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b. Aziza has GHC 5.00, Ahmed has GHC 6.50 and Koby has GHC 2.50 more than Aziza and Ahmed together. Find the total amount of money the three boys have altogether. c. Simplify i. 5(3)/(4) - 2(7)/(8) + 1(1)/(2) ii. (8)/(9) x (4)/(6)

Mathematics

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3 parts
b

GH¢ 25.50\text{GH¢ } 25.50

c(i)

4384\frac{3}{8}

c(ii)

1627\frac{16}{27}

Step-by-step solution

9 steps

Part b· 3 steps

Total amount of money the three boys have altogether.

  1. Calculate the total amount Aziza and Ahmed have.

    Aziza’s money=GH¢ 5.00\text{Aziza's money} = \text{GH¢ } 5.00 Ahmed’s money=GH¢ 6.50\text{Ahmed's money} = \text{GH¢ } 6.50 Aziza and Ahmed together=GH¢ 5.00+GH¢ 6.50=GH¢ 11.50\text{Aziza and Ahmed together} = \text{GH¢ } 5.00 + \text{GH¢ } 6.50 = \text{GH¢ } 11.50
  2. Calculate the amount Koby has.

    Koby has GH¢ 2.50 more than Aziza and Ahmed together.

    Koby’s money=GH¢ 11.50+GH¢ 2.50=GH¢ 14.00\text{Koby's money} = \text{GH¢ } 11.50 + \text{GH¢ } 2.50 = \text{GH¢ } 14.00
  3. Calculate the total amount of money the three boys have altogether.

    Total money=Aziza’s money+Ahmed’s money+Koby’s money\text{Total money} = \text{Aziza's money} + \text{Ahmed's money} + \text{Koby's money} Total money=GH¢ 5.00+GH¢ 6.50+GH¢ 14.00=GH¢ 25.50\text{Total money} = \text{GH¢ } 5.00 + \text{GH¢ } 6.50 + \text{GH¢ } 14.00 = \text{GH¢ } 25.50

    The total amount of money the three boys have altogether is GH¢ 25.50\boxed{\text{GH¢ } 25.50}.

Part c(i)

4384\frac{3}{8}

534−278+1125\frac{3}{4} - 2\frac{7}{8} + 1\frac{1}{2}

Simplify

  1. Convert mixed numbers to improper fractions.

    534=(5×4)+34=20+34=2345\frac{3}{4} = \frac{(5 \times 4) + 3}{4} = \frac{20 + 3}{4} = \frac{23}{4} 278=(2×8)+78=16+78=2382\frac{7}{8} = \frac{(2 \times 8) + 7}{8} = \frac{16 + 7}{8} = \frac{23}{8} 112=(1×2)+12=2+12=321\frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{2 + 1}{2} = \frac{3}{2}
  2. Rewrite the expression with improper fractions and find a common denominator, which is 8.

    234−238+32\frac{23}{4} - \frac{23}{8} + \frac{3}{2} 23×24×2−238+3×42×4\frac{23 \times 2}{4 \times 2} - \frac{23}{8} + \frac{3 \times 4}{2 \times 4} 468−238+128\frac{46}{8} - \frac{23}{8} + \frac{12}{8}
  3. Perform the subtraction and addition.

    46−23+128=23+128=358\frac{46 - 23 + 12}{8} = \frac{23 + 12}{8} = \frac{35}{8}
  4. Convert the improper fraction back to a mixed number.

    358=438\frac{35}{8} = 4\frac{3}{8}

    The simplified expression is 438\boxed{4\frac{3}{8}}.

Part c(ii)

1627\frac{16}{27}

89×46\frac{8}{9} \times \frac{4}{6}

  1. Multiply the numerators and the denominators.

    89×46=8×49×6=3254\frac{8}{9} \times \frac{4}{6} = \frac{8 \times 4}{9 \times 6} = \frac{32}{54}
  2. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 2.

    32÷254÷2=1627\frac{32 \div 2}{54 \div 2} = \frac{16}{27}

    The simplified expression is 1627\boxed{\frac{16}{27}}.

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