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What are the solutions to Question 11: Add 3.25 + 2.573 + 4.6; Question 12: Order 1/8, 1/4, 1/2, 5/8, 3/4; and Question 13: Find the missing side of a right triangle with one side 12cm and hypotenuse

Mathematics

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2 parts
12

18,14,12,58,34\frac{1}{8}, \frac{1}{4}, \frac{1}{2}, \frac{5}{8}, \frac{3}{4}

18

2312\frac{23}{12}

Step-by-step solution

34 steps

Part 11· 2 steps

  1. Add the given numbers.

    3.25+2.573+4.63.25 + 2.573 + 4.6

  2. Align the decimal points and sum.

    3.2502.573+4.60010.423\begin{array}{c} 3.250 \\ 2.573 \\ + 4.600 \\ \hline 10.423 \end{array}

    The sum is 10.423.

Part 12

18,14,12,58,34\frac{1}{8}, \frac{1}{4}, \frac{1}{2}, \frac{5}{8}, \frac{3}{4}

  1. Convert all fractions to have a common denominator.

    The least common multiple of 2, 4, and 8 is 8.

    12=1×42×4=48\frac{1}{2} = \frac{1 \times 4}{2 \times 4} = \frac{4}{8} 14=1×24×2=28\frac{1}{4} = \frac{1 \times 2}{4 \times 2} = \frac{2}{8} 18=18\frac{1}{8} = \frac{1}{8} 34=3×24×2=68\frac{3}{4} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8} 58=58\frac{5}{8} = \frac{5}{8}

  2. Arrange the fractions in increasing order based on their numerators.

    18,28,48,58,68\frac{1}{8}, \frac{2}{8}, \frac{4}{8}, \frac{5}{8}, \frac{6}{8}

  3. Write the original fractions in increasing order.

    18,14,12,58,34\frac{1}{8}, \frac{1}{4}, \frac{1}{2}, \frac{5}{8}, \frac{3}{4}

    The correct order is 18,14,12,58,34\boxed{\frac{1}{8}, \frac{1}{4}, \frac{1}{2}, \frac{5}{8}, \frac{3}{4}}.

Part 13· 4 steps

  1. Use the Pythagorean theorem, a2+b2=c2a^2 + b^2 = c^2, where cc is the hypotenuse and a,ba, b are the other two sides.

    Given one side a=12a = 12 cm and hypotenuse c=13c = 13 cm. We need to find the other side bb.

    122+b2=13212^2 + b^2 = 13^2

  2. Calculate the squares.

    144+b2=169144 + b^2 = 169

  3. Solve for b2b^2.

    b2=169−144b^2 = 169 - 144 b2=25b^2 = 25

  4. Find the square root of b2b^2.

    b=25b = \sqrt{25} b=5 cmb = 5 \text{ cm}

    The length of the other side is 5 cm.

Part 14· 5 steps

  1. Use the formula for the area of a circle, A=πr2A = \pi r^2, to find the radius rr.

    Given A=2464 cm2A = 2464 \text{ cm}^2 and π=227\pi = \frac{22}{7}.

    2464=227×r22464 = \frac{22}{7} \times r^2

  2. Solve for r2r^2.

    r2=2464×722r^2 = \frac{2464 \times 7}{22} r2=112×7r^2 = 112 \times 7 r2=784r^2 = 784

  3. Find the radius rr.

    r=784r = \sqrt{784} r=28 cmr = 28 \text{ cm}

  4. Calculate the diameter d=2rd = 2r.

    d=2×28 cmd = 2 \times 28 \text{ cm} d=56 cmd = 56 \text{ cm}

  5. Approximate to 2 significant figures.

    Since 56 already has two significant figures, no further rounding is needed.
    The diameter is 56 cm.

Part 15· 2 steps

  1. Multiply the number of patients by the amount of milk each patient gets.

    Total milk=Number of patients×Milk per patient\text{Total milk} = \text{Number of patients} \times \text{Milk per patient} Total milk=36×12 litres\text{Total milk} = 36 \times \frac{1}{2} \text{ litres}

  2. Perform the multiplication.

    Total milk=362 litres\text{Total milk} = \frac{36}{2} \text{ litres} Total milk=18 litres\text{Total milk} = 18 \text{ litres}

    18 litres of milk are needed.

Part 16· 2 steps

  1. To divide by a fraction, multiply by its reciprocal.

    14÷116=14×161\frac{1}{4} \div \frac{1}{16} = \frac{1}{4} \times \frac{16}{1}

  2. Perform the multiplication.

    14×16=164\frac{1}{4} \times 16 = \frac{16}{4} =4= 4

    The value is 4.

Part 17· 3 steps

  1. The clock shows 1:10 p.m.

    and is 20 minutes fast. To find the correct time, subtract 20 minutes from 1:10 p.m.

  2. Subtract 10 minutes from 1:10 p.m.

    to get 1:00 p.m.

  3. Subtract the remaining 10 minutes (20 - 10) from 1:00 p.m.

    1:00 p.m. - 10 minutes = 12:50 p.m.
    The correct time is 12:50 p.m.

Part 18

2312\frac{23}{12}

  1. Convert the mixed number to an improper fraction.

    112=(1×2)+12=321\frac{1}{2} = \frac{(1 \times 2) + 1}{2} = \frac{3}{2}

  2. Find a common denominator for 2, 4, and 3.

    The least common multiple is 12.

    32=3×62×6=1812\frac{3}{2} = \frac{3 \times 6}{2 \times 6} = \frac{18}{12} 14=1×34×3=312\frac{1}{4} = \frac{1 \times 3}{4 \times 3} = \frac{3}{12} 23=2×43×4=812\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12}

  3. Perform the operations.

    1812−312+812\frac{18}{12} - \frac{3}{12} + \frac{8}{12} =18−3+812= \frac{18 - 3 + 8}{12} =15+812= \frac{15 + 8}{12} =2312= \frac{23}{12}

    The simplified value is 2312\boxed{\frac{23}{12}}.

Part 19· 3 steps

  1. Calculate the total toll from buses.

    Toll from buses=500 buses×N10/bus\text{Toll from buses} = 500 \text{ buses} \times \text{N}10/\text{bus} Toll from buses=N5000\text{Toll from buses} = \text{N}5000

  2. Calculate the total toll from trailers.

    Toll from trailers=100 trailers×N50/trailer\text{Toll from trailers} = 100 \text{ trailers} \times \text{N}50/\text{trailer} Toll from trailers=N5000\text{Toll from trailers} = \text{N}5000

  3. Find the total amount collected.

    Total amount=N5000+N5000\text{Total amount} = \text{N}5000 + \text{N}5000 Total amount=N10,000\text{Total amount} = \text{N}10,000

    The total amount collected is N10,000.00.

Part 20· 3 steps

  1. Find the factors of each number.

    Factors of 12: 1, 2, 3, 4, 6, 12
    Factors of 18: 1, 2, 3, 6, 9, 18
    Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36

  2. Identify the common factors.

    Common factors: 1, 2, 3, 6

  3. The greatest common factor is the largest number among the common factors.

    The greatest number is 6.

Part 21· 4 steps

  1. Identify the first two significant figures in 3053.56.

    The first significant figure is 3, and the second is 0.

  2. Look at the digit immediately after the second significant figure, which is 5.

  3. Since 5 is 5 or greater, round up the second significant figure.

    The 0 becomes 1.

  4. Replace all digits after the second significant figure with zeros to maintain the place value.

    3053.56≈31003053.56 \approx 3100

    The approximation to 2 significant figures is 3100.

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