Abudu takes 6 days to complete work.

Fraction of work done by Abudu in a day = $\frac{1}{6}$

Efah takes 3 days to complete the same work.

Fraction of work completed by Efah in a day = $\frac{1}{3}$

Fraction of work done by both in a day is the sum of fractions of work done by each.

Fraction of work done by both = $\frac{1}{6}$ + $\frac{1}{3}$

Fraction of work done by both = $\frac{\mathrm{1\; +\; 2}}{6}$

Fraction of work done by both = $\frac{3}{6}$

Fraction of work done by both = $\frac{1}{2}$

Alternatively

Let y the work to be done

Abudu takes 6 days to complete work.

Work completed by Abudu in a day = $\frac{1}{6}$ x y

Work completed by Abudu in a day = $\frac{\mathrm{y}}{6}$

Efah takes 3 days to complete the same work.

Work completed by Efah in a day = $\frac{1}{3}$ x y

Work completed by Efah in a day = $\frac{\mathrm{y}}{3}$

Work completed by both Abudu and Efah in a day is the sum of work done by each in a day.

Work done by both = $\frac{\mathrm{y}}{6}$ + $\frac{\mathrm{y}}{3}$

Work done by both = $\frac{\mathrm{y\; +\; 2y}}{6}$

Work done by both = $\frac{\mathrm{3y}}{6}$

Work done by both = $\frac{\mathrm{y}}{2}$

Fraction of work done in a day = $\frac{\mathrm{Work\; done\; in\; a\; day}}{\mathrm{Total\; work\; to\; be\; done}}$

Total work to be done is y

Work done by both in a day = $\frac{\mathrm{y}}{2}$

Fraction of work done in a day = $\frac{\mathrm{y}}{2}$ ÷ y

Every number is divisible by 1

Fraction of work done in a day = $\frac{\mathrm{y}}{2}$ ÷ $\frac{\mathrm{y}}{1}$

Reciprocate the fraction at the right of ÷ and change the ÷ to multiplication (x)

Note: reciprocate means the numerator becomes the denominator and the denominator becomes the numerator.

Fraction of work done in a day = $\frac{\mathrm{y}}{2}$ x $\frac{1}{\mathrm{y}}$

The y cancels each other.

Fraction of work done in a day = $\frac{1}{2}$

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = 8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$

Change the mixed fractions to improper fractions

8$\frac{1}{6}$ = $\frac{\mathrm{6\; x\; 8\; +\; 1}}{6}$ = $\frac{49}{6}$

11$\frac{2}{3}$ = $\frac{\mathrm{3\; x\; 11\; +\; 2}}{3}$ = $\frac{35}{3}$

2$\frac{2}{3}$ = $\frac{\mathrm{3\; x\; 2\; +\; 2}}{3}$ = $\frac{8}{3}$

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{49}{6}$ - $(\frac{35}{3}÷\frac{8}{3})$

Reciprocate the fraction at the right of ÷ and change the ÷ to multiplication (x)

Note: reciprocate means the numerator becomes the denominator and the denominator, numerator.

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{49}{6}$ - $(\frac{35}{3}x\frac{3}{8})$

Note: 3 cancel out each other.

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{49}{6}$ - $\left(\frac{35}{8}\right)$

Remove the bracket.

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{49}{6}$ - $\frac{35}{8}$

The L.C.M of 6 and 8 is 24.

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{\mathrm{49\; x\; 4\; -\; 35\; x\; 3}}{24}$

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{\mathrm{196\; -\; 105}}{24}$

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{91}{24}$

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = 3$\frac{19}{24}$

Change the mixed fractions to improper fractions.

