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Solve the following arithmetic problems: 1.1 28694 428, 1.2 187296 / 4, 1.3 46514 / 17, 1.4 563 18 - 4, 1.5 Divide R350 in the ratio 3:4.

Mathematics

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here are the solutions with full steps for the problems in the image:

Part 1.1· 2 steps

  1. Multiply the two given numbers.

    28694×42828694 \times 428
  2. Perform the multiplication.

    28694×428=1228035228694 \times 428 = 12280352

    The product is 12280352\boxed{\text{12280352}}.

Part 1.2· 2 steps

  1. Divide the first number by the second number.

    187296÷4187296 \div 4
  2. Perform the division.

    187296÷4=46824187296 \div 4 = 46824

    The quotient is 46824\boxed{\text{46824}}.

Part 1.3· 3 steps

  1. Divide the first number by the second number.

    46514÷1746514 \div 17
  2. Perform the division.

    46514÷17=2736.1176...46514 \div 17 = 2736.1176...
  3. Express the quotient, noting it's not an exact division.

    The quotient is approximately 2736.12\boxed{\text{2736.12}}.

Part 1.4· 2 steps

  1. According to the order of operations (multiplication before subtraction), perform the multiplication first.

    563×18=10134563 \times 18 = 10134
  2. Perform the subtraction using the result from Step 1.

    10134−4=1013010134 - 4 = 10130

    The result is 10130\boxed{\text{10130}}.

Part 1.5· 4 steps

  1. Determine the total number of parts in the ratio.

    Total parts =3+4=7= 3 + 4 = 7

  2. Calculate the value of one part by dividing the total amount by the total number of parts.

    Value of one part =R3507=R50= \frac{\text{R}350}{7} = \text{R}50

  3. Calculate Kenzie's share by multiplying her ratio part by the value of one part.

    Kenzie's share =3×R50=R150= 3 \times \text{R}50 = \text{R}150

  4. Calculate Connor's share by multiplying his ratio part by the value of one part.

    Connor's share =4×R50=R200= 4 \times \text{R}50 = \text{R}200
    Kenzie gets R150\boxed{\text{R150}} and Connor gets R200\boxed{\text{R200}}.

Part 1.6· 2 steps

  1. Identify the given speed and time, and recall the formula for distance.

    Given: Speed =60 km/hour= 60 \text{ km/hour}, Time =8 hours= 8 \text{ hours}.
    Formula: Distance = Speed ×\times Time.

  2. Substitute the given values into the formula and calculate the distance.

    Distance=60 km/hour×8 hours=480 km\text{Distance} = 60 \text{ km/hour} \times 8 \text{ hours} = 480 \text{ km}

    We can travel 480 km\boxed{\text{480 km}}.

Part 1.7· 2 steps

  1. Identify the given distance and time, and recall the formula for speed.

    Given: Distance =480 km= 480 \text{ km}, Time =4 hours= 4 \text{ hours}.
    Formula: Speed = Distance ÷\div Time.

  2. Substitute the given values into the formula and calculate the speed.

    Speed=480 km4 hours=120 km/hour\text{Speed} = \frac{480 \text{ km}}{4 \text{ hours}} = 120 \text{ km/hour}

    We are driving at a speed of 120 km/hour\boxed{\text{120 km/hour}}.

Part 1.8· 3 steps

  1. Start the factor tree by finding two factors of 24.

    24/ \2   12\begin{array}{c} 24 \\ / \ \backslash \\ 2 \ \ \ 12 \end{array}
  2. Continue breaking down composite factors until all branches end in prime numbers.

    24/ \2   12   / \   2   6      / \      2   3\begin{array}{c} 24 \\ / \ \backslash \\ 2 \ \ \ 12 \\ \ \ \ / \ \backslash \\ \ \ \ 2 \ \ \ 6 \\ \ \ \ \ \ \ / \ \backslash \\ \ \ \ \ \ \ 2 \ \ \ 3 \end{array}
  3. Write the prime factorization using exponents for repeated prime factors.

    24=2×2×2×3=23×324 = 2 \times 2 \times 2 \times 3 = 2^3 \times 3

    The prime factorization of 24 is 23×3\boxed{2^3 \times 3}.

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