Question

homework helper
stephen’s father gave him $10 to buy lunch at the concession stand. if his lunch cost $7.74, how much change should stephen give his father?
find $10 - $7.74.
estimate 10 - 8 = 2
1 line up the decimal points. annex zeros so that both numbers end in the same place value.
2 subtract the digits in the same place - value positions. rename as necessary.
3 bring the decimal point straight down in the difference.
so, stephen should give his father $2.26.
check use addition to check your answer.
$2.26 + $7.74 = $10.00
practice
subtract. use addition to check your answer.
1.
\

$$\begin{array}{r} 9.03 \\ - 4.09 \\ \\hline \\end{array}$$

1. 71.65 - 55.12 =

3.
\

$$\begin{array}{r} $18.94 \\ - $3.25 \\ \\hline \\end{array}$$

Explanation:

Problem 1: \(

$$\begin{array}{r} 9.03 \\ - 4.09 \\ \hline \end{array}$$

\)

Step 1: Line up decimals

Ensure decimal points are aligned:

$$\begin{array}{r} 9.03 \\ - 4.09 \\ \hline \end{array}$$

Step 2: Subtract hundredths place

\( 3 - 9 \) is not possible, so borrow from tenths place. Tenths place: \( 0 \) becomes \( -1 \), so we borrow from ones place. Ones place: \( 9 \) becomes \( 8 \), tenths place becomes \( 10 \), then borrow \( 1 \) from tenths to hundredths: tenths becomes \( 9 \), hundredths becomes \( 13 \). Now subtract hundredths: \( 13 - 9 = 4 \).

Step 3: Subtract tenths place

Tenths place: \( 9 - 0 = 9 \) (wait, no: original tenths after borrowing: we had \( 10 \) tenths, gave \( 1 \) to hundredths, so \( 9 \) tenths. Subtract \( 0 \) (from \( 4.09 \) tenths): \( 9 - 0 = 9 \)? Wait, no, let's redo. Wait, \( 9.03 \) is \( 9 + 0.03 \), \( 4.09 \) is \( 4 + 0.09 \). Wait, correct borrowing:

Ones: \( 9 \), tenths: \( 0 \), hundredths: \( 3 \)

Subtract \( 4.09 \): ones \( 4 \), tenths \( 0 \), hundredths \( 9 \)

Hundredths: \( 3 < 9 \), so we need to borrow from tenths. But tenths is \( 0 \), so we borrow from ones: ones becomes \( 8 \), tenths becomes \( 10 \) tenths. Now, borrow \( 1 \) tenth (which is \( 10 \) hundredths) to hundredths: tenths becomes \( 9 \) tenths, hundredths becomes \( 13 \) hundredths.

Now subtract hundredths: \( 13 - 9 = 4 \)

Subtract tenths: \( 9 - 0 = 9 \) (wait, no, the other number's tenths is \( 0 \), so \( 9 - 0 = 9 \))

Subtract ones: \( 8 - 4 = 4 \)

Wait, no, let's do it properly:

$$\begin{array}{r@{}l} & 8 \quad 9 \quad 13 \\ & 9.03 \\ - & 4.09 \\ \hline & 4.94 \\ \end{array}$$

Wait, no, \( 9.03 - 4.09 \):

\( 9.03 - 4.09 = (9 - 4) + (0.03 - 0.09) = 5 + (-0.06) = 4.94 \). Wait, my borrowing was wrong earlier. Let's use decimal subtraction:

\( 9.03 - 4.09 = (8 + 1.03) - 4.09 = 8 - 4 + (1.03 - 4.09) \)? No, better to write as \( 9.03 = 8.9 + 0.13 \), \( 4.09 = 4.0 + 0.09 \). Then \( 8.9 - 4.0 = 4.9 \), \( 0.13 - 0.09 = 0.04 \), so total \( 4.9 + 0.04 = 4.94 \).

Step 4: Check with addition

\( 4.94 + 4.09 = 9.03 \), which matches the minuend. So the result is \( 4.94 \).

Step 1: Line up decimals

$$\begin{array}{r} 71.65 \\ - 55.12 \\ \hline \end{array}$$

Step 2: Subtract hundredths place

\( 5 - 2 = 3 \)

Step 3: Subtract tenths place

\( 6 - 1 = 5 \)

Step 4: Subtract ones place

\( 1 - 5 \) is not possible, so borrow from tens place. Tens place: \( 7 \) becomes \( 6 \), ones place becomes \( 11 \). Now subtract ones: \( 11 - 5 = 6 \)

Step 5: Subtract tens place

\( 6 - 5 = 1 \)

Step 6: Combine results

Tens: \( 1 \), ones: \( 6 \), tenths: \( 5 \), hundredths: \( 3 \), so \( 16.53 \)

Step 7: Check with addition

\( 16.53 + 55.12 = 71.65 \), which matches.

Step 1: Line up decimals

$$\begin{array}{r} 18.94 \\ - 3.25 \\ \hline \end{array}$$

Step 2: Subtract hundredths place

\( 4 - 5 \) is not possible, so borrow from tenths place. Tenths place: \( 9 \) becomes \( 8 \), hundredths becomes \( 14 \). Subtract hundredths: \( 14 - 5 = 9 \)

Step 3: Subtract tenths place

\( 8 - 2 = 6 \)

Step 4: Subtract ones place

\( 8 - 3 = 5 \) (wait, ones place of \( 18.94 \) is \( 8 \), subtract \( 3 \) from \( 3.25 \) ones: \( 8 - 3 = 5 \))

Step 5: Subtract tens place

\( 1 - 0 = 1 \) (tens place of \( 3.25 \) is \( 0 \))

Step 6: Combine results

Tens: \( 1 \), ones: \( 5 \), tenths: \( 6 \), hundredths: \( 9 \), so \( \$15.69 \)

Step 7: Check with addition

\( \$15.69 + \$3.25 = \$18.94 \), which matches.

Answer:

\( 4.94 \)

Problem 2: \( 71.65 - 55.12 \)