2$\frac{1}{6}$ = $\frac{\mathrm{2\; x\; 6\; +\; 1}}{6}$ = $\frac{\mathrm{12\; +\; 1}}{6}$ = $\frac{13}{6}$

2$\frac{7}{12}$ = $\frac{\mathrm{2\; x\; 12\; +\; 7}}{12}$ = $\frac{\mathrm{24\; +\; 7}}{12}$ = $\frac{31}{12}$

3$\frac{1}{4}$ = $\frac{\mathrm{4\; x\; 3\; +\; 1}}{4}$ = $\frac{\mathrm{12\; +\; 1}}{4}$ = $\frac{13}{4}$

Let x the number to be subtracted.

Sum is addition.

$\frac{13}{6}$ + $\frac{31}{12}$ - x = $\frac{13}{4}$

$\frac{\mathrm{2\; x\; 13\; +\; 1\; x\; 31}}{12}$ - x = $\frac{13}{4}$

$\frac{\mathrm{26\; +\; 31}}{12}$ - x = $\frac{13}{4}$

$\frac{57}{12}$ - x = $\frac{13}{4}$

$\frac{57}{12}$ - $\frac{13}{4}$ = x

$\frac{\mathrm{1\; x\; 57\; -\; 3\; x\; 13}}{12}$ = x

$\frac{\mathrm{57\; -\; 39}}{12}$ = x

$\frac{18}{12}$ = x

$\frac{3}{2}$ = x

x = $\frac{3}{2}$ = 1$\frac{1}{2}$

$\frac{\frac{1}{4}x2\frac{1}{2}}{12 ÷ 1\frac{1}{2}}$ = $\frac{\frac{1}{4}x2\frac{1}{2}}{12 ÷ 1\frac{1}{2}}$

$\frac{1}{4}x2\frac{1}{2}$ = $\frac{1}{4}x2\frac{1}{2}$

Change the mixed fraction to improper fraction.

2$\frac{1}{2}$ = $\frac{\mathrm{2\; x\; 2\; +\; 1}}{2}$ = $\frac{\mathrm{4\; +\; 1}}{2}$ = $\frac{5}{2}$

$\frac{1}{4}x2\frac{1}{2}$ = $\frac{1}{4}x\frac{5}{2}$

$\frac{1}{4}x2\frac{1}{2}$ = $\frac{\mathrm{1\; x\; 5}}{\mathrm{4\; x\; 2}}$ = $\frac{5}{8}$

$12 ÷ 1\frac{1}{2}$ = $12 ÷ 1\frac{1}{2}$

Change the mixed fraction to improper fraction.

1$\frac{1}{2}$ = $\frac{\mathrm{1\; x\; 2\; +\; 1}}{2}$ = $\frac{\mathrm{2\; +\; 1}}{2}$ = $\frac{3}{2}$

$12 ÷ 1\frac{1}{2}$ = 12 ÷ $\frac{3}{2}$

Reciprocate the fraction at the right of the ÷ and change ÷ to multiplication (x)

Note: reciprocate means the numerator becomes the denominator and the denominator becomes the numerator.

$12 ÷ 1\frac{1}{2}$ = 12 x $\frac{2}{3}$ = 4 x 2 = 8

$\frac{\frac{1}{4}x2\frac{1}{2}}{12 ÷ 1\frac{1}{2}}$ = $\frac{5}{8}$ ÷ 8

Every number is being divided by 1

8 = $\frac{8}{1}$

$\frac{\frac{1}{4}x2\frac{1}{2}}{12 ÷ 1\frac{1}{2}}$ = $\frac{5}{8}$ ÷ $\frac{8}{1}$

Reciprocate the fraction at the right of the ÷ and change ÷ to multiplication (x)

Note: reciprocate means the numerator becomes the denominator and the denominator becomes the numerator.

$\frac{\frac{1}{4}x2\frac{1}{2}}{12 ÷ 1\frac{1}{2}}$ = $\frac{5}{8}$ x $\frac{1}{8}$ = $\frac{\mathrm{5\; x\; 1}}{\mathrm{8\; x\; 8}}$ = $\frac{5}{64}$

Change the fraction and decimal to percentage so that they will all be in percentages.

Percentage is simply multiplying by 100%.

