) by the denominator (5): \(5 \times 5 = 25\). Then add the numerator (2) to the result: \(25 + 2 = 27\). The improper fraction is \(\frac{27}{5}\).
03

(c) Convert \(7 \frac{1}{2}\) to an improper fraction

First, multiply the whole number (7) by the denominator (2): \(7 \times 2 = 14\). Then add the numerator (1) to the result: \(14 + 1 = 15\). The improper fraction is \(\frac{15}{2}\).
04

(d) Convert \(-9 \frac{3}{4}\) to an improper fraction

First, multiply the whole number (-9) by the denominator (4): \(-9 \times 4 = -36\). Then add the numerator (3) to the result: \(-36 + 3 = -33\). The improper fraction is \(\frac{-33}{4}\).
05

(e) Convert \(10 \frac{4}{7}\) to an improper fraction

First, multiply the whole number (10) by the denominator (7): \(10 \times 7 = 70\). Then add the numerator (4) to the result: \(70+ 4 = 74\). The improper fraction is \(\frac{74}{7}\).

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Most popular questions from this chapter

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) \(10 \frac{5}{6} \div\left(-4 \frac{1}{2}\right)\)

Express each fraction as an equivalent fraction with a denominator of 32 : (a) \(\frac{1}{16}\) (b) \(\frac{3}{8}\) (c) \(\frac{1}{4}\)

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) \(\frac{16}{21} \times\left(-\frac{3}{4}\right)\)

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) \(-10 \frac{2}{5}\)

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