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Solve the following multiplication and addition problems.

Mathematics

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Step-by-step solution

5 steps

Here's how to solve 15×215 \times 2 using the distributive property, filling in the blanks as shown in the image:

  1. Identify the problem and the final answer.

    The problem is 15×215 \times 2.

    15×2=3015 \times 2 = 30

    The top box should contain the final answer.

  2. Break down 15 into 10+510 + 5.

    The visual aid shows 10 and 5 next to ×2\times 2, indicating that 15 is split into 10 and 5.

  3. Apply the distributive property.

    The line with four boxes for multiplication and addition represents the distributive property: (10×2)+(5×2)(10 \times 2) + (5 \times 2).

    =10×2+5×2= \boxed{10} \times \boxed{2} + \boxed{5} \times \boxed{2}
  4. Calculate the individual products.

    Multiply 10×210 \times 2 and 5×25 \times 2.

    10×2=2010 \times 2 = 20 5×2=105 \times 2 = 10

    The next line shows the sum of these products.

    =20+10= \boxed{20} + \boxed{10}
  5. Calculate the final sum.

    Add the results from the previous step.

    20+10=3020 + 10 = 30

    The last line shows the final sum.

    =30= \boxed{30}

    Now, let's address the first line of blanks: =+×= \boxed{ } + \boxed{ } \times \boxed{ }.
    Given the subsequent steps, this line is likely meant to show an intermediate calculation where one part of the multiplication is already done.
    If 10×2=2010 \times 2 = 20, then the expression becomes 20+(5×2)20 + (5 \times 2).

    =20+5×2= \boxed{20} + \boxed{5} \times \boxed{2}

    Here are the filled steps:

    15×2=3015 \times 2 = \boxed{30} =20+5×2= \boxed{20} + \boxed{5} \times \boxed{2} =10×2+5×2= \boxed{10} \times \boxed{2} + \boxed{5} \times \boxed{2} =20+10= \boxed{20} + \boxed{10} =30= \boxed{30}

    The final answer is 30\boxed{\text{30}}.

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