0.45 ⇒ 0.45 x 100% = 45%

$\frac{3}{4}$ ⇒ $\frac{3}{4}$ x 100% = 75%

25% is already in percentage

Now arrange in ascending order

Note: Ascending means from lowest to highest.

25%, 45%, 75%

45% = 0.45

75% = $\frac{3}{4}$

Hence the ascending order is 25%,0.45,$\frac{3}{4}$

Change the fraction and decimal to percentage so that they will all be in percentages.

Percentage is simply multiplying by 100%.

0.45 ⇒ 0.45 x 100% = 45%

$\frac{3}{4}$ ⇒ $\frac{3}{4}$ x 100% = 75%

25% is already in percentage

Now arrange in ascending order

Note: Ascending means from lowest to highest.

25%, 45%, 75%

45% = 0.45

75% = $\frac{3}{4}$

Hence the ascending order is 25%,0.45,$\frac{3}{4}$

Method I

Calculating fraction for SHS 3 and later calculating the number

Number of students in form = Fraction x Total Population

The total fraction is 1 which represents the 1800 students

Fraction in SHS 1 and 2 = $\frac{4}{9}$ + $\frac{13}{36}$

Fraction in SHS 1 and 2 = $\frac{\mathrm{4\; x\; 4\; +\; 1\; x\; 13}}{36}$

Fraction in SHS 1 and 2 = $\frac{\mathrm{16\; +\; 13}}{36}$

Fraction in SHS 1 and 2 = $\frac{29}{36}$

Fraction in SHS 3 = 1 - $\frac{29}{36}$

Fraction in SHS 3 = $\frac{\mathrm{36\; -\; 29}}{36}$

Fraction in SHS 3 = $\frac{7}{36}$

Number of students in SHS 3 = $\frac{7}{36}$ x 1800

Number of students in SHS 3 = 350

Method II

Calculating number of students in SHS 1 and 2

Number of students in SHS 1 = $\frac{4}{9}$ x 1800

Number of students in SHS 1 = 800

Number of students in SHS 2 = $\frac{13}{36}$ x 1800

Number of students in SHS 2 = 650

Total number of students in SHS 1 and 2 = 800 + 650 = 1450

Number of students in SHS 3 = Total Population - Number of students in SHS 1 and 2

Number of students in SHS 3 = 1800 - 1450

Number of students in SHS 3 = 350

Abudu takes 6 days to complete work.

Fraction of work done by Abudu in a day = $\frac{1}{6}$

Efah takes 3 days to complete the same work.

Fraction of work completed by Efah in a day = $\frac{1}{3}$

Fraction of work done by both in a day is the sum of fractions of work done by each.

Fraction of work done by both = $\frac{1}{6}$ + $\frac{1}{3}$

Fraction of work done by both = $\frac{\mathrm{1\; +\; 2}}{6}$

Fraction of work done by both = $\frac{3}{6}$

Fraction of work done by both = $\frac{1}{2}$

Alternatively

Let y the work to be done

Abudu takes 6 days to complete work.

Work completed by Abudu in a day = $\frac{1}{6}$ x y

Work completed by Abudu in a day = $\frac{\mathrm{y}}{6}$

Efah takes 3 days to complete the same work.

Work completed by Efah in a day = $\frac{1}{3}$ x y

Work completed by Efah in a day = $\frac{\mathrm{y}}{3}$

Work completed by both Abudu and Efah in a day is the sum of work done by each in a day.

Work done by both = $\frac{\mathrm{y}}{6}$ + $\frac{\mathrm{y}}{3}$

Work done by both = $\frac{\mathrm{y\; +\; 2y}}{6}$

Work done by both = $\frac{\mathrm{3y}}{6}$

Work done by both = $\frac{\mathrm{y}}{2}$

Fraction of work done in a day = $\frac{\mathrm{Work\; done\; in\; a\; day}}{\mathrm{Total\; work\; to\; be\; done}}$

Total work to be done is y

Work done by both in a day = $\frac{\mathrm{y}}{2}$

Fraction of work done in a day = $\frac{\mathrm{y}}{2}$ ÷ y

Every number is divisible by 1

Fraction of work done in a day = $\frac{\mathrm{y}}{2}$ ÷ $\frac{\mathrm{y}}{1}$

Reciprocate the fraction at the right of ÷ and change the ÷ to multiplication (x)

Note: reciprocate means the numerator becomes the denominator and the denominator becomes the numerator.

