Solved on Jan 19, 2024

Find the sum: $378.03+17.5$ . Find the difference: $18.398-4.37$ . Compute: $18 \cdot 348 - 437 = 61$ .

STEP 1

Assumptions
1. We are performing basic arithmetic operations: addition and subtraction.
2. The numbers involved are in decimal form.
3. The subtraction in the second part involves both decimal subtraction and integer subtraction.

STEP 2

To find the sum of the two decimal numbers, we align the decimal points and add the numbers column by column starting from the rightmost digit.
$\begin{array}{r} 378.03 \\ + 17.5 \\ \end{array}$

STEP 3

We place a zero in the hundredths place of the number 17.5 to align the decimal places.
$\begin{array}{r} 378.03 \\ + 17.50 \\ \end{array}$

STEP 4

Now we add the numbers starting from the rightmost column (hundredths place).
$\begin{array}{r} 378.03 \\ + 17.50 \\ \hline 395.53 \\ \end{array}$

STEP 5

The sum of the two numbers is $395.53$ .

STEP 6

To find the difference between two decimal numbers, we align the decimal points and subtract the numbers column by column starting from the rightmost digit.
$\begin{array}{r} 18.398 \\ - 4.37 \\ \end{array}$

STEP 7

We place a zero in the thousandths place of the number 4.37 to align the decimal places.
$\begin{array}{r} 18.398 \\ - 4.370 \\ \end{array}$

STEP 8

Now we subtract the numbers starting from the rightmost column (thousandths place).
$\begin{array}{r} 18.398 \\ - 4.370 \\ \hline 14.028 \\ \end{array}$

STEP 9

The difference between the two decimal numbers is $14.028$ .

STEP 10

For the integer subtraction, we align the numbers vertically and subtract the bottom number from the top number.
$\begin{array}{r} 18 \cdot 348 \\ -\quad 437 \\ \end{array}$

STEP 11

We notice that the subtraction is not possible in the units place (8 - 7 is possible, but 4 - 3 is not without borrowing). We need to borrow from the hundreds place.

STEP 12

After borrowing, the number 18 becomes 17 and the number 348 becomes 1448.
$\begin{array}{r} 17 \cdot 1448 \\ -\quad 437 \\ \end{array}$

STEP 13

Now we subtract starting from the rightmost digit.
$\begin{array}{r} 17 \cdot 1448 \\ -\quad 437 \\ \hline 17 \cdot 1011 \\ \end{array}$

STEP 14

The difference between the two integers is $17 \cdot 1011$ .

STEP 15

We interpret the dot as multiplication and calculate the product of 17 and 1011.
$17 \times 1011$

STEP 16

Multiply the two numbers.
$17 \times 1011 = 17187$

STEP 17

The result of the integer subtraction, interpreted as a multiplication, is $17187$ .
The solutions to the problems are:
1. The sum of $378.03$ and $17.5$ is $395.53$ .
2. The difference between $18.398$ and $4.37$ is $14.028$ .
3. The difference between $18 \cdot 348$ and $437$ , interpreted as a multiplication, is $17187$ .

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Find the sum: $378.03+17.5$ . Find the difference: $18.398-4.37$ . Compute: $18 \cdot 348 - 437 = 61$ .

STEP 1

Assumptions
1. We are performing basic arithmetic operations: addition and subtraction.
2. The numbers involved are in decimal form.
3. The subtraction in the second part involves both decimal subtraction and integer subtraction.

STEP 2

To find the sum of the two decimal numbers, we align the decimal points and add the numbers column by column starting from the rightmost digit.
$\begin{array}{r} 378.03 \\ + 17.5 \\ \end{array}$

STEP 3

We place a zero in the hundredths place of the number 17.5 to align the decimal places.
$\begin{array}{r} 378.03 \\ + 17.50 \\ \end{array}$

STEP 4

Now we add the numbers starting from the rightmost column (hundredths place).
$\begin{array}{r} 378.03 \\ + 17.50 \\ \hline 395.53 \\ \end{array}$

STEP 5

The sum of the two numbers is $395.53$ .

STEP 6

To find the difference between two decimal numbers, we align the decimal points and subtract the numbers column by column starting from the rightmost digit.
$\begin{array}{r} 18.398 \\ - 4.37 \\ \end{array}$

STEP 7

We place a zero in the thousandths place of the number 4.37 to align the decimal places.
$\begin{array}{r} 18.398 \\ - 4.370 \\ \end{array}$

STEP 8

Now we subtract the numbers starting from the rightmost column (thousandths place).
$\begin{array}{r} 18.398 \\ - 4.370 \\ \hline 14.028 \\ \end{array}$

STEP 9

The difference between the two decimal numbers is $14.028$ .

STEP 10

For the integer subtraction, we align the numbers vertically and subtract the bottom number from the top number.
$\begin{array}{r} 18 \cdot 348 \\ -\quad 437 \\ \end{array}$

STEP 11

We notice that the subtraction is not possible in the units place (8 - 7 is possible, but 4 - 3 is not without borrowing). We need to borrow from the hundreds place.

STEP 12

After borrowing, the number 18 becomes 17 and the number 348 becomes 1448.
$\begin{array}{r} 17 \cdot 1448 \\ -\quad 437 \\ \end{array}$

STEP 13

Now we subtract starting from the rightmost digit.
$\begin{array}{r} 17 \cdot 1448 \\ -\quad 437 \\ \hline 17 \cdot 1011 \\ \end{array}$

STEP 14

The difference between the two integers is $17 \cdot 1011$ .

