Solved Examples and Worksheet for Subtracting Rational Numbers

Q1Find the difference between 834 and 545
A. 21920
B. 21921
C. 2121
D. 22021

Step: 1
834 - 545
[Original expression.]
Step: 2
= 81520 - 51620
[Rewrite the fractions of the mixed numbers using the LCD, 20.]
Step: 3
= 73520 - 51620
[Write 81520 as 7 + 11520 = 73520.]
Step: 4
= 21920
[Subtract the whole numbers and fractions separately.]
Step: 5
So, the difference is 21920.
Q2Find the difference between 1011 and 310.
A. 1321
B. 7
C. 107
D. 67110

Step: 1
1011 - 310
[Original expression.]
Step: 2
The LCM of 11 and 10 is 110, so the LCD of 1011 and 310 is 110.
Step: 3
1011 - 310 = (1011 × 1010) - (310 × 1111)
[Write equivalent fractions with a denominator of 110.]
Step: 4
= 100110 - 33110
[Multiply inside the grouping symbols.]
Step: 5
= 100 - 33110
[Write the difference over the common denominator.]
Step: 6
= 67110
[Simplify.]
Step: 7
The difference between 1011 and 310 is 67110.
Q3What is the value of - 3 - (- 9)?

A. 8
B. 7
C. - 2
D. 6

Step: 1
- 3 - (- 9)
[Original equation.]
Step: 2
= - 3 + 9
[To subtract - 9, add its opposite 9.]
Step: 3
= 6
[Simplify.]
Q4What is the value of - 326 - 452?

A. -126
B. 126
C. 778
D. - 778

Step: 1
- 326 - 452
[Original equation.]
Step: 2
= - 326 + (- 452)
[To subtract 452, add its opposite - 452.]
Step: 3
= - 778
[Simplify.]
Correct Answer is :   - 778
Q5Simplify:
2 - (- 5) - (- 2)

A. -9
B. 9
C. 10
D. 5

Step: 1
2 - (- 5) - (- 2)
[Original expression.]
Step: 2
= 2 + 5 + 2
[To subtract - 5, add its opposite, 5 and to subtract - 2, add its opposite, 2.]
Step: 3
= 9
Q6William bought 314 lbs of candy for his daughter Diane. He gave her 112 lbs of candy. How much candy was he left with?

A. 47
B. 1
C. 114
D. 134

Step: 1
314 - 112
[Original expression.]
Step: 2
= 314 - 124
[Rewrite the fractions of the mixed numbers using the LCD, 4.]
Step: 3
= 254 - 124
[Rewrite 314 as 2 + 114 = 254.]
Step: 4
= 134
[Subtract the whole numbers and then subtract the fractions.]
Step: 5
134 lbs of candy is left with William.
Q7Find the difference.
456 - 57

A. 17442
B. 17343
C. 17342
D. 17443

Step: 1
456 - 57
[Original expression.]
Step: 2
296 - 57
[Rewrite the mixed fraction as improper fraction.]
Step: 3
The LCM of 6 and 7 is 42, so the LCD of 296 and 57 is 42.
Step: 4
296 - 57 = 20342 - 3042
[Write equivalent fractions with a denominator of 42.]
Step: 5
= 203 - 3042
[Write the difference over the common denominator.]
Step: 6
= 17342
[Simplify.]
Q8Find the difference.
514 - 312

A. 85
B. 74
C. 84
D. 75

Step: 1
514 - 312
[Original expression.]
Step: 2
214 - 72
[Rewrite the mixed fractions as improper fractions.]
Step: 3
The LCM of 4 and 2 is 4, so the LCD of 214 and 72 is 4.
Step: 4
214 - 144
[Write equivalent fractions with a denominator of 4.]
Step: 5
= 21 - 144
[Write the difference over the common denominator.]
Step: 6
= 74
[Simplify.]
Q9Simplify the expression 78 - 58.
A. 15
B. 16
C. 17
D. 14

Step: 1
78 - 58
[Original expression.]
Step: 2
= 7 - 58
[Write the difference over the common denominator, 8.]
Step: 3
= 28
[Divide numerator and denominator with their GCF, 2.]
Step: 4
= 14
Q10Simplify the expression.
825 - 315

A. 515
B. 235
C. 615
D. 55

Step: 1
825 - 315
[Original expression.]
Step: 2
= 515
[Subtract the whole numbers. Subtract the fractions.]
Step: 3
825 - 315 = 515
Q11Stephanie ate 12 of a veg roll. What fraction of the veg roll should she eat to complete 34 of the veg roll?

