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Simplify the questions below without using a calculator

Mathematics

ScanSolve AI Answer

Answer

B

5

Step-by-step solution

24 steps

Part 1

Part 1.1· 2 steps

  1. Perform the operations from left to right.

    6−8+(−3)=6−8−36 - 8 + (-3) = 6 - 8 - 3

  2. Subtract and add.

    6−8−3=−2−3=−56 - 8 - 3 = -2 - 3 = -5

    The correct option is B. -5.

Part 1.2· 3 steps

The question asks for the answer to (−2)(−2)(−2)(−2)(-2)(-2)(-2)(-2).

  1. Multiply the first two terms.

    (−2)×(−2)=4(-2) \times (-2) = 4

  2. Multiply the result by the next term.

    4×(−2)=−84 \times (-2) = -8

  3. Multiply the result by the last term.

    −8×(−2)=16-8 \times (-2) = 16

    However, 16 is not among the given options. It is possible there is a typo in the question and it intended to ask for (−2)(−2)(−2)(-2)(-2)(-2). Assuming this, we proceed:

    (−2)×(−2)×(−2)=4×(−2)=−8(-2) \times (-2) \times (-2) = 4 \times (-2) = -8

    The correct option, based on the assumption of three factors, is D. -8.

Part 1.3· 3 steps

  1. Write the fraction and simplify the signs.

    −150−350=150350\frac{-150}{-350} = \frac{150}{350}

  2. Divide both the numerator and the denominator by their greatest common divisor.

    First, divide by 10.

    150÷10350÷10=1535\frac{150 \div 10}{350 \div 10} = \frac{15}{35}

  3. Divide by 5.

    15÷535÷5=37\frac{15 \div 5}{35 \div 5} = \frac{3}{7}

    The correct option is C. 37\frac{3}{7}.

Part 1.4· 1 step

  1. Divide the numerator by the denominator.

    740=7÷40=0.175\frac{7}{40} = 7 \div 40 = 0.175

    The correct option is A. 0,175.

Part 1.5· 2 steps

  1. Identify the pattern.

    The given sequence is 1;112;2;212;...1; 1\frac{1}{2}; 2; 2\frac{1}{2}; ...
    This can be written as 1;1.5;2;2.5;...1; 1.5; 2; 2.5; ...
    The common difference between consecutive terms is 0.5 or 12\frac{1}{2}.

  2. Calculate the next three terms.

    The next term after 2122\frac{1}{2} is 212+12=32\frac{1}{2} + \frac{1}{2} = 3.
    The term after that is 3+12=3123 + \frac{1}{2} = 3\frac{1}{2}.
    The term after that is 312+12=43\frac{1}{2} + \frac{1}{2} = 4.
    The next three terms are 3;312;43; 3\frac{1}{2}; 4.
    The correct option is C. 3;312;43; 3\frac{1}{2}; 4.

Part 1.6· 2 steps

  1. Evaluate the exponent first.

    5×(−5)2=5×(25)5 \times (-5)^2 = 5 \times (25)

  2. Perform the multiplication.

    5×25=1255 \times 25 = 125

    The correct option is D. 125.

Part 1.7· 2 steps

  1. Simplify each term.

    3×2×m−3×1×m=6m−3m3 \times 2 \times m - 3 \times 1 \times m = 6m - 3m

  2. Combine like terms.

    6m−3m=3m6m - 3m = 3m

    The correct option is D. 3m3m.

Part 1.8· 2 steps

  1. Write the equation.

    x4=3\frac{x}{4} = 3

  2. Multiply both sides by 4 to solve for xx.

    x=3×4x = 3 \times 4 x=12x = 12

    The correct option is A. x=12x=12.

Part 2

Part 2.1· 3 steps

  1. Perform the operation inside the parentheses.

    (3−3)×1+2+2=(0)×1+2+2(3-3) \times 1 + 2 + 2 = (0) \times 1 + 2 + 2

  2. Perform the multiplication.

    0×1+2+2=0+2+20 \times 1 + 2 + 2 = 0 + 2 + 2

  3. Perform the additions.

    0+2+2=40 + 2 + 2 = 4

    The simplified answer is 4\boxed{\text{4}}.

Part 2.2· 3 steps

  1. Express the ratio as a fraction.

    6:18=6186:18 = \frac{6}{18}

  2. Simplify the fraction by dividing the numerator and denominator by their greatest common divisor, which is 6.

    6÷618÷6=13\frac{6 \div 6}{18 \div 6} = \frac{1}{3}

  3. Write the simplified fraction back as a ratio.

    13=1:3\frac{1}{3} = 1:3

    The simplified answer is 1:3\boxed{\text{1:3}}.

Part 2.3· 1 step

  1. Multiply the two negative numbers.

    Remember that a negative number multiplied by a negative number results in a positive number.

    (−3)×(−6)=18(-3) \times (-6) = 18

    The simplified answer is 18\boxed{\text{18}}.

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