Fraction of work done in a day = $\frac{\mathrm{y}}{2}$ x $\frac{1}{\mathrm{y}}$

The y cancels each other.

Fraction of work done in a day = $\frac{1}{2}$

$\frac{1}{2}$(x-1)-$\frac{1}{3}$($\frac{1}{2}$x-1)

Expand the brackets

$\frac{1}{2}$(x-1)-$\frac{1}{3}$($\frac{1}{2}$x-1) = $\frac{\mathrm{x}}{2}$ - $\frac{1}{2}$ - $\frac{\mathrm{x}}{6}$ + $\frac{1}{3}$

Note: - x - = +

-$\frac{1}{3}$ x - 1 = $\frac{1}{3}$

The Least Common Multiples (L.C.M) of the denominators (2,3 and 6) is 6

$\frac{1}{2}$(x-1)-$\frac{1}{3}$($\frac{1}{2}$x-1) = $\frac{\mathrm{3\; x\; x\; -\; 3\; x\; 1\; -\; 1\; x\; x\; +\; 2\; x\; 1}}{6}$

$\frac{1}{2}$(x-1)-$\frac{1}{3}$($\frac{1}{2}$x-1) = $\frac{\mathrm{3x\; -\; 3\; -\; x\; +\; 2}}{6}$

$\frac{1}{2}$(x-1)-$\frac{1}{3}$($\frac{1}{2}$x-1) = $\frac{\mathrm{3x\; -\; x\; -\; 3\; +\; 2}}{6}$

$\frac{1}{2}$(x-1)-$\frac{1}{3}$($\frac{1}{2}$x-1) = $\frac{\mathrm{2x\; -\; 1}}{6}$

$\frac{1}{2}$(x-1)-$\frac{1}{3}$($\frac{1}{2}$x-1) = $\frac{1}{6}$(2x - 1)

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = 8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$

Change the mixed fractions to improper fractions

8$\frac{1}{6}$ = $\frac{\mathrm{6\; x\; 8\; +\; 1}}{6}$ = $\frac{49}{6}$

11$\frac{2}{3}$ = $\frac{\mathrm{3\; x\; 11\; +\; 2}}{3}$ = $\frac{35}{3}$

2$\frac{2}{3}$ = $\frac{\mathrm{3\; x\; 2\; +\; 2}}{3}$ = $\frac{8}{3}$

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{49}{6}$ - $(\frac{35}{3}÷\frac{8}{3})$

Reciprocate the fraction at the right of ÷ and change the ÷ to multiplication (x)

Note: reciprocate means the numerator becomes the denominator and the denominator, numerator.

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{49}{6}$ - $(\frac{35}{3}x\frac{3}{8})$

Note: 3 cancel out each other.

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{49}{6}$ - $\left(\frac{35}{8}\right)$

Remove the bracket.

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{49}{6}$ - $\frac{35}{8}$

The L.C.M of 6 and 8 is 24.

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{\mathrm{49\; x\; 4\; -\; 35\; x\; 3}}{24}$

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{\mathrm{196\; -\; 105}}{24}$

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = $\frac{91}{24}$

8$\frac{1}{6}$ - $(11\frac{2}{3}÷2\frac{2}{3})$ = 3$\frac{19}{24}$

Change the mixed fractions to improper fractions.