A. 47
B. 14
C. 12
D. 25

Step: 1
34 - 12 = 34 - 1 × 22 × 2
[Use LCD 4 to write equivalent fractions.]
Step: 2
= 34 - 24
[Simplify.]
Step: 3
= 3 - 24
[Since the denominators are equal, subtract the numerators.]
Step: 4
= 14

Step: 5
She has to eat 14 more of the veg roll to complete 34 of the veg roll.
Q12Find the difference.
345 - 35

A. 275
B. 165
C. 225
D. 175

Step: 1
345 - 35
[Original expression.]
Step: 2
= 195 - 35
[Rewrite the mixed fraction as improper fraction.]
Step: 3
The LCM of 5 and 5 is 5, so the LCD of 195 and 35 is 5.
Step: 4
195 - 35 = 195 - 35
[Write equivalent fractions with a denominator of 5.]
Step: 5
= 19-35
[Write the difference over the common denominator.]
Step: 6
= 165
[Simplify.]
Q13Find the difference between 45 and 34.

A. 120
B. -120
C. 1920
D. -1920

Step: 1
45 - 34
[Write the expression.]
Step: 2
The LCM of 5 and 4 is 20, so the LCD of 45 and 34 is 20.
Step: 3
= ( 45 × 44) - ( 34 × 55 )
[Write equivalent fractions with a denominator of 20.]
Step: 4
= (1620) - (1520)
[Simplify.]
Step: 5
= 16-1520
[Write the difference between over the common denominator.]
Step: 6
= 120
[Simplify.]
Step: 7
The difference between 45 and 34 is 120 .
Q14Gary and Ed ate 23 of a pie together. If Gary ate 25 of the pie, then how much did Ed eat?

A. 23
B. 415
C. 27
D. 45

Step: 1
The fraction of pie Ed ate = 23 - 25
Step: 2
= 1015 - 615
[Write equivalent fractions using the LCD, 15.]
Step: 3
= (10 - 6)15
[Since denominators are same, subtract numerators.]
Step: 4
= 415

Step: 5
Ed ate 415 of the pie.
Q15William built a sand sculpture that was 314 ft high. Andy is 534 ft tall. How much taller is Andy than the sculpture?

A. 12 ft
B. 34 ft
C. 212 ft
D. 214 ft

Step: 1
The difference between Andy's height and the height of the sculpture = 534 - 314
Step: 2
= (5 - 3) + (34 - 14)
[Subtract the whole numbers and fractions separately.]
Step: 3
= 2 + 24
[Simplify.]
Step: 4
= 224
[Rewrite as mixed number.]
Step: 5
= 212
[Simplify 24 using the GCF 2.]
Step: 6
Andy is 212 ft taller than the sculpture.
Correct Answer is :   212 ft
The content structure consists of a series of questions (Q1 to Q15) that involve subtracting rational numbers, followed by step-by-step solutions and the correct answer for each question.
multiple_questions_with_answers
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Solved Examples and Worksheet for Subtracting Rational Numbers

Q1Find the difference between 834 and 545
A. 21920
B. 21921
C. 2121
D. 22021

Step: 1
834 - 545
[Original expression.]
Step: 2
= 81520 - 51620
[Rewrite the fractions of the mixed numbers using the LCD, 20.]
Step: 3
= 73520 - 51620
[Write 81520 as 7 + 11520 = 73520.]
Step: 4
= 21920
[Subtract the whole numbers and fractions separately.]
Step: 5
So, the difference is 21920.
Q2Find the difference between 1011 and 310.
A. 1321
B. 7
C. 107
D. 67110

Step: 1
1011 - 310
[Original expression.]
Step: 2
The LCM of 11 and 10 is 110, so the LCD of 1011 and 310 is 110.
Step: 3
1011 - 310 = (1011 × 1010) - (310 × 1111)
[Write equivalent fractions with a denominator of 110.]
Step: 4
= 100110 - 33110
[Multiply inside the grouping symbols.]
Step: 5
= 100 - 33110
[Write the difference over the common denominator.]
Step: 6
= 67110
[Simplify.]
Step: 7
The difference between 1011 and 310 is 67110.
Q3What is the value of - 3 - (- 9)?

A. 8
B. 7
C. - 2
D. 6

Step: 1
- 3 - (- 9)
[Original equation.]
Step: 2
= - 3 + 9
[To subtract - 9, add its opposite 9.]
Step: 3
= 6
[Simplify.]
Q4What is the value of - 326 - 452?

A. -126
B. 126
C. 778
D. - 778

Step: 1
- 326 - 452
[Original equation.]
Step: 2
= - 326 + (- 452)
[To subtract 452, add its opposite - 452.]
Step: 3
= - 778
[Simplify.]
Correct Answer is :   - 778
Q5Simplify:
2 - (- 5) - (- 2)

A. -9
B. 9
C. 10
D. 5

Step: 1
2 - (- 5) - (- 2)
[Original expression.]
Step: 2
= 2 + 5 + 2
[To subtract - 5, add its opposite, 5 and to subtract - 2, add its opposite, 2.]
Step: 3
= 9
Q6William bought 314 lbs of candy for his daughter Diane. He gave her 112 lbs of candy. How much candy was he left with?

