Evaluate Numerical Expressions Involving Fractions: Problems with Solutions

Solution:
[tex](5.8-2.3)\times 1.24=(3.5)\times 1.24=4.34[/tex]

Solution:
[tex]LCM(5, 4, 3)=60[/tex] [tex](\frac{3}{5}-\frac{1}{4}+\frac{2}{3})\frac{2}{5}=(\frac{12 \times 3-15+20\times2}{60})\frac{2}{5}[/tex]

[tex](\frac{12\times3-15+20\times2}{60})\frac{2}{5}[/tex] =[tex]\frac{61}{60}\times \frac{2}{5}=\frac{122}{300}=\frac{61}{150}[/tex]

Solution:
[tex]LCM(5,3)=15[/tex]

[tex](\frac{3}{7}\div \frac{3}{2})(\frac{1}{5}+\frac{2}{3})=\frac{6}{21}\times (\frac{3+10}{15})=\frac{6}{21}\times \frac{13}{15}=\frac{78}{315}=\frac{26}{105}[/tex]

Solution:
[tex](3.2-1.9+2.5)\times 2.35=3.8\times 2.35=8.93[/tex]

Solution:
First off, we must change the mixed numbers into improper fractions.

[tex]2\frac{1}{5}=2+\frac{1}{5}=\frac{10+1}{5}=\frac{11}{5}[/tex]
[tex]3\frac{2}{7}=3+\frac{2}{7}=\frac{21+2}{7}=\frac{23}{7}[/tex]
[tex]1\frac{1}{4}=1+\frac{1}{4}=\frac{4+1}{4}=\frac{5}{4}[/tex]

Now we can perform the operations
[tex]LCM(5,7,4)=140[/tex]
[tex]2\frac{1}{5}-3\frac{2}{7}+1\frac{1}{4}=\frac{11}{5}-\frac{23}{7}+\frac{5}{4}[/tex]

[tex]\frac{11}{5}-\frac{23}{7}+\frac{5}{4}=\frac{308-460+175}{140}=\frac{23}{140}[/tex]

Solution:
We must change the mixed numbers into decimals.

[tex]4\frac{3}{5} = 4+\frac{3}{5} = \frac{20+3}{5} = \frac{23}{5} = 4.6[/tex]

[tex]3\frac{1}{4} = 3+\frac{1}{4} = 3 + 0.25 = 3.25[/tex]

We then carry out the operations

[tex](4\frac{3}{5}-2.24)3\frac{1}{4} = (4.6-2.24)3.25[/tex]

[tex](4.6-2.24)3.25 = 2.36\times 3.25 = 7.67[/tex]

Solution:
[tex]\frac{27}{8}\div \frac{4}{9}+\frac{3-20}{15}=\frac{27}{8}\div \frac{4}{9}- \frac{17}{15}[/tex]

[tex]\frac{27}{8}\div \frac{4}{9}-\frac{17}{15}=\frac{27 \times 9}{8\times4}-\frac{17}{15}= \frac{243}{32}-\frac{17}{15}=\frac{243\times 15-32 \times 17}{480}=\frac{3645-544}{480}= \frac{3101}{480}[/tex]

Solution:
[tex]3\frac{1}{3}=3+\frac{1}{3}=\frac{10}{3}\qquad 2\frac{1}{5}=2+\frac{1}{5}=\frac{11}{5}[/tex]

[tex](3.25+1.25-2.01)\div (3\frac{1}{3}+2\frac{1}{5})=(3.25+1.25-2.01)\div (\frac{10}{3}+\frac{11}{5})[/tex]

[tex](3.25+1.25-2.01)\div (\frac{10}{3}+\frac{11}{5})=2.49\div (\frac{50+33}{15})=2.49\div \frac{83}{15}[/tex]

[tex]2.49\div \frac{83}{15}=2.49\div 5.53=0.45[/tex]

Solution:
[tex]\left[ \left( \frac{3}{4}-\frac{1}{2}\right) +\left( \frac{2}{5}-\frac{1}{4}\right) \right] ^{2}=\left[ \left( \frac{3-2}{4}\right) +\left( \frac{8-5}{20}\right) \right]^{2}=\left[ \left( \frac{1}{4}\right) +\left( \frac{3}{20}\right) \right] ^{2}[/tex]

[tex]\left[ \left( \frac{1}{4}\right) +\left( \frac{3}{20}\right) \right]^{2}=\left[ \frac{5+3}{20}\right] ^{2}=\left[ \frac{8}{20}\right] ^{2}[/tex]
[tex]LCM(4,20)=20[/tex]

[tex]\left[ \frac{8}{20}\right] ^{2}=\frac{64}{400}=\frac{32}{200}=\frac{16}{100}=\frac{8}{50}=\frac{4}{25}[/tex]

Solution:
First off, we must change the mixed numbers into improper fractions.

