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A cleft sentence is a complex sentence (one having a main clause and a dependent clause) that has a meaning that could be expressed by a simple sentence. Clefts typically put a particular constituent into focus. In spoken language, this focusing is often accompanied by a special intonation. In English, a cleft sentence can be constructed as ...
[2] [3] Thus, in the expression 1 + 2 × 3, the multiplication is performed before addition, and the expression has the value 1 + (2 × 3) = 7, and not (1 + 2) × 3 = 9. When exponents were introduced in the 16th and 17th centuries, they were given precedence over both addition and multiplication and placed as a superscript to the right of ...
Four bags with three marbles per bag gives twelve marbles (4 × 3 = 12). Multiplication can also be thought of as scaling. Here, 2 is being multiplied by 3 using scaling, giving 6 as a result. Animation for the multiplication 2 × 3 = 6 4 × 5 = 20. The large rectangle is made up of 20 squares, each 1 unit by 1 unit.
This example uses peasant multiplication to multiply 11 by 3 to arrive at a result of 33. Decimal: Binary: 11 3 1011 11 5 6 101 110 2 12 10 1100 1 24 1 11000 —— —————— 33 100001 Describing the steps explicitly: 11 and 3 are written at the top
so 3 × 17 = 30 + 21 = 51. This is the "grid" or "boxes" structure which gives the multiplication method its name. Faced with a slightly larger multiplication, such as 34 × 13, pupils may initially be encouraged to also break this into tens. So, expanding 34 as 10 + 10 + 10 + 4 and 13 as 10 + 3, the product 34 × 13 might be represented:
(For example, the sixth row is read as: 0 ⁄ 6 1 ⁄ 2 3 ⁄ 6 → 756). Like in multiplication shown before, the numbers are read from right to left and add the diagonal numbers from top-right to left-bottom (6 + 0 = 6; 3 + 2 = 5; 1 + 6 = 7). The largest number less than the current remainder, 1078 (from the eighth row), is found.