Write the math expression, 4(5 + 7). Use the distributive property to distribute, or break down, the expression into smaller problems to help you find a solution. The distributive property says 4(5 + 7) = (4 x 5) + (4 x 7). The first term can be multiplied by each of the addends, and the sums added together.
Solve 4(5 + 7) = ? using the distributive property. 4(5 + 7) = (4 x 5) + (4 x 7) or 20 + 28. Add the partial products together, 20 + 28 = 48.
Write the math expression 678 x 8. Use the distributive property starting in the ones place. Eight x 8 = 64. Move to the tens place. The 7 in the tens place means 70, so multiply 70 x 8 = 560. Move to the hundreds place. The 6 in the hundreds place mean 600. Multiply 600 x 8 = 4,800.
Add the three partial products together. Sixty-four + 560 + 4,800 = 5,424.
Rearrange the order of the expression in Step 3 to 8 x 678, if this method is easier for you to solve. Use the distributive property, follow the order of operations -- perform operations inside parentheses first -- to obtain partial products and add the partial products for the solution. Eight x 600 + 8 x 70 + 8 x 8 = 4,800 + 560 + 64 = 5,524.
Solve 456 x 37. Although the multiplier is now a 2-digit number, begin as though you are multiplying by a single digit. When you finish multiplying by 7, you see the 3 in the tens place means 30. Multiply as before, using 30 instead of 7. Four hundred x 7 + 50 x 7 + 6 x 7, then 400 x 30 + 50 x 30 + 6 x 30 = 2,800 + 350 + 42 + 12,000 + 1,500 + 180 = 16,872. For multipliers with three or more digits, use the same process. You'll have more partial products.
Draw two columns. Label the right column "Ones" and the left column "Tens." Visualize the numbers to add or subtract using manipulatives.
Place eight units in the Ones column, and two rods worth 10 units each in the Tens column. This represents the number 28. Add 32 to it by moving down a row, placing two units in the Ones column and three rods in the Tens column.
Add the units in the Ones column 8 + 2 = 10. You can only have nine or fewer units in the Ones column. Remove the units from the Ones column, leaving the column empty, and exchange, or regroup, the units for a rod. Put the rod in the Tens column.
Add the rods in the Tens column. There are six rods worth 10 units each, or 60. Follow the same process for larger numbers, such as exchanging 10 rods for a hundred block, and so on.
Place six units in the Ones column and four rods in the Tens column. Drop down a row and place seven units in the Ones column and three rods in the Tens column. Start in the Ones column. You can't subtract 7 from 6. Regroup by borrowing a group of 10 from the Tens column. Exchange it for 10 units. The Ones column now has 16 units. Subtract 7 from 16 to get 9 in the Ones column. There are no rods in the Tens column, so the answer is 9.