Question

1. calculate each of the following sums and then use front-end estimation to 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: Calculate the sum

To find \(13.1 + 2.4\), we add the decimal numbers:

$$13.1+2.4 = 15.5$$

Step 2: Front - end estimation

Front - end estimation means we use the leading digits. For \(13.1\), the front - end digit is \(13\) (we can consider the whole number part), and for \(2.4\), the front - end digit is \(2\). Then \(13 + 2=15\). The actual sum \(15.5\) is close to \(15\), so the answer is reasonable.

Part (b)

Step 1: Calculate the sum

To find \(4.52+3.09\), we add the decimal numbers:

$$4.52 + 3.09=7.61$$

Step 2: Front - end estimation

For \(4.52\), the front - end digit (whole number part) is \(4\), and for \(3.09\), the front - end digit is \(3\). Then \(4 + 3 = 7\). The actual sum \(7.61\) is close to \(7\), so the answer is reasonable.

Part (c)

Step 1: Calculate the sum

To find \(3.51+9.73\), we add the decimal numbers:

$$3.51+9.73 = 13.24$$

Step 2: Front - end estimation

For \(3.51\), the front - end digit (whole number part) is \(3\), and for \(9.73\), the front - end digit is \(9\). Then \(3+9 = 12\). The actual sum \(13.24\) is close to \(12\), so the answer is reasonable.

Part (d)

Step 1: Calculate the sum

To find \(2.168+0.948\), we add the decimal numbers:

$$2.168+0.948=3.116$$

Step 2: Front - end estimation

For \(2.168\), the front - end digit (whole number part) is \(2\), and for \(0.948\), the front - end digit is \(0\) (or we can consider \(1\) since \(0.948\) is close to \(1\)). If we take \(2 + 1=3\). The actual sum \(3.116\) is close to \(3\), so the answer is reasonable.

Answer:

(a) Sum: \(15.5\), Estimation check: \(13 + 2=15\) (close to \(15.5\))
(b) Sum: \(7.61\), Estimation check: \(4+3 = 7\) (close to \(7.61\))
(c) Sum: \(13.24\), Estimation check: \(3 + 9=12\) (close to \(13.24\))
(d) Sum: \(3.116\), Estimation check: \(2+1 = 3\) (close to \(3.116\))