Multiply : 1) 754 X 368
2) 25634 x 78
The correct answer and explanation is:
Sure! Let’s first perform the multiplications:
1) 754×368754 \times 368
754×368=277,472754 \times 368 = 277,472
2) 25634×7825634 \times 78
25634×78=1,998,55225634 \times 78 = 1,998,552
Explanation (Approx. 300 words):
Multiplication is a basic arithmetic operation that represents repeated addition. When we multiply two numbers, we’re essentially adding one number to itself as many times as indicated by the other number.
1) Multiplying 754 by 368:
Let’s break this down to understand it better. We can use the distributive property of multiplication: 754×368=754×(300+60+8)754 \times 368 = 754 \times (300 + 60 + 8)
Now multiply each part:
- 754×300=226,200754 \times 300 = 226,200
- 754×60=45,240754 \times 60 = 45,240
- 754×8=6,032754 \times 8 = 6,032
Adding all these: 226,200+45,240+6,032=277,472226,200 + 45,240 + 6,032 = 277,472
This is the same result we obtained earlier using direct multiplication.
2) Multiplying 25,634 by 78:
Again, using distributive property: 25634×78=25634×(70+8)25634 \times 78 = 25634 \times (70 + 8)
- 25634×70=1,794,38025634 \times 70 = 1,794,380
- 25634×8=204,27225634 \times 8 = 204,272
Adding these: 1,794,380+204,272=1,998,5521,794,380 + 204,272 = 1,998,552
This demonstrates how breaking down complex multiplication into smaller steps can simplify the process and make it easier to verify.
Why It’s Important:
Multiplication is foundational in math and appears in nearly all areas of life: from calculating prices, distances, and areas to more complex operations in science, engineering, and data analysis. Understanding how to break multiplication into parts helps improve mental math, estimation, and problem-solving skills.
Being able to verify answers manually (as we did using distributive property) is crucial when calculators aren’t available or to check errors. It also builds confidence and strengthens number sense.
So, the correct answers are:
- 754×368=277,472754 \times 368 = \boxed{277,472}
- 25,634×78=1,998,55225,634 \times 78 = \boxed{1,998,552}