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Solve the following arithmetic problems: b) 3 (3)/(5) + 1 (2)/(5) c) 14 - (-26) d) 0.357 x 2.7 e) -17 - (60 - 84) f) 6 (2)/(3) - (1)/(8)

Mathematics

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38 steps

Part b· 3 steps

  1. Convert mixed numbers to improper fractions or add whole numbers and fractions separately.

    335+125=(3+1)+(35+25)3\frac{3}{5} + 1\frac{2}{5} = (3+1) + \left(\frac{3}{5} + \frac{2}{5}\right)

  2. Add the whole numbers and the fractions.

    4+3+25=4+554 + \frac{3+2}{5} = 4 + \frac{5}{5}

  3. Simplify the fraction.

    4+1=54 + 1 = 5

    The answer is 5\boxed{5}.

Part c· 2 steps

  1. Rewrite the subtraction of a negative number as addition.

    14−(−26)=14+2614 - (-26) = 14 + 26

  2. Perform the addition.

    14+26=4014 + 26 = 40

    The answer is 40\boxed{40}.

Part d· 3 steps

  1. Multiply the numbers as if they were integers.

    357×27=9639357 \times 27 = 9639

  2. Count the total number of decimal places in the original numbers (3 in 0.357 and 1 in 2.7, for a total of 4).

  3. Place the decimal point in the product.

    0.357×2.7=0.96390.357 \times 2.7 = 0.9639

    The answer is 0.9639\boxed{0.9639}.

Part e· 4 steps

  1. Perform the operation inside the parentheses first.

    60−84=−2460 - 84 = -24

  2. Substitute the result back into the expression.

    −17−(−24)-17 - (-24)

  3. Rewrite the subtraction of a negative number as addition.

    −17+24-17 + 24

  4. Perform the addition.

    −17+24=7-17 + 24 = 7

    The answer is 7\boxed{7}.

Part f· 5 steps

  1. Convert the mixed number to an improper fraction.

    623=(6×3)+23=18+23=2036\frac{2}{3} = \frac{(6 \times 3) + 2}{3} = \frac{18 + 2}{3} = \frac{20}{3}

  2. Find a common denominator for the fractions 203\frac{20}{3} and 18\frac{1}{8}.

    The least common multiple of 3 and 8 is 24.

  3. Convert both fractions to have the common denominator.

    203=20×83×8=16024\frac{20}{3} = \frac{20 \times 8}{3 \times 8} = \frac{160}{24} 18=1×38×3=324\frac{1}{8} = \frac{1 \times 3}{8 \times 3} = \frac{3}{24}

  4. Perform the subtraction.

    16024−324=160−324=15724\frac{160}{24} - \frac{3}{24} = \frac{160 - 3}{24} = \frac{157}{24}

  5. Convert the improper fraction back to a mixed number.

    157÷24=6 with a remainder of 13157 \div 24 = 6 \text{ with a remainder of } 13

    So, 15724=61324\frac{157}{24} = 6\frac{13}{24}.
    The answer is 61324\boxed{6\frac{13}{24}}.

Part g· 4 steps

  1. Perform the division.

    130.2÷62130.2 \div 62

  2. Divide 130 by 62.

    130÷62=2 with a remainder of 6130 \div 62 = 2 \text{ with a remainder of } 6

  3. Bring down the 2 after the decimal point.

    62÷62=162 \div 62 = 1

  4. Place the decimal point in the quotient.

    130.2÷62=2.1130.2 \div 62 = 2.1

    The answer is 2.1\boxed{2.1}.

Part h· 3 steps

  1. Multiply 403 by 2.

    403×2=806403 \times 2 = 806

  2. Multiply 403 by 40.

    403×40=16120403 \times 40 = 16120

  3. Add the results from Step 1 and Step 2.

    806+16120=16926806 + 16120 = 16926

    The answer is 16926\boxed{16926}.

Part h(i)· 14 steps

  1. Add the whole numbers.

    9+16=259 + 16 = 25

  2. Add the fractions.

    Since they have the same denominator, add the numerators.

    46+26=4+26=66\frac{4}{6} + \frac{2}{6} = \frac{4+2}{6} = \frac{6}{6}

  3. Simplify the fraction.

    66=1\frac{6}{6} = 1

  4. Add the results from Step 1 and Step 3.

    25+1=2625 + 1 = 26

    The answer is 26\boxed{26}.

    j)

  5. Perform the division.

    3857÷193857 \div 19

  6. Divide 38 by 19.

    38÷19=238 \div 19 = 2

  7. Bring down 5.

    5÷19=05 \div 19 = 0 with a remainder of 5.

  8. Bring down 7.

    57÷19=357 \div 19 = 3.

    3857÷19=2033857 \div 19 = 203

    The answer is 203\boxed{203}.

    2. a)

  9. Identify the range for the number

    greater than 160 and smaller than 180.

  10. List multiples of 17 until one falls within the specified range.

    17×9=15317 \times 9 = 153 17×10=17017 \times 10 = 170 17×11=18717 \times 11 = 187

  11. Select the multiple that is between 160 and 180.

    The number is 170\boxed{170}.

    2. b)

  12. List all integers between 20 and 45.

    21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,4421, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44

  13. Identify prime numbers (numbers greater than 1 that have no positive divisors other than 1 and themselves) from the list.

    • 23 (prime)
    • 29 (prime)
    • 31 (prime)
    • 37 (prime)
    • 41 (prime)
    • 43 (prime)

  14. Count the identified prime numbers.

    There are 6 prime numbers between 20 and 45.
    The answer is 6\boxed{6}.

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