Fill in the blanks.
(i) 1,381 x 74 = ___ x 1,381
(ii) ___ x 67 = 67 x 1,287
(iii) 7,635 x ___ = 7,635
(iv) 6,081 x 28 = ___ x 6,081
Name the property.
(i) 1,438 x 713 = 713 x 1,438
(ii) 2,317 x 0 = 0
(iii) 1,432 x (8 x 15) = (1,432 x 8) x 15
(iv) 4,135 x (10 + 9) = 4,135 x 10 + 4,135 x 9
Fill in the blanks.
(i) 4,379 x 10 = ___
(ii) 8,376 x 100 = ___
(iii) 4,518 x 10 = ___
(iv) 98 x 1,000 = ___
(v) 94 x 1,000 = ___
(vi) 1,000 x 45 = ___
Answer (2)
Let's solve each part of the question step-by-step:
Fill in the blanks:
(i) 1,381 \times 74 = ___ \times 1,381
The property being used here is the commutative property of multiplication , which states that changing the order of the factors does not change the product.
So, 1 , 381 × 74 = 74 × 1 , 381 . Therefore, the blank is 74 .
(ii) ___ × 67 = 67 × 1 , 287
Again, using the commutative property of multiplication.
So, 1 , 287 × 67 = 67 × 1 , 287 . Therefore, the blank is 1,287 .
(iii) 7,635 \times ___ = 7,635
This uses the identity property of multiplication , which states that any number multiplied by 1 is the number itself.
Therefore, the blank is 1 .
(iv) 6,081 \times 28 = ___ \times 6,081
Using the commutative property again.
So, 6 , 081 × 28 = 28 × 6 , 081 . Therefore, the blank is 28 .
Name the property:
(i) 1 , 438 × 713 = 713 × 1 , 438
This is the commutative property of multiplication .
(ii) 2 , 317 × 0 = 0
This is the zero property of multiplication , which states any number multiplied by 0 is 0.
(iii) 1 , 432 × ( 8 × 15 ) = ( 1 , 432 × 8 ) × 15
This is the associative property of multiplication , which states that how factors are grouped does not change the product.
(iv) 4 , 135 × ( 10 + 9 ) = 4 , 135 × 10 + 4 , 135 × 9
This is the distributive property , which relates multiplication and addition.
Fill in the blanks:
(i) 4,379 \times 10 = _
To solve, multiply: 4 , 379 × 10 = 43 , 790 . Therefore, the blank is 43,790 .
(ii) 8,376 \times 100 = _
Multiplying: 8 , 376 × 100 = 837 , 600 . Therefore, the blank is 837,600 .
(iii) 4,518 \times 10 = _
This gives: 4 , 518 × 10 = 45 , 180 . Therefore, the blank is 45,180 .
(iv) 98 \times 1,000 = _
Calculating: 98 × 1 , 000 = 98 , 000 . Therefore, the blank is 98,000 .
(v) 94 \times 1,000 = _
Multiplying: 94 × 1 , 000 = 94 , 000 . Therefore, the blank is 94,000 .
(vi) 1,000 \times 45 = _
Solving this gives: 1 , 000 × 45 = 45 , 000 . Therefore, the blank is 45,000 .
The properties of multiplication simplify calculations and help us understand how numbers interact with each other in multiplication scenarios. These properties include commutative, associative, distributive, identity, and zero properties, each playing a specific role in mathematical operations.
We solved various multiplication problems by identifying the correct number to fill in and naming the related properties. The properties include the commutative property, identity property, and distributive property. We also calculated the results of multiplying by 10, 100, and 1,000 easily using these concepts.
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