Math

QuestionFind all expressions equivalent to 45×1145 \times 11:
1. (11×40)+(11×5)(11 \times 40)+(11 \times 5)
2. (11×50)(11×5)(11 \times 50)-(11 \times 5)
3. (45×10)+(45×1)(45 \times 10)+(45 \times 1)
4. (40×10)+(11+5)(40 \times 10)+(11+5)

Studdy Solution

STEP 1

Assumptions1. The multiplication operation is distributive over addition and subtraction. This means that for any numbers a, b, and c, the equation a * (b + c) = (a * b) + (a * c) holds true. . The multiplication operation is associative. This means that for any numbers a, b, and c, the equation a * (b * c) = (a * b) * c holds true.
3. The multiplication operation is commutative. This means that for any numbers a and b, the equation a * b = b * a holds true.

STEP 2

Calculate the value of 45×1145 \times11.
45×11=49545 \times11 =495

STEP 3

Calculate the value of (11×40)+(11×5)(11 \times40)+(11 \times5).
(11×40)+(11×5)=440+55=495 (11 \times40)+(11 \times5) =440 +55 =495

STEP 4

Calculate the value of (11×50)(11×)(11 \times50)-(11 \times).
(11×50)(11×)=55055=495 (11 \times50)-(11 \times) =550 -55 =495

STEP 5

Calculate the value of (45×10)+(45×1)(45 \times10)+(45 \times1).
(45×10)+(45×1)=450+45=495 (45 \times10)+(45 \times1) =450 +45 =495

STEP 6

Calculate the value of (40×10)+(11+5)(40 \times10)+(11+5).
(40×10)+(11+5)=400+16=416 (40 \times10)+(11+5) =400 +16 =416

STEP 7

Compare the calculated values with the value of 45×1145 \times11.
The equivalent expressions to 45×1145 \times11 are1. (11×40)+(11×5)(11 \times40)+(11 \times5)2. (11×50)(11×5)(11 \times50)-(11 \times5)3. (45×10)+(45×1)(45 \times10)+(45 \times1)The expression (40×10)+(11+5)(40 \times10)+(11+5) is not equivalent to 45×1145 \times11.

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