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Chapter 1: Problem 7

Evaluate. a. \(123-91\) b. \(543-125\) c. \(78-49\) d. \(1002-250\) e. \(2001-1962\) f. \(696-384\)

Short Answer

Expert verified
a. 123 - 91 b. 543 - 125 c. 78 - 49 d. 1002 - 250 e. 2001 - 1962 f. 696 - 384 Answer: a. 32 b. 418 c. 29 d. 752 e. 39 f. 312

Step by step solution

01

Properly align the numbers to subtract

We need to align the numbers vertically, with \(91\) placed under \(123\). This allows us to subtract each number in the correct place value: ``` 123 - 91 ```
02

Perform the subtraction, starting from the rightmost digit

We start by subtracting the rightmost pair of numbers (3 and 1): ``` 123 - 91 _____ 2 ``` Now, we move on to the next set of numbers (2 and 9). Since 2 is smaller than 9, we need to borrow from the numbers to the left. So, we take 1 from 100's place and add 10 to the 10's place. This gives us 12 - 9: ``` 1 1 2 - 9 1 _____ 32 ``` The final answer is 32. b. Evaluate \(543-125\)
03

Properly align the numbers to subtract

We need to align the numbers vertically, with \(125\) under \(543\). ``` 543 - 125 ```
04

Perform the subtraction, starting from the rightmost digit

We subtract the rightmost pair of numbers (3 and 5). Since, 3 is smaller than 5, borrow from the left: ``` 5 4 2 - 1 2 5 _____ 8 ``` Now, proceed to the middle pair of numbers (4 and 2): ``` 5 4 2 - 1 2 5 _____ 1 8 ``` Finally, subtract the leftmost pair of numbers (5 and 1): ``` 5 4 2 - 1 2 5 _____ 4 1 8 ``` The final answer is 418. Repeat the same steps for the remaining subtraction problems: c. Evaluate \(78-49\) ``` 78 - 49 _____ 29 ``` d. Evaluate \(1002-250\) ``` 1002 - 250 _____ 752 ``` e. Evaluate \(2001-1962\) ``` 2001 -1962 _____ 39 ``` f. Evaluate \(696-384\) ``` 696 -384 _____ 312 ```

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