A. 47
B. 1
C. 114
D. 134

Step: 1
314 - 112
[Original expression.]
Step: 2
= 314 - 124
[Rewrite the fractions of the mixed numbers using the LCD, 4.]
Step: 3
= 254 - 124
[Rewrite 314 as 2 + 114 = 254.]
Step: 4
= 134
[Subtract the whole numbers and then subtract the fractions.]
Step: 5
134 lbs of candy is left with William.
Q7Find the difference.
456 - 57

A. 17442
B. 17343
C. 17342
D. 17443

Step: 1
456 - 57
[Original expression.]
Step: 2
296 - 57
[Rewrite the mixed fraction as improper fraction.]
Step: 3
The LCM of 6 and 7 is 42, so the LCD of 296 and 57 is 42.
Step: 4
296 - 57 = 20342 - 3042
[Write equivalent fractions with a denominator of 42.]
Step: 5
= 203 - 3042
[Write the difference over the common denominator.]
Step: 6
= 17342
[Simplify.]
Q8Find the difference.
514 - 312

A. 85
B. 74
C. 84
D. 75

Step: 1
514 - 312
[Original expression.]
Step: 2
214 - 72
[Rewrite the mixed fractions as improper fractions.]
Step: 3
The LCM of 4 and 2 is 4, so the LCD of 214 and 72 is 4.
Step: 4
214 - 144
[Write equivalent fractions with a denominator of 4.]
Step: 5
= 21 - 144
[Write the difference over the common denominator.]
Step: 6
= 74
[Simplify.]
Q9Simplify the expression 78 - 58.
A. 15
B. 16
C. 17
D. 14

Step: 1
78 - 58
[Original expression.]
Step: 2
= 7 - 58
[Write the difference over the common denominator, 8.]
Step: 3
= 28
[Divide numerator and denominator with their GCF, 2.]
Step: 4
= 14
Q10Simplify the expression.
825 - 315

A. 515
B. 235
C. 615
D. 55

Step: 1
825 - 315
[Original expression.]
Step: 2
= 515
[Subtract the whole numbers. Subtract the fractions.]
Step: 3
825 - 315 = 515
Q11Stephanie ate 12 of a veg roll. What fraction of the veg roll should she eat to complete 34 of the veg roll?

A. 47
B. 14
C. 12
D. 25

Step: 1
34 - 12 = 34 - 1 × 22 × 2
[Use LCD 4 to write equivalent fractions.]
Step: 2
= 34 - 24
[Simplify.]
Step: 3
= 3 - 24
[Since the denominators are equal, subtract the numerators.]
Step: 4
= 14

Step: 5
She has to eat 14 more of the veg roll to complete 34 of the veg roll.
Q12Find the difference.
345 - 35

A. 275
B. 165
C. 225
D. 175

Step: 1
345 - 35
[Original expression.]
Step: 2
= 195 - 35
[Rewrite the mixed fraction as improper fraction.]
Step: 3
The LCM of 5 and 5 is 5, so the LCD of 195 and 35 is 5.
Step: 4
195 - 35 = 195 - 35
[Write equivalent fractions with a denominator of 5.]
Step: 5
= 19-35
[Write the difference over the common denominator.]
Step: 6
= 165
[Simplify.]
Q13Find the difference between 45 and 34.

A. 120
B. -120
C. 1920
D. -1920

Step: 1
45 - 34
[Write the expression.]
Step: 2
The LCM of 5 and 4 is 20, so the LCD of 45 and 34 is 20.
Step: 3
= ( 45 × 44) - ( 34 × 55 )
[Write equivalent fractions with a denominator of 20.]
Step: 4
= (1620) - (1520)
[Simplify.]
Step: 5
= 16-1520
[Write the difference between over the common denominator.]
Step: 6
= 120
[Simplify.]
Step: 7
The difference between 45 and 34 is 120 .
Q14Gary and Ed ate 23 of a pie together. If Gary ate 25 of the pie, then how much did Ed eat?

A. 23
B. 415
C. 27
D. 45

Step: 1
The fraction of pie Ed ate = 23 - 25
Step: 2
= 1015 - 615
[Write equivalent fractions using the LCD, 15.]
Step: 3
= (10 - 6)15
[Since denominators are same, subtract numerators.]
Step: 4
= 415

Step: 5
Ed ate 415 of the pie.
Q15William built a sand sculpture that was 314 ft high. Andy is 534 ft tall. How much taller is Andy than the sculpture?

A. 12 ft
B. 34 ft
C. 212 ft
D. 214 ft

Step: 1
The difference between Andy's height and the height of the sculpture = 534 - 314
Step: 2
= (5 - 3) + (34 - 14)
[Subtract the whole numbers and fractions separately.]
Step: 3
= 2 + 24
[Simplify.]
Step: 4
= 224
[Rewrite as mixed number.]
Step: 5
= 212
[Simplify 24 using the GCF 2.]
Step: 6
Andy is 212 ft taller than the sculpture.
Correct Answer is :   212 ft
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The content structure consists of a series of questions (Q1 to Q15) that involve subtracting rational numbers, followed by step-by-step solutions and the correct answer for each question.

TYPE: MULTIPLE_QUESTIONS_WITH_ANSWERS