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Increase £1.45 by £1.65. 2. What is the cost of 25 cm at £1.20 per metre? 3. This clock is 20 min fast. Write the correct time in digits. Use a.m. or p.m. 4. Find the total cost of two toy cars each c

Mathematics

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Here are the solutions to the problems.

  1. Increase £1.45\pounds 1.45 by £1.65\pounds 1.65.
  1. Add the two amounts together.

    $$
    \pounds 1.45 + \pounds 1.65 = \pounds 3.10
    $$
    The increased amount is $\boxed{\pounds 3.10}$.
    

    2. What is the cost of 25 cm25 \text{ cm} at £1.20\pounds 1.20 per metre?

  2. Convert 25 cm25 \text{ cm} to meters.

    There are $100 \text{ cm}$ in $1 \text{ m}$.
    $$
    25 \text{ cm} = \frac{25}{100} \text{ m} = 0.25 \text{ m}
    $$
    
  3. Calculate the cost.

    Multiply the length in meters by the cost per meter.
    $$
    0.25 \text{ m} \times \pounds 1.20/\text{m} = \pounds 0.30
    $$
    The cost is $\boxed{\pounds 0.30}$.
    

    3. This clock is 20 min20 \text{ min} fast. Write the correct time in digits. Use a.m. or p.m.

  4. Read the time shown on the clock.

    The hour hand is between 7 and 8. The minute hand is pointing at 3, which represents 15 minutes past the hour. Since it says "morning", the time shown is 7:15 a.m.
    
  5. Subtract 20 minutes20 \text{ minutes} from the displayed time to find the correct time.

    $$
    7:15 \text{ a.m.} - 20 \text{ minutes}
    $$
    Subtracting 15 minutes brings it to 7:00 a.m.  
    Subtracting another 5 minutes (20 - 15 = 5) brings it to 6:55 a.m.  
    The correct time is $\boxed{6:55 \text{ a.m.}}$.
    

    4. Find the total cost of two toy cars each costing £1.38\pounds 1.38.

  6. Multiply the cost of one toy car by 2.

    $$
    2 \times \pounds 1.38 = \pounds 2.76
    $$
    The total cost is $\boxed{\pounds 2.76}$.
    

    5. How much less than a whole one is the smallest of these fractions? 12,17,14,110,13\frac{1}{2}, \frac{1}{7}, \frac{1}{4}, \frac{1}{10}, \frac{1}{3}

  7. Identify the smallest fraction.

    For unit fractions (fractions with a numerator of 1), the fraction with the largest denominator is the smallest.  
    Comparing the denominators (2, 7, 4, 10, 3), the largest denominator is 10.  
    Therefore, the smallest fraction is $\frac{1}{10}$.
    
  8. Calculate how much less than a whole one (which is 1) the smallest fraction is.

    $$
    1 - \frac{1}{10} = \frac{10}{10} - \frac{1}{10} = \frac{9}{10}
    $$
    The smallest fraction is $\boxed{\frac{9}{10}}$ less than a whole one.
    
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