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Solve the following number sentences for the unknown:

Mathematics

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Step-by-step solution

21 steps

here are the solutions for the number sentences:

1.

  1. Rewrite the equation to isolate the unknown.

    1172−□=2711172 - \square = 271 □=1172−271\square = 1172 - 271
  2. Perform the subtraction.

    □=901\square = 901

    The correct value is 901\boxed{\text{901}}.

    2.

  3. Rewrite the equation to isolate the unknown.

    □×3=396\square \times 3 = 396 □=3963\square = \frac{396}{3}
  4. Perform the division.

    □=132\square = 132

    The correct value is 132\boxed{\text{132}}.

    3.

  5. Subtract 3 from both sides of the equation.

    42÷□+3=942 \div \square + 3 = 9 42÷□=9−342 \div \square = 9 - 3 42÷□=642 \div \square = 6
  6. Rewrite the equation to isolate the unknown.

    □=426\square = \frac{42}{6}
  7. Perform the division.

    □=7\square = 7

    The correct value is 7\boxed{\text{7}}.

    4.

  8. Rewrite the equation to isolate the unknown.

    8×□=48 \times \square = 4 □=48\square = \frac{4}{8}
  9. Simplify the fraction.

    □=12\square = \frac{1}{2}

    The correct value is 12\boxed{\frac{1}{2}} or 0.5\boxed{0.5}.

    5.

  10. Rewrite the equation to isolate the unknown.

    (Assuming 13,8 means 13.8)

    13.8+□=2813.8 + \square = 28 □=28−13.8\square = 28 - 13.8
  11. Perform the subtraction.

    □=14.2\square = 14.2

    The correct value is 14.2\boxed{\text{14.2}}.

    6.

  12. Subtract 1 from both sides of the equation.

    15=2×□+115 = 2 \times \square + 1 15−1=2×□15 - 1 = 2 \times \square 14=2×□14 = 2 \times \square
  13. Rewrite the equation to isolate the unknown.

    □=142\square = \frac{14}{2}
  14. Perform the division.

    □=7\square = 7

    The correct value is 7\boxed{\text{7}}.

    7.

  15. Rewrite the equation to isolate the unknown.

    23×□=1\frac{2}{3} \times \square = 1 □=1÷23\square = 1 \div \frac{2}{3}
  16. Multiply by the reciprocal of the fraction.

    □=1×32\square = 1 \times \frac{3}{2} □=32\square = \frac{3}{2}

    The correct value is 32\boxed{\frac{3}{2}} or 1.5\boxed{1.5}.

    8.

  17. Convert the mixed number to a decimal or improper fraction.

    112=1.51\frac{1}{2} = 1.5
  18. Rewrite the equation to isolate the unknown.

    1.5+□=41.5 + \square = 4 □=4−1.5\square = 4 - 1.5
  19. Perform the subtraction.

    □=2.5\square = 2.5

    The correct value is 2.5\boxed{\text{2.5}} or 212\boxed{2\frac{1}{2}}.

    9.

  20. Take the square root of both sides of the equation.

    □2=49\square^2 = 49 □=49\square = \sqrt{49}
  21. Calculate the square root.

    □=7\square = 7

    The correct value is 7\boxed{\text{7}}.

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