2$\frac{1}{6}$ = $\frac{\mathrm{2\; x\; 6\; +\; 1}}{6}$ = $\frac{\mathrm{12\; +\; 1}}{6}$ = $\frac{13}{6}$

2$\frac{7}{12}$ = $\frac{\mathrm{2\; x\; 12\; +\; 7}}{12}$ = $\frac{\mathrm{24\; +\; 7}}{12}$ = $\frac{31}{12}$

3$\frac{1}{4}$ = $\frac{\mathrm{4\; x\; 3\; +\; 1}}{4}$ = $\frac{\mathrm{12\; +\; 1}}{4}$ = $\frac{13}{4}$

Let x the number to be subtracted.

Sum is addition.

$\frac{13}{6}$ + $\frac{31}{12}$ - x = $\frac{13}{4}$

$\frac{\mathrm{2\; x\; 13\; +\; 1\; x\; 31}}{12}$ - x = $\frac{13}{4}$

$\frac{\mathrm{26\; +\; 31}}{12}$ - x = $\frac{13}{4}$

$\frac{57}{12}$ - x = $\frac{13}{4}$

$\frac{57}{12}$ - $\frac{13}{4}$ = x

$\frac{\mathrm{1\; x\; 57\; -\; 3\; x\; 13}}{12}$ = x

$\frac{\mathrm{57\; -\; 39}}{12}$ = x

$\frac{18}{12}$ = x

$\frac{3}{2}$ = x

x = $\frac{3}{2}$ = 1$\frac{1}{2}$

$\frac{\frac{1}{4}x2\frac{1}{2}}{12 ÷ 1\frac{1}{2}}$ = $\frac{\frac{1}{4}x2\frac{1}{2}}{12 ÷ 1\frac{1}{2}}$

$\frac{1}{4}x2\frac{1}{2}$ = $\frac{1}{4}x2\frac{1}{2}$

Change the mixed fraction to improper fraction.

2$\frac{1}{2}$ = $\frac{\mathrm{2\; x\; 2\; +\; 1}}{2}$ = $\frac{\mathrm{4\; +\; 1}}{2}$ = $\frac{5}{2}$

$\frac{1}{4}x2\frac{1}{2}$ = $\frac{1}{4}x\frac{5}{2}$

$\frac{1}{4}x2\frac{1}{2}$ = $\frac{\mathrm{1\; x\; 5}}{\mathrm{4\; x\; 2}}$ = $\frac{5}{8}$

$12 ÷ 1\frac{1}{2}$ = $12 ÷ 1\frac{1}{2}$

Change the mixed fraction to improper fraction.

1$\frac{1}{2}$ = $\frac{\mathrm{1\; x\; 2\; +\; 1}}{2}$ = $\frac{\mathrm{2\; +\; 1}}{2}$ = $\frac{3}{2}$

$12 ÷ 1\frac{1}{2}$ = 12 ÷ $\frac{3}{2}$

Reciprocate the fraction at the right of the ÷ and change ÷ to multiplication (x)

Note: reciprocate means the numerator becomes the denominator and the denominator becomes the numerator.

$12 ÷ 1\frac{1}{2}$ = 12 x $\frac{2}{3}$ = 4 x 2 = 8

$\frac{\frac{1}{4}x2\frac{1}{2}}{12 ÷ 1\frac{1}{2}}$ = $\frac{5}{8}$ ÷ 8

Every number is being divided by 1

8 = $\frac{8}{1}$

$\frac{\frac{1}{4}x2\frac{1}{2}}{12 ÷ 1\frac{1}{2}}$ = $\frac{5}{8}$ ÷ $\frac{8}{1}$

Reciprocate the fraction at the right of the ÷ and change ÷ to multiplication (x)

Note: reciprocate means the numerator becomes the denominator and the denominator becomes the numerator.

$\frac{\frac{1}{4}x2\frac{1}{2}}{12 ÷ 1\frac{1}{2}}$ = $\frac{5}{8}$ x $\frac{1}{8}$ = $\frac{\mathrm{5\; x\; 1}}{\mathrm{8\; x\; 8}}$ = $\frac{5}{64}$