High School

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a) \( \frac{4}{3} : \frac{48}{12} + 7^2 - 5^0 = \)

Answer :

Let's solve the expression step-by-step:

First, evaluate the individual parts of the expression:

  1. The division part of the expression is [tex]\frac{4}{3} : \frac{48}{12}[/tex]. In mathematics, the symbol ':' means division, so this simplifies to:

    [tex]\frac{4}{3} \div \frac{48}{12}[/tex]

    To divide fractions, multiply by the reciprocal of the second fraction:

    [tex]\frac{4}{3} \times \frac{12}{48} = \frac{4 \times 12}{3 \times 48}[/tex]

    Simplifying this gives:

    [tex]\frac{48}{144} = \frac{1}{3}[/tex]

  2. Now evaluate the exponent part, which is [tex]7^2[/tex]:

    [tex]7^2 = 49[/tex]

  3. Evaluate the exponent in [tex]5^0[/tex]:

    [tex]5^0 = 1[/tex] (Any number raised to the power of 0 is 1.)

Now, substitute these results back into the original expression:

[tex]\frac{1}{3} + 49 - 1[/tex]

  1. Calculate this step-by-step:

    First add [tex]\frac{1}{3} + 49[/tex]:

    Convert 49 to a fraction to be added:

    [tex]\frac{147}{3} + \frac{1}{3} = \frac{148}{3}[/tex]

  2. Subtract 1:

    Convert 1 to a fraction with a denominator of 3:

    [tex]\frac{148}{3} - \frac{3}{3} = \frac{145}{3}[/tex]

Thus, the final result is:

[tex]\frac{145}{3}[/tex].

This expression ultimately simplifies to approximately 48.333.

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