Exercise 14.4 More multiplying Estimate the answers to the following sums. Then use the method that yous most comfortable with to work out the sums: \( \begin{array}{lll}\text { 1. } 21,42 \times 3,6 & \text { 2. } 7,325 \times 2,6 & \text { 3. } 12,93 \times 0,4 \\ \text { 4. } 5,425 \times 10,75 & \text { 5. } 30,41 \times 4,57 & \text { 6. } 14,03 \times 1,23\end{array} \)

Below are the six problems. For each one we first estimate by rounding the numbers and then “work‐through” a calculation to get the more exact product. ───────────────────────────── 1. Multiply 21,42 × 3,6  • Estimation:   ­Round 21,42 ≈ 21 and 3,6 ≈ 4. Then 21 × 4 = 84.  • Exact calculation:   21,42 × 3,6   Step 1: Multiply 21,42 by 3:    21,42 × 3 = 64,26   Step 2: Multiply 21,42 by 0,6:    21,42 × 0,6 = 12,852   Step 3: Add the two results:    64,26 + 12,852 = 77,112  • Answer: 77,112 ───────────────────────────── 2. Multiply 7,325 × 2,6  • Estimation:   Round 7,325 ≈ 7,3 and 2,6 ≈ 2,6 (or 2,5–2,6). Using 7,3 × 2,6 roughly gives about 19.  • Exact calculation:   Step 1: Multiply 7,325 by 2:    7,325 × 2 = 14,65   Step 2: Multiply 7,325 by 0,6:    7,325 × 0,6 = 4,395   Step 3: Add these:    14,65 + 4,395 = 19,045  • Answer: 19,045 ───────────────────────────── 3. Multiply 12,93 × 0,4  • Estimation:   Round 12,93 ≈ 13. Then 13 × 0,4 = 5,2.  • Exact calculation:   Directly, 12,93 × 0,4 = 5,172  • Answer: 5,172 ───────────────────────────── 4. Multiply 5,425 × 10,75  • Estimation:   Round 5,425 ≈ 5,4 and 10,75 ≈ 10,8. Then 5,4 × 10,8 is around 58 (since 5,4 × 10 = 54 and 5,4 × 0,8 ≈ 4,32, so 54 + 4,32 ≈ 58,32).  • Exact calculation:   Step 1: Multiply 5,425 by 10:    5,425 × 10 = 54,25   Step 2: Multiply 5,425 by 0,75:    5,425 × 0,75 = 4,06875   Step 3: Sum the two parts:    54,25 + 4,06875 = 58,31875  • Answer: 58,31875 ───────────────────────────── 5. Multiply 30,41 × 4,57  • Estimation:   Round 30,41 ≈ 30 and 4,57 ≈ 4,6. Then 30 × 4,6 = 138.  • Exact calculation:   Step 1: Multiply 30,41 by 4:    30,41 × 4 = 121,64   Step 2: Multiply 30,41 by 0,57:    30,41 × 0,57 ≈ 17,3397   Step 3: Add the two parts:    121,64 + 17,3397 = 138,9797  • Answer: 138,9797 ───────────────────────────── 6. Multiply 14,03 × 1,23  • Estimation:   Round 14,03 ≈ 14 and 1,23 ≈ 1,2 (or use 1,23). Then 14 × 1,23 ≈ 17,22.  • Exact calculation:   Step 1: Multiply 14,03 by 1:    14,03   Step 2: Multiply 14,03 by 0,23:    14,03 × 0,2 = 2,806    14,03 × 0,03 = 0,4209    Sum for the 0,23 part: 2,806 + 0,4209 = 3,2269   Step 3: Total sum:    14,03 + 3,2269 = 17,2569  • Answer: 17,2569 ───────────────────────────── Summary of Answers: 1. 77,112 2. 19,045 3. 5,172 4. 58,31875 5. 138,9797 6. 17,2569 You can choose the method with which you feel most comfortable, whether by splitting into parts as shown above or using a standard algorithm on paper.