Fractions: answer key to 5th grade math exercises in PDF.

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The answer key to the 5th grade math exercises on fractions in PDF. Develop skills in addition and subtraction and comparison of fractions in fifth grade.

Exercise 1:

$A=\frac{2}{3}-\frac{1}{6}$

$A=\frac{2\times \,2}{3\times \,2}-\frac{1}{6}$

$A=\frac{4}{6}-\frac{1}{6}$

$A=\frac{3:3}{6:3}$

${\color{DarkRed}\,A=\frac{1}{2}}$

$B=\frac{2\times \,10}{3\times \,10}+\frac{7}{30}$

$B=\frac{20}{30}+\frac{7}{30}$

$B=\frac{27:3}{30:3}$

${\color{DarkRed}\,B=\frac{9}{10}}$

$C=\frac{17}{18}-\frac{1}{6}$

$C=\frac{17}{18}-\frac{1\times \,3}{6\times \,3}$

$C=\frac{17}{18}-\frac{3}{18}$

$C=\frac{14:2}{18:2}$

${\color{DarkRed}\,C=\frac{7}{9}}$

$D=\frac{1}{21}+\frac{2}{3}$

$D=\frac{1}{21}+\frac{2\times \,7}{3\times \,7}$

$D=\frac{1}{21}+\frac{14}{21}$

$D=\frac{15:3}{21:3}$

${\color{DarkRed}\,D=\frac{5}{7}}$

Exercise 2:

Calculate:

$A=\frac{3}{5}+\frac{6}{5}$

$A=\frac{3+6}{5}=\frac{9}{5}$

$B=\frac{7-2}{9}=\frac{5}{9}$

$C=\frac{6}{10}+\frac{1}{10}$

$C=\frac{6+1}{10}=\frac{7}{10}$

$D=\frac{8}{13}-\frac{3}{13}$

$D=\frac{8-3}{13}=\frac{5}{13}$

Exercise 3:
Express the shaded area as a fraction of the area of the large square.

Detail your calculations.

$\frac{1}{3}+\frac{1}{6}+\frac{1}{9}=\frac{6}{18}+\frac{3}{18}+\frac{2}{18}=\frac{11}{18}$

The shaded area represents the $\frac{11}{18}$ of the area of the large square.

Exercise 4:

For each of the figures below, express the colored part

using a fraction of the area of the large square.

Figure 1:

$\frac{7}{16}$

Figure 2:

$\frac{1}{3}+\frac{1}{6}+\frac{1}{9}=\frac{6}{18}+\frac{3}{18}+\frac{2}{18}=\frac{6+3+2}{18}=\frac{11}{18}$

Figure 3:

$\frac{1}{32}+\frac{2}{32}+\frac{4}{32}+\frac{8}{32}=\frac{1+2+4+8}{32}=\frac{15}{32}$

$Colored fraction and corrected$

Exercise 5:
a) $\frac{2}{4}$ of 200 L;
$\frac{2}{4}\times \,200=100\,L$
b) $\frac{2}{5}$ of 40 kg;
$\frac{2}{5}\times \,40=16\,kg$
c) $\frac{7}{8}$ of 5,60 €;
$\frac{7}{8}\times \,5,6=4,90\,$ €
d) $\frac{13}{12}$ of 8.4 km.
$\frac{13}{12}\times \,8,4=9,1\,km$

Exercise 6:

a) Find a fraction equal to $\frac{2}{5}$ whose denominator is 35.

$\frac{2\times \,7}{5\times \,7}=\frac{14}{35}$

b) Find a fraction equal to $\frac{4}{3}$ whose numerator is 20.

$\frac{4\times \,5}{3\times \,5}=\frac{20}{15}$

c) Find a fraction equal to $\frac{11}{4}$ whose denominator is 28.

$\frac{11\times \,7}{4\times \,7}=\frac{77}{28}$

Exercise 7:

Exercise 8:

$\frac{3}{17}$ of the animals are geese, $\frac{7}{17}$ of the animals are chickens, $\frac{3}{3}$ of the chickens are white.

$animals and fractions.$

Exercise 9:

$A=\frac{5}{4}\times \,\frac{1}{3}=\frac{5\times \,1}{4\times \,3}=\frac{5}{12}$

$B=\frac{1}{2}\times \,\frac{3}{4}=\frac{3}{8}$

$C=\frac{3}{10}\times \,\frac{7}{10}=\frac{21}{100}$

$D=\frac{5}{7}\times \,\frac{4}{3}=\frac{20}{21}$

Exercise 10:

$A=7+\frac{1}{2}=\frac{14}{2}+\frac{1}{2}=\frac{15}{2}$

$B=4-\frac{1}{3}=\frac{12}{3}-\frac{1}{3}=\frac{11}{3}$

$C=\frac{3}{4}+3=\frac{3}{4}+\frac{12}{4}=\frac{15}{4}$

$D=\frac{15}{7}-2=\frac{15}{7}-\frac{14}{7}=\frac{1}{7}$

Exercise 11:

$A=\frac{1}{6}+\frac{3}{4}-\frac{7}{24}$

$A=\frac{1\times \,4}{6\times \,4}+\frac{3\times \,6}{4\times \,6}-\frac{7}{24}$

$A=\frac{4}{24}+\frac{18}{24}-\frac{7}{24}$

$A=\frac{4+18-7}{24}$

$A=\frac{15:3}{24:3}$

${\color{DarkRed}\,A=\frac{5}{8}}$

$B=\frac{2}{3}-\frac{7}{18}+\frac{2}{9}$

$B=\frac{2\times \,6}{3\times \,6}-\frac{7}{18}+\frac{2\times \,2}{9\times \,2}$

$B=\frac{12}{18}-\frac{7}{18}+\frac{4}{18}$

$B=\frac{12-7+4}{18}$

$B=\frac{9:9}{18:9}$

${\color{DarkRed}\,B=\frac{1}{2}}$

Exercise 12:

a) 12% of 21 ;

$\frac{12}{100}\times \,21=2,52$

b) 120% of 36.

$\frac{120}{100}\times \,36=43,2$

c) 200% of 7.52 ;

$\frac{200}{100}\times \,7,52=15,04$

(d) three percent of 240 ;

$\frac{3}{100}\times \,240=7,2$

(e) thirty percent of 12.4.

$\frac{30}{100}\times \,12,4=3,72$

Exercise 13:
(a) half of 2,800 ;
$\frac{1}{2}\times \,2800=1400$
b) the two sevenths of 35 ;
$\frac{2}{7}\times \,35=10$
c) seven quarters of 2.8 ;
$\frac{7}{4}\times \,28=49$
(d) three-tenths of 7.5 ;
$\frac{3}{10}\times \,7,5=2,25$
e) the sixth of 36.
$\frac{1}{6}\times \,36=6$

Exercise 14:

1. Exhibit 1 represents $\frac{1}{6}$ of the figure

Exhibit 2 represents $\frac{1}{18}$ of the figure

Exhibit 3 represents $\frac{1}{3}$ of the figure

The set of hatched parts represents $\frac{8}{18}$ of the figure.

Exhibit 1 represents $\frac{1}{8}$ of the figure

Exhibit 2 represents $\frac{1}{24}$ . of the figure

The set of hatched parts represents $\frac{7}{24}$ .of the figure.

$Piece and answer key on fractions.$

The answer key to the math exercises on fractions in 5th grade.

After consulting the answers to these exercises on fractions in 5th grade, you can return to the exercises in 5th grade.

Fifth grade exercises.

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