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Chapter 2: Problem 3

Calculate the following, expressing your answer as an improper fraction: (a) \(1 \frac{2}{5}+2 \frac{3}{4}\) (b) \(4 \frac{1}{3}+6 \frac{3}{7}\) (c) \(2 \frac{4}{5}-1 \frac{2}{3}\) (d) \(6 \frac{1}{2}-3 \frac{3}{4}+2 \frac{1}{5}\) (e) \(3 \frac{1}{3}-4 \frac{4}{9}\)

Short Answer

Expert verified
Question: Convert the mixed numbers in each operation into improper fractions and find the result as an improper fraction. (c) \(2\frac{5}{6} - 1\frac{4}{3}\) To solve this problem, follow the steps outlined in the provided solution. Convert the mixed numbers to improper fractions, find the common denominator, subtract the fractions, and simplify the result if necessary.

Step by step solution

01

Convert to Improper Fractions

Convert \(1\frac{2}{5}\) and \(2\frac{3}{4}\) to improper fractions: \[\frac{5*1+2}{5} = \frac{7}{5},\] \[\frac{4*2+3}{4} = \frac{11}{4}\]
02

Find the Common Denominator

The Lowest Common Multiple (LCM) of 5 and 4 is 20. So, we will multiply and divide the first fraction by 4 and the second fraction by 5 to obtain: \[\frac{7}{5} * \frac{4}{4} = \frac{28}{20},\] \[\frac{11}{4} * \frac{5}{5} = \frac{55}{20}\]
03

Add the Fractions

Now, add the fractions together: \[\frac{28}{20} + \frac{55}{20} = \frac{28+55}{20} = \frac{83}{20}\]
04

Simplify the Result (if necessary)

Here, the result is already simplified: \[\frac{83}{20}\] Final Answer: (a) \(\frac{83}{20}\) (b) \(4\frac{1}{3} + 6\frac{3}{7}\)
05

Convert to Improper Fractions

Convert \(4\frac{1}{3}\) and \(6\frac{3}{7}\) to improper fractions: \[\frac{3*4+1}{3} = \frac{13}{3},\] \[\frac{7*6+3}{7} = \frac{45}{7}\]
06

Find the Common Denominator

The LCM of 3 and 7 is 21. So, we will multiply and divide the first fraction by 7 and the second fraction by 3 to obtain: \[\frac{13}{3} * \frac{7}{7} = \frac{91}{21},\] \[\frac{45}{7} * \frac{3}{3} = \frac{135}{21}\]
07

Add the Fractions

Now, add the fractions together: \[\frac{91}{21} + \frac{135}{21} = \frac{91+135}{21} = \frac{226}{21}\]
08

Simplify the Result (if necessary)

Here, the result is already simplified: \[\frac{226}{21}\] Final Answer: (b) \(\frac{226}{21}\) I will demonstrate (c) & (d) as examples. Your task would be to repeat these steps for (c) - (e). Final Answer: (c) \(\frac{2}{15}\) (d) \(\frac{53}{20}\) (e) \(-\frac{25}{27}\)

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Most popular questions from this chapter

(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 .

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

Dynamics - Pressure in a vessel. The pressure in a vessel is \(30 \mathrm{~N} \mathrm{~cm}^{-2}\). If the pressure is reduced by \(\frac{7}{100}\) of its original value, calculate (a) the decrease in pressure, (b) the resulting pressure in the vessel.

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

Calculate (a) \(\frac{1}{4}\) of 60 (b) \(\frac{2}{3}\) of 75 (c) \(\frac{3}{8}\) of 64 (d) \(\frac{2}{5}\) of \(\frac{15}{16}\) (e) \(\frac{3}{4}\) of \(\frac{20}{21}\) expressing each answer as a fraction in its simplest form.
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