Question

section 3.6 adding and subtracting decimals
whether we are adding or subtracting decimal numbers we will always check the reasonableness of our answer using estimation.
adding decimals (no calculators)
to add decimal numbers we must line up the decimals so the place values line up.
example: 5.763 + 3.94
\

$$\begin{align} 5.763 \\\\ + \\underline{3.940} \\\\ 9.703 \\end{align}$$

we add going down each column carrying when needed.
we will now use front-end estimation to make sure this answer is reasonable.
so, 5.763 becomes 5 and 3.94 becomes 3. 5 + 3 = 8 which is reasonable.

1. calculate each of the following sums and then use front-end estimation to check the reasonableness of your answer.

(a) 13.1 + 2.4 =
estimation check:
(b) 4.52 + 3.09 =
estimation check:
(c) 3.51 + 9.73 =
estimation check:
(d) 2.168 + 0.948 =
estimation check:

Explanation:

Part (a)

Step 1: Add the decimals

Line up the decimals:

$$\begin{align*} 13.1\\ + \ 2.4\\ \hline 15.5 \end{align*}$$

Step 2: Front - end estimation

Front - end digits: 13 (from 13.1) and 2 (from 2.4).
Estimated sum: \(13 + 2=15\), which is close to 15.5, so the answer is reasonable.

Part (b)

Step 1: Add the decimals

Line up the decimals:

$$\begin{align*} 4.52\\ + \ 3.09\\ \hline 7.61 \end{align*}$$

Step 2: Front - end estimation

Front - end digits: 4 (from 4.52) and 3 (from 3.09).
Estimated sum: \(4+3 = 7\), which is close to 7.61, so the answer is reasonable.

Part (c)

Step 1: Add the decimals

Line up the decimals:

$$\begin{align*} 3.51\\ + \ 9.73\\ \hline 13.24 \end{align*}$$

Step 2: Front - end estimation

Front - end digits: 3 (from 3.51) and 9 (from 9.73).
Estimated sum: \(3 + 9=12\), which is close to 13.24, so the answer is reasonable.

Part (d)

Step 1: Add the decimals

Line up the decimals:

$$\begin{align*} 2.168\\ + \ 0.948\\ \hline 3.116 \end{align*}$$

Step 2: Front - end estimation

Front - end digits: 2 (from 2.168) and 0 (from 0.948).
Estimated sum: \(2+0 = 2\), which is close to 3.116 (the difference is due to the non - front - end digits, but still reasonable as the actual sum is just over 3).

Answer:

(a) \(13.1 + 2.4=\boldsymbol{15.5}\), Estimation check: \(13+2 = 15\)

(b) \(4.52+3.09=\boldsymbol{7.61}\), Estimation check: \(4 + 3=7\)

(c) \(3.51+9.73=\boldsymbol{13.24}\), Estimation check: \(3+9 = 12\)

(d) \(2.168+0.948=\boldsymbol{3.116}\), Estimation check: \(2+0 = 2\)