e":"Multiply by the tens","content":"Next, multiply $804$ by the tens digit, which is $6$ (representing $60$). We put a placeholder $0$ in the units column and multiply by $6$:\n\n$$\\begin{aligned}\n804 \\times 60 &= 804 \\times 6 \\times 10 \\\\\n&= 4824 \\times 10 \\\\\n&= 48240\n\\end{aligned}$$\n\nWrite down **48240** as our second row."},{"type":"text","order":3,"title":"Add the rows together","content":"Now we add the two rows together to get the total product:\n\n$$\\begin{aligned}\n\\phantom{+1}5628 \\\\\n+\\ \\ 48240 \\\\\n\\hline\n\\phantom{11}53868\n\\end{aligned}$$\n\nSo, $804 \\times 67 = 53868$. This step earns the method mark M1."},{"type":"text","order":4,"title":"Place the decimal point","content":"Finally, we place the decimal point back into our answer. Since our original numbers had a total of $3$ decimal places, we count $3$ decimal places from the right of $53868$:\n\n$$53868 \\rightarrow 53.868$$\n\nThus, the final answer is **$53.868$** A1."}]},{"id":"10e96d63-f711-4e62-a6ef-d26a1d3bc1f7:grid_method","label":"Grid Method","steps":[{"type":"text","order":0,"title":"Count the Decimal Places","content":"To multiply decimals easily, we can first ignore the decimal points and multiply the numbers as if they were whole numbers. \n\nBefore we do that, let's count how many decimal places we have in our original numbers:\n* $8.04$ has **2** decimal places.\n* $6.7$ has **1** decimal place.\n\nIn total, our final answer must have $2 + 1 = 3$ decimal places. \n\nNow, let's focus on calculating the whole-number multiplication: \n\n$$804 \\times 67$$"},{"type":"text","order":1,"title":"Set Up the Grid","content":"We will use the **Grid Method** to multiply $804 \\times 67$. First, we partition each number into its place value components:\n* $804 = 800 + 4$\n* $67 = 60 + 7$\n\nLet's draw a grid with these partitioned values:\n\n$$\n\\begin{array}{c|c|c}\n\\times & 800 & 4 \\\\\n\\hline\n60 & & \\\\\n\\hline\n7 & & \\\\\n\\end{array}\n$$"},{"type":"text","order":2,"title":"Calculate Partial Products","content":"Now, we multiply the numbers in each row and column to find the partial products:\n\n* Top-left: $60 \\times 800 = 48,000$\n* Top-right: $60 \\times 4 = 240$\n* Bottom-left: $7 \\times 800 = 5,600$\n* Bottom-right: $7 \\times 4 = 28$\n\nLet's fill these values into our grid:\n\n$$\n\\begin{array}{c|c|c}\n\\times & 800 & 4 \\\\\n\\hline\n60 & 48,000 & 240 \\\\\n\\hline\n7 & 5,600 & 28 \\\\\n\\end{array}\n$$"},{"type":"text","order":3,"title":"Sum the Partial Products","content":"Next, we add all the partial products together to get our total product. This step shows your working for long multiplication and earns you the first mark M1:\n\n$$\\begin{aligned}\n\\text{Sum} &= 48,000 + 5,600 + 240 + 28 \\\\\n&= 53,600 + 240 + 28 \\\\\n&= 53,840 + 28 \\\\\n&= 53,868\n\\end{aligned}$$\n\nSo, $804 \\times 67 = 53,868$."},{"type":"text","order":4,"title":"Place the Decimal Point","content":"Finally, we need to place the decimal point back into our result. \n\nSince we determined in Step 1 that our final answer must have **3** decimal places, we count 3 digits from the right of $53,868$:\n\n$$53,868 \\rightarrow 53.868$$\n\nThus, the final answer is:\n\n$$\\mathbf{53.868}$$\n\nThis final correct answer secures the accuracy mark A1."}]}],"generatedAt":"2026-06-12T13:50:47.068Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"firstAttemptFullMarks":{"percent":48,"sampleSize":221}},{"id":"8594ef7b-c8c5-4ebd-9f40-b3e74a41d0fa","revisionId":"596da3a1-98b0-498c-ba09-45ffa4e4b53d","questionNumber":null,"questionType":"LA","specification":"","difficulty":1,"difficultyBand":"easy","totalMarks":2,"sourceTitle":null,"calculatorUse":"non_calc","parts":[{"id":"868a2753-de23-4886-922b-bfbca7cdb8d8","label":"a","content":"Work out $487 \\times 6$","markscheme":"- Award method mark for evidence of a complete multiplication method, such as grid method, long multiplication, or partitioning. M1\n- Final answer 2922. A1","marks":2,"

Multiplication and Division Questions

Multiplication and Division Questions

Multiplication and Division Questions

Multiplication and Division Questions