This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
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Fresh day Maths, let's solve. 1. 1.342 × 13 Step 1: Set up the multiplication using the column method. @c@\,c@c@c@c@c & 1 & . & 3 & 4 & 2 \\ × & & & & 1 & 3 \\ Step 2: Multiply 1.342 by 3 (the ones digit of 13). 3 × 2 = 6 3 × 4 = 12 (write down 2, carry over 1) 3 × 3 = 9 + 1 (carry-over) = 10 (write down 0, carry over 1) 3 × 1 = 3 + 1 (carry-over) = 4 @c@\,c@c@c@c@c & 1 & . & 3 & 4 & 2 \\ × & & & & 1 & 3 \\ & 4 & . & 0 & 2 & 6 \\ Step 3: Multiply 1.342 by 10 (the tens digit of 13). Add a placeholder zero. 10 × 2 = 20 (write down 0, carry over 2) 10 × 4 = 40 + 2 (carry-over) = 42 (write down 2, carry over 4) 10 × 3 = 30 + 4 (carry-over) = 34 (write down 4, carry over 3) 10 × 1 = 10 + 3 (carry-over) = 13 @c@\,c@c@c@c@c & 1 & . & 3 & 4 & 2 \\ × & & & & 1 & 3 \\ & 4 & . & 0 & 2 & 6 \\ 1 & 3 & . & 4 & 2 & 0 \\ Step 4: Add the results from Step 2 and Step 3. @c@\,c@c@c@c@c & 1 & . & 3 & 4 & 2 \\ × & & & & 1 & 3 \\ & 4 & . & 0 & 2 & 6 \\ + 1 & 3 & . & 4 & 2 & 0 \\ 1 & 7 & . & 4 & 4 & 6 \\ The result is 17.446. 2. 542 × 11 Step 1: Set up the multiplication. @c@\,c@c@c & 5 & 4 & 2 \\ × & & 1 & 1 \\ Step 2: Multiply 542 by 1 (the ones digit). @c@\,c@c@c & 5 & 4 & 2 \\ × & & 1 & 1 \\ & 5 & 4 & 2 \\ Step 3: Multiply 542 by 10 (the tens digit). Add a placeholder zero. @c@\,c@c@c & 5 & 4 & 2 \\ × & & 1 & 1 \\ & 5 & 4 & 2 \\ 5 & 4 & 2 & 0 \\ Step 4: Add the results. @c@\,c@c@c & 5 & 4 & 2 \\ × & & 1 & 1 \\ & 5 & 4 & 2 \\ + 5 & 4 & 2 & 0 \\ 5 & 9 & 6 & 2 \\ The result is 5962. 3. 430 × 12 Step 1: Set up the multiplication. @c@\,c@c@c & 4 & 3 & 0 \\ × & & 1 & 2 \\ Step 2: Multiply 430 by 2. 2 × 0 = 0 2 × 3 = 6 2 × 4 = 8 @c@\,c@c@c & 4 & 3 & 0 \\ × & & 1 & 2 \\ & 8 & 6 & 0 \\ Step 3: Multiply 430 by 10. Add a placeholder zero. 10 × 0 = 0 10 × 3 = 30 (write down 0, carry over 3) 10 × 4 = 40 + 3 (carry-over) = 43 @c@\,c@c@c & 4 & 3 & 0 \\ × & & 1 & 2 \\ & 8 & 6 & 0 \\ 4 & 3 & 0 & 0 \\ Step 4: Add the results. @c@\,c@c@c & 4 & 3 & 0 \\ × & & 1 & 2 \\ & 8 & 6 & 0 \\ + 4 & 3 & 0 & 0 \\ 5 & 1 & 6 & 0 \\ The result is 5160. 4. 417 × 14 Step 1: Set up the multiplication. @c@\,c@c@c & 4 & 1 & 7 \\ × & & 1 & 4 \\ Step 2: Multiply 417 by 4. 4 × 7 = 28 (write down 8, carry over 2) 4 × 1 = 4 + 2 (carry-over) = 6 4 × 4 = 16 @c@\,c@c@c & 4 & 1 & 7 \\ × & & 1 & 4 \\ 1 & 6 & 6 & 8 \\ Step 3: Multiply 417 by 10. Add a placeholder zero. 10 × 7 = 70 (write down 0, carry over 7) 10 × 1 = 10 + 7 (carry-over) = 17 (write down 7, carry over 1) $10 × 4 = 40