We read your photo as:

Find the base five numeral expanded to give (3 x 5 x 5) + (4 x 1) and workout 212three - 121three.

Mathematics

ScanSolve AI Answer

Step-by-step solution

8 steps

Here are the solutions to the problems:

: Find the base five numeral expanded to give (3×5×5)+(4×1)(3 \times 5 \times 5) + (4 \times 1)

  1. Rewrite the expanded form using powers of 5.

    The given expression is (3×5×5)+(4×1)(3 \times 5 \times 5) + (4 \times 1).
    This can be written as:

    (3×52)+(4×50)(3 \times 5^2) + (4 \times 5^0)
  2. Identify the coefficients for each power of 5.

    In base five, a number dndn−1…d1d0d_n d_{n-1} \dots d_1 d_0 is represented as dn×5n+dn−1×5n−1+⋯+d1×51+d0×50d_n \times 5^n + d_{n-1} \times 5^{n-1} + \dots + d_1 \times 5^1 + d_0 \times 5^0.
    Comparing this to our expression:
    The coefficient for 525^2 is 3.
    There is no 515^1 term, so its coefficient is 0.
    The coefficient for 505^0 (which is 1) is 4.

  3. Construct the base five numeral.

    The digits are 3 (for 525^2), 0 (for 515^1), and 4 (for 505^0).
    Therefore, the base five numeral is 3045304_5.

    The base five numeral is 3045\boxed{304_5}.

    : Workout: 212three−121three212_{\text{three}} - 121_{\text{three}}

  4. Set up the subtraction in base three.

    We subtract column by column from right to left.

    212three−121three\begin{array}{r} 212_{\text{three}} \\ -121_{\text{three}} \\ \hline \end{array}
  5. Subtract the rightmost digits (units place).

    2three−1three=1three2_{\text{three}} - 1_{\text{three}} = 1_{\text{three}}.

    212three−121three1three\begin{array}{r} 212_{\text{three}} \\ -121_{\text{three}} \\ \hline \quad 1_{\text{three}} \end{array}
  6. Subtract the middle digits (3s place).

    We need to calculate 1three−2three1_{\text{three}} - 2_{\text{three}}. Since 1<21 < 2, we must borrow from the next place value (the 323^2 place).
    Borrow 1 from the 2three2_{\text{three}} in the 323^2 place. This borrowed 1 is equivalent to 3three3_{\text{three}} in the 313^1 place.
    So, the 1three1_{\text{three}} in the 313^1 place becomes 1three+3three=4three1_{\text{three}} + 3_{\text{three}} = 4_{\text{three}}.
    Now, subtract: 4three−2three=2three4_{\text{three}} - 2_{\text{three}} = 2_{\text{three}}.
    The 2three2_{\text{three}} in the 323^2 place becomes 1three1_{\text{three}} after borrowing.

    212three1(1+3)−121three21three\begin{array}{r} \cancel{2} \quad \cancel{1} \quad 2_{\text{three}} \\ 1 \quad (1+3) \quad \\ -1 \quad 2 \quad 1_{\text{three}} \\ \hline \quad 2 \quad 1_{\text{three}} \end{array}
  7. Subtract the leftmost digits (323^2 place).

    We now have 1three−1three=0three1_{\text{three}} - 1_{\text{three}} = 0_{\text{three}}.

    142three−121three021three\begin{array}{r} 1 \quad 4 \quad 2_{\text{three}} \\ -1 \quad 2 \quad 1_{\text{three}} \\ \hline 0 \quad 2 \quad 1_{\text{three}} \end{array}
  8. Combine the results.

    The result is 021three021_{\text{three}}, which is written as 21three21_{\text{three}}.

    The result of the workout is 21three\boxed{21_{\text{three}}}.

Was this helpful?

Still stuck on this one?

Ask a follow-up, and the answer starts from this question.

Got a different question?Ask your own question
Handwritten step-by-step solution preview

Handwritten Step-by-Step Solution

Get this as a handwritten image on WhatsApp — like a tutor wrote it for you.

Try on WhatsApp