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Problems 25 and 26: a) Simplify: 1/5 + 3/5 + 2/5. b) Arrange 2/3, 5/12, 1/8 in ascending order. c) Study the bill table and complete it.

Mathematics

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Here are the solutions to problems 25 and 26.

:

a) Simplify: 15+35+25\frac{1}{5} + \frac{3}{5} + \frac{2}{5}

  1. Add the numerators since the denominators are the same.

    15+35+25=1+3+25\frac{1}{5} + \frac{3}{5} + \frac{2}{5} = \frac{1+3+2}{5}
  2. Perform the addition.

    =65= \frac{6}{5}

    The simplified expression is 65\boxed{\frac{6}{5}}.

    b) Arrange 23\frac{2}{3}, 512\frac{5}{12} and 18\frac{1}{8} in ascending order.

  3. Find the Least Common Multiple (LCM) of the denominators (3, 12, 8).

    The LCM of 3, 12, and 8 is 24.

  4. Convert each fraction to an equivalent fraction with a denominator of 24.

    23=2×83×8=1624\frac{2}{3} = \frac{2 \times 8}{3 \times 8} = \frac{16}{24} 512=5×212×2=1024\frac{5}{12} = \frac{5 \times 2}{12 \times 2} = \frac{10}{24} 18=1×38×3=324\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}
  5. Compare the numerators and arrange the fractions in ascending order (smallest to largest).

    The numerators are 16, 10, and 3.
    In ascending order, they are 3, 10, 16.
    So, the fractions in ascending order are 324,1024,1624\frac{3}{24}, \frac{10}{24}, \frac{16}{24}.

  6. Write the fractions in their original form.

    18,512,23\frac{1}{8}, \frac{5}{12}, \frac{2}{3}

    The fractions in ascending order are 18,512,23\boxed{\frac{1}{8}, \frac{5}{12}, \frac{2}{3}}.

    :
    Study the bill table below and complete it correctly.

    a) Complete the table.

  7. Calculate the Amount for Sugar.

    Quantity = 3 kg3 \text{ kg}
    Unit Cost = sh 4200 per kg\text{sh } 4200 \text{ per kg}
    Amount = Quantity ×\times Unit Cost = 3 kg×sh 4200/kg=sh 126003 \text{ kg} \times \text{sh } 4200/\text{kg} = \text{sh } 12600.

  8. Calculate the Quantity for Rice.

    Unit Cost = sh 4900 per kg\text{sh } 4900 \text{ per kg}
    Amount = sh 9800\text{sh } 9800
    Quantity = Amount / Unit Cost = sh 9800/(sh 4900/kg)=2 kg\text{sh } 9800 / (\text{sh } 4900/\text{kg}) = 2 \text{ kg}.

  9. Calculate the Unit Cost for Salt.

    Quantity = 500 gm=0.5 kg500 \text{ gm} = 0.5 \text{ kg}
    Amount = sh 800\text{sh } 800
    Unit Cost = Amount / Quantity = sh 800/0.5 kg=sh 1600 per kg\text{sh } 800 / 0.5 \text{ kg} = \text{sh } 1600 \text{ per kg}.

  10. Calculate the Total Amount.

    Total Amount = Amount (Sugar) + Amount (Rice) + Amount (Salt)
    Total Amount = sh 12600+sh 9800+sh 800=sh 23200\text{sh } 12600 + \text{sh } 9800 + \text{sh } 800 = \text{sh } 23200.

    The completed table is:

    ITEMQUANTITYUNIT COSTAMOUNT
    Sugar3 kg3 \text{ kg}sh 4200 per kg\text{sh } 4200 \text{ per kg}sh 12600\boxed{\text{sh } 12600}
    Rice2 kg\boxed{2 \text{ kg}}sh 4900 per kg\text{sh } 4900 \text{ per kg}sh 9800\text{sh } 9800
    Salt500 gm500 \text{ gm}sh 1600 per kg\boxed{\text{sh } 1600 \text{ per kg}}sh 800\text{sh } 800
    Totalsh 23200\boxed{\text{sh } 23200}

    b) If Joseph was given a discount of sh 400, how much did he pay?

  11. Identify the Total Amount and the Discount.

    Total Amount = sh 23200\text{sh } 23200
    Discount = sh 400\text{sh } 400

  12. Subtract the discount from the total amount.

    Amount Paid = Total Amount - Discount
    Amount Paid = sh 23200−sh 400=sh 22800\text{sh } 23200 - \text{sh } 400 = \text{sh } 22800.
    Joseph paid sh 22800\boxed{\text{sh } 22800}.

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