STEP 15

We interpret the dot as multiplication and calculate the product of 17 and 1011.
$17 \times 1011$

STEP 16

Multiply the two numbers.
$17 \times 1011 = 17187$

STEP 17

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Find the sum: 378.03+17.5378.03+17.5378.03+17.5. Find the difference: 18.398−4.3718.398-4.3718.398−4.37. Compute: 18⋅348−437=6118 \cdot 348 - 437 = 6118⋅348−437=61.

STEP 1

Assumptions1. We are performing basic arithmetic operations: addition and subtraction.2. The numbers involved are in decimal form.3. The subtraction in the second part involves both decimal subtraction and integer subtraction.

STEP 2

To find the sum of the two decimal numbers, we align the decimal points and add the numbers column by column starting from the rightmost digit.378.03+17.5 \begin{array}{r} 378.03 \\ + 17.5 \\ \end{array} 378.03+17.5​

STEP 3

We place a zero in the hundredths place of the number 17.5 to align the decimal places.378.03+17.50 \begin{array}{r} 378.03 \\ + 17.50 \\ \end{array} 378.03+17.50​

STEP 4

Now we add the numbers starting from the rightmost column (hundredths place).378.03+17.50395.53 \begin{array}{r} 378.03 \\ + 17.50 \\ \hline 395.53 \\ \end{array} 378.03+17.50395.53​​

STEP 5

The sum of the two numbers is 395.53395.53395.53.

STEP 6

To find the difference between two decimal numbers, we align the decimal points and subtract the numbers column by column starting from the rightmost digit.18.398−4.37 \begin{array}{r} 18.398 \\ - 4.37 \\ \end{array} 18.398−4.37​

STEP 7

We place a zero in the thousandths place of the number 4.37 to align the decimal places.18.398−4.370 \begin{array}{r} 18.398 \\ - 4.370 \\ \end{array} 18.398−4.370​

STEP 8

Now we subtract the numbers starting from the rightmost column (thousandths place).18.398−4.37014.028 \begin{array}{r} 18.398 \\ - 4.370 \\ \hline 14.028 \\ \end{array} 18.398−4.37014.028​​

STEP 9

The difference between the two decimal numbers is 14.02814.02814.028.

STEP 10

For the integer subtraction, we align the numbers vertically and subtract the bottom number from the top number.18⋅348−437 \begin{array}{r} 18 \cdot 348 \\ -\quad 437 \\ \end{array} 18⋅348−437​

STEP 11

We notice that the subtraction is not possible in the units place (8 - 7 is possible, but 4 - 3 is not without borrowing). We need to borrow from the hundreds place.

STEP 12

After borrowing, the number 18 becomes 17 and the number 348 becomes 1448.17⋅1448−437 \begin{array}{r} 17 \cdot 1448 \\ -\quad 437 \\ \end{array} 17⋅1448−437​

STEP 13

Now we subtract starting from the rightmost digit.17⋅1448−43717⋅1011 \begin{array}{r} 17 \cdot 1448 \\ -\quad 437 \\ \hline 17 \cdot 1011 \\ \end{array} 17⋅1448−43717⋅1011​​

STEP 14

The difference between the two integers is 17⋅101117 \cdot 101117⋅1011.

STEP 15

We interpret the dot as multiplication and calculate the product of 17 and 1011.17×1011 17 \times 1011 17×1011

STEP 16

Multiply the two numbers.17×1011=17187 17 \times 1011 = 17187 17×1011=17187

STEP 17

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Find the sum: $378.03+17.5$ . Find the difference: $18.398-4.37$ . Compute: $18 \cdot 348 - 437 = 61$ .

Assumptions
1. We are performing basic arithmetic operations: addition and subtraction.
2. The numbers involved are in decimal form.
3. The subtraction in the second part involves both decimal subtraction and integer subtraction.

To find the sum of the two decimal numbers, we align the decimal points and add the numbers column by column starting from the rightmost digit.
$\begin{array}{r} 378.03 \\ + 17.5 \\ \end{array}$

We place a zero in the hundredths place of the number 17.5 to align the decimal places.
$\begin{array}{r} 378.03 \\ + 17.50 \\ \end{array}$

Now we add the numbers starting from the rightmost column (hundredths place).
$\begin{array}{r} 378.03 \\ + 17.50 \\ \hline 395.53 \\ \end{array}$

The sum of the two numbers is $395.53$ .

To find the difference between two decimal numbers, we align the decimal points and subtract the numbers column by column starting from the rightmost digit.
$\begin{array}{r} 18.398 \\ - 4.37 \\ \end{array}$

We place a zero in the thousandths place of the number 4.37 to align the decimal places.
$\begin{array}{r} 18.398 \\ - 4.370 \\ \end{array}$

Now we subtract the numbers starting from the rightmost column (thousandths place).
$\begin{array}{r} 18.398 \\ - 4.370 \\ \hline 14.028 \\ \end{array}$

The difference between the two decimal numbers is $14.028$ .

For the integer subtraction, we align the numbers vertically and subtract the bottom number from the top number.
$\begin{array}{r} 18 \cdot 348 \\ -\quad 437 \\ \end{array}$

After borrowing, the number 18 becomes 17 and the number 348 becomes 1448.
$\begin{array}{r} 17 \cdot 1448 \\ -\quad 437 \\ \end{array}$

Now we subtract starting from the rightmost digit.
$\begin{array}{r} 17 \cdot 1448 \\ -\quad 437 \\ \hline 17 \cdot 1011 \\ \end{array}$

The difference between the two integers is $17 \cdot 1011$ .

We interpret the dot as multiplication and calculate the product of 17 and 1011.
$17 \times 1011$

Multiply the two numbers.
$17 \times 1011 = 17187$