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Solve the following arithmetic problems: h) (-48) (-7), i) 11 1/5 - 8 4/5, j) 16.12 3.9

Mathematics

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7 parts
h
336
h(i)

2252\frac{2}{5}

62.868
a
90.4
c
97938
d
3
e
6000
f

34\frac{3}{4}

Step-by-step solution

21 steps

Here are the solutions to the problems:

Part h· 2 steps

(−48)×(−7)(-48) \times (-7)

  1. Multiply the absolute values of the numbers.

    48×7=33648 \times 7 = 336
  2. Determine the sign of the product.

    A negative number multiplied by a negative number results in a positive number.

    (−48)×(−7)=336(-48) \times (-7) = 336

    The product is 336\boxed{336}.

Part h(i)

2252\frac{2}{5}

1115−84511\frac{1}{5} - 8\frac{4}{5}

  1. Convert the mixed numbers to improper fractions.

    1115=(11×5)+15=55+15=56511\frac{1}{5} = \frac{(11 \times 5) + 1}{5} = \frac{55 + 1}{5} = \frac{56}{5} 845=(8×5)+45=40+45=4458\frac{4}{5} = \frac{(8 \times 5) + 4}{5} = \frac{40 + 4}{5} = \frac{44}{5}
  2. Subtract the improper fractions.

    565−445=56−445=125\frac{56}{5} - \frac{44}{5} = \frac{56 - 44}{5} = \frac{12}{5}
  3. Convert the improper fraction back to a mixed number.

    125=225\frac{12}{5} = 2\frac{2}{5}

    The difference is 225\boxed{2\frac{2}{5}}.

    j) 16.12×3.916.12 \times 3.9

  4. Multiply the numbers as if they were whole numbers, ignoring the decimal points for now.

    1612×391612 \times 39
  5. Perform the multiplication.

    1612×3914508(1612×9)48360(1612×30)62868\begin{align*} 1612 \\ \times 39 \\ \hline 14508 & (1612 \times 9) \\ 48360 & (1612 \times 30) \\ \hline 62868 \end{align*}
  6. Count the total number of decimal places in the original numbers.

    16.12 has 2 decimal places.

    3.9 has 1 decimal place.
    Total decimal places = 2+1=32 + 1 = 3.

  7. Place the decimal point in the product so that it has 3 decimal places.

    62.86862.868

    The product is 62.868\boxed{62.868}.

    SECTION B:

Part a90.4

Round off 90.361 to the nearest tenths.

  1. Identify the digit in the tenths place, which is 3.

  2. Look at the digit immediately to its right, which is 6.

  3. Since 6 is 5 or greater, round up the tenths digit.

    The 3 in the tenths place becomes 4.

    90.361≈90.490.361 \approx 90.4

    The rounded number is 90.4\boxed{90.4}.

Part b

Write 10.014 in words.

The number 10.014 is written as Ten and fourteen thousandths.

Part c97938

Which number is expanded to get 30+8+900+7000+9000030 + 8 + 900 + 7000 + 90000?

  1. Arrange the terms in descending order of place value.

    90000+7000+900+30+890000 + 7000 + 900 + 30 + 8
  2. Add the terms together.

    90000+7000=9700090000 + 7000 = 97000 97000+900=9790097000 + 900 = 97900 97900+30=9793097900 + 30 = 97930 97930+8=9793897930 + 8 = 97938

    The number is 97938\boxed{97938}.

Part d3

How many prime numbers are there between 101 and 110?

  1. List the integers between 101 and 110

    $102, 103, 104, 105, 106, 107, 108, 109$.

  2. Identify prime numbers (numbers greater than 1 that have no positive divisors other than 1 and themselves).

    • 102 is even, so it's not prime.
    • 103: Not divisible by 2,3,5,7,112, 3, 5, 7, 11. It is a prime number.
    • 104 is even, so it's not prime.
    • 105 ends in 5, so it's not prime.
    • 106 is even, so it's not prime.
    • 107: Not divisible by 2,3,5,7,112, 3, 5, 7, 11. It is a prime number.
    • 108 is even, so it's not prime.
    • 109: Not divisible by 2,3,5,7,112, 3, 5, 7, 11. It is a prime number. The prime numbers between 101 and 110 are 103,107,109103, 107, 109. There are 3\boxed{3} prime numbers.

Part e6000

Write the place value of 6 in the number 96784.

  1. Identify the position of the digit 6 in the number 96784.

    The digit 6 is in the thousands place.

  2. Determine its value based on its position.

    The place value of 6 is 6×1000=60006 \times 1000 = 6000.
    The place value of 6 is 6000\boxed{6000}.

Part f

34\frac{3}{4}

Which fraction is bigger between 23\frac{2}{3} and 34\frac{3}{4}?

  1. Find a common denominator for the two fractions.

    The least common multiple of 3 and 4 is 12.

  2. Convert each fraction to an equivalent fraction with the common denominator.

    23=2×43×4=812\frac{2}{3} = \frac{2 \times 4}{3 \times 4} = \frac{8}{12} 34=3×34×3=912\frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}
  3. Compare the numerators of the equivalent fractions.

    Since 9>89 > 8, it means 912>812\frac{9}{12} > \frac{8}{12}.
    Therefore, 34\frac{3}{4} is bigger than 23\frac{2}{3}.
    The bigger fraction is 34\boxed{\frac{3}{4}}.

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