[tex]3\frac{1}{2}=3+\frac{1}{2}=\frac{7}{2}[/tex]

[tex]2\frac{3}{4}=2+\frac{3}{4}=\frac{11}{4}[/tex]

[tex]\frac{\left( 3\frac{1}{2}-2\right) }{\left( 2\frac{3}{4}+1\right) }=\frac{ \left( \frac{7}{2}-2\right) }{\left( \frac{11}{4}+1\right) }=\frac{\left( \frac{7-4}{2}\right) }{\left( \frac{11+4}{4}\right) }=\frac{\frac{3}{2}}{ \frac{15}{4}}=\frac{12}{30}=\frac{6}{15}=\frac{2}{5}[/tex]

Solution:
[tex](2.5+1.8+3.4)\div \left( 2.35-1.25\right) =7.7\div 1.1=7[/tex]

Solution:
First off, we must change [tex]2\frac{3}{4}[/tex] into an improper fractions.

[tex]2\frac{3}{4}=2+\frac{3}{4}=\frac{11}{4}[/tex]

[tex]\frac{\left[ \left( \frac{3}{2}+\frac{1}{3}\right) \times \left( \frac{2}{5}+\frac{1}{4}\right) \right] }{\frac{11}{4}}=\frac{\left[ \left( \frac{9+2}{6}\right) \times \left( \frac{8+5}{20}\right) \right] }{\frac{11}{4}}[/tex]

[tex]LCM(4,5)=20\qquad LCM(2,3)=6[/tex]

[tex]\frac{\left[ \left( \frac{9+2}{6}\right) \times \left( \frac{8+5}{20}\right)\right] }{\frac{11}{4}}=\frac{\left[ \left( \frac{11}{6}\right) \times \left( \frac{13}{20}\right) \right] }{\frac{11}{4}}=\frac{\frac{143}{120}}{\frac{11}{4}}=\frac{572}{1320}=\frac{286}{660}=\frac{143}{330}[/tex]

Solution:
First off, we must change [tex]2\frac{1}{4}[/tex] into a decimal.

[tex]2\frac{1}{4} = \frac{9}{4} = 2.25[/tex]

[tex](4.7-1.6+2.3)\times 2\frac{1}{4} = (4.7-1.6+2.3)\times 2.25[/tex]

[tex](4.7-1.6+2.3)\times 2.25 = 5.4\times 2.25 = 12.15[/tex]

Solution:
[tex]3\frac{1}{4}=\frac{13}{4}[/tex]

[tex]2\frac{3}{5}=\frac{13}{5}[/tex]

[tex]5\frac{2}{3}=\frac{17}{3}[/tex]

[tex]1\frac{1}{2}=\frac{3}{2}[/tex]

[tex](3\frac{1}{4}-2\frac{3}{5})\div (5\frac{2}{3}+1\frac{1}{2})=(\frac{13}{4}-\frac{13}{5})\div (\frac{17}{3}+\frac{3}{2})[/tex]

[tex](\frac{13}{4}-\frac{13}{5})\div (\frac{17}{3}+\frac{3}{2})=(\frac{65-52}{20})\div (\frac{34+9}{6})=(\frac{13}{20})\div (\frac{43}{6})=\frac{13\times 6}{43\times 20}=\frac{78}{860}=\frac{39}{430}[/tex]

Solution:
First let we convert the fractions to decimals.

[tex]\frac{7}{4}=1.75\qquad 2\frac{1}{4}=2.25[/tex]

[tex](\frac{7}{4}+2\frac{1}{4}+5.25)^{2}=(1.75+2.25+5.25)^{2}=(9.25)^{2}=85.56[/tex]

Solution:
[tex]3\frac{3}{2}=\frac{9}{2}=4.5[/tex]

[tex](3\frac{3}{2})^{2}\div (7.20-2.35)=(4.5)^{2}\div (4.85)[/tex]

[tex](4.5)^{2}\div (4.85)=20.25\div 4.85=4.18[/tex]

Solution:
[tex](\frac{4}{3}-\frac{2}{5}+1)\div (\frac{3}{2}+3)=(\frac{20-6+15}{15})\div (\frac{3+6}{2})[/tex]

[tex]LCM(3,5,1)=15\qquad LCM(2,1)=2[/tex]

[tex](\frac{20-6+15}{15})\div (\frac{3+6}{2})=\frac{29}{15}\div \frac{9}{2}=\frac{58}{135}=\frac{58}{135}[/tex]

Solution:
[tex]2\frac{1}{4}=\frac{9}{4}=2.25[/tex]

[tex](5.24-2.49+2.25)^{2}=5^{2}=25[/tex]