Solved Examples and Worksheet for Application of Subtracting Fractions-Unlike Denominators

Q1Jim bought 1320 lb of yogurt. If he ate 310 lb of it, how much is left?
A. 1630 lb
B. 720 lb
C. 620 lb
D. 1020 lb

Solutions
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Step: 1
= 1320 - 310
  [Substitute the values.]
Step: 2
= 1320 - 3 × 210 × 2
  [Multiply the numerator and the denominator of 310 by 2 to make the denominators of both the fractions equal.]
Step: 3
= 1320 - 620
  [Simplify.]
Step: 4
= 13 - 620
  [Write the difference over the common denominator.]
Step: 5
= 720
  [Subtract the numerator.]
Step: 6
So, 720 lb of yogurt was still left.
Correct Answer is :   720 lb
Q2Tim spends $12 on food each month, and Arthur spends $54 on food each month. What is the difference in their spending?

A. $25
B. $65
C. $76
D. $34

Solutions
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Step: 1
The difference between their expenditures on food = amount spent by Arthur - amount spent by Tim
Step: 2
= 54 - 12
  [Substitute the values.]
Step: 3
= 54- 1×22×2
  [Multiply the numerator and the denominator of 12 by 2 to make the denominators of both the fractions equal.]
Step: 4
= 54 - 24
  [Simplify.]
Step: 5
= 5 - 24
  [Write the difference over the common denominator.]
Step: 6
= 34
  [Subtract the numerators.]
Step: 7
The difference between their expenditures on food is $34 .
Correct Answer is :    $34
Q3Emily uses 1615 yd of fabric to make an outfit. Ed uses 85 yd to make the same outfit. How many yards of fabric does Ed use in excess of that used by Emily?
A. 815
B. 1615
C. 916
D. None of the above

Solutions
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Step: 1
The length of the fabric that Ed uses in excess to that used by Emily = length of the fabric used by Ed - length of the fabric used by Emily
Step: 2
= 85 - 1615
  [Substitute the values.]
Step: 3
= 8 × 35 × 3 - 1615
  [Multiply the numerator and the denominator of 85 by 3 to make the denominators of both the fractions equal.]
Step: 4
= 2415 - 1615
  [Simplify.]
Step: 5
= 24 - 1615
  [Write the difference over the common denominator.]
Step: 6
= 815
  [Subtract the numerators.]
Step: 7
Ed uses 815 yd of fabric more than Emily.
Correct Answer is :   815
Q4In order to make 94 cups of cake batter you need 115 cups of cocoa and the rest needs to be flour. How much flour is needed for the recipe?
A. 120 cups
B. 19 cups
C. 145 cups
D. None of the above

Solutions
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Step: 1
94 - 115
  [Original expression.]
Step: 2
= 9 × 54 × 5 - 11 × 45 × 4
  [Multiply the numerator and the denominator of 94 by 5 and 115 by 4 to make the denominators of both the fractions equal.]
Step: 3
= 4520 - 4420
  [Simplify.]
Step: 4
= (45 - 44)20
  [Write the difference over the common denominator.]
Step: 5
= 120
  [Subtract the numerator.]
Step: 6
120 cups of flour is required in the recipe.
Correct Answer is :   120 cups
Q5Bill drives his car from Chicago to Detroit and then to Cleveland. He reached Cleveland in 5112 hours. If he took 103 hours to travel from Chicago to Detroit, then how long did he take to travel from Detroit to Cleveland?

A. 1112 hour
B. 1012 hour
C. 9112 hours
D. 419 hours

Solutions
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Step: 1
Time taken by Bill to travel from Detroit to Cleveland = time taken by Bill to travel from Chicago to Cleveland - Time taken by Bill to travel from Chicago to Detroit
Step: 2
= 5112 - 103
  [Substitute the values.]
Step: 3
= 5112 - (10×4)(3×4)
  [Multiply the numerator and the denominator of 103 by 4 to make the denominators of both the fractions equal.]
Step: 4
= 5112 - 4012
  [Simplify.]
Step: 5
= (51-40)12
  [Write the difference over the common denominator.]
Step: 6
= 1112
  [Subtract the numerator.]
Step: 7
The time taken by Bill to travel from Detroit to Cleveland is 1112 hour.
Correct Answer is :   1112 hour
Q6Brad walks 23 miles and Jim walks 67 miles in one hour. Find the distance between Jim and Brad at the end of one hour if both Jim and Brad start walking at the same time from the same starting point in the same direction.

A. 421 mile
B. 521 mile
C. 621 mile
D. 17 mile

Solutions
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Step: 1
Distance between Jim and Brad at the end of one hour = Distance Jim walks in one hour - Distance Brad walks in one hour
Step: 2
= 67 - 23
  [Substitute the values.]
Step: 3
= 6 × 37 × 3 -2 × 73 × 7
  [Multiply the numerator and the denominator of 67 by 3 and 23 by 7 to make the denominators of both the fractions equal.]
Step: 4
= 1821 - 1421
  [Simplify.]
Step: 5
= 18 - 1421
  [Write the difference over the common denominator.]
Step: 6
= 421
  [Subtract the numerator.]
Step: 7
So, the distance between Jim and Brad at the end of one hour is 421 mile.
Correct Answer is :   421 mile
Q7It takes 12 hour on foot and 14 hour on a bike for Jeff to reach his home. How much time does Jeff save by going on his bike?

A. 20 minutes
B. 10 minutes
C. 25 minutes
D. 15 minutes

Solutions
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Step: 1
Time taken by Jeff to reach his home on foot = 12 hour
Step: 2
Time taken by Jeff to reach his home on bike = 14 hour
Step: 3
Time saved = 12 - 14
  [time taken to reach his home on foot - time taken to reach his home on bike.]
Step: 4
12 hour = 30 minutes
  [1 hour = 60 minutes, 12 hour = 602= 30 minutes.]
Step: 5
14 hour = 15 minutes
  [1 hour = 60 minutes, 14 hour = 604 = 15 minutes.]
Step: 6
Time saved = 30 minutes - 15 minutes = 15 minutes
  [Subtract.]
Step: 7
Jeff saves 15 minutes by going on a bike.
Correct Answer is :   15 minutes
Q8Sunny bought 49 gallons of paint. He used 118 gallons of paint. How much paint was he left with?

A. 117
B. 819
C. 17
D. 718

Solutions
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Step: 1
We need to subtract, 49 - 118 to find the amount of paint Sunny has left.
Step: 2
The denominators in the two fractions are not the same. So, we change the fraction 49 to a fraction whose denominator is 18.
Step: 3
= 49 × 22 - 118
  [Multiply the fraction 49 by 22.]
Step: 4
= 818 - 118
  [Simplify.]
Step: 5
= 8 - 118 = 718
  [Subtract the numerators.]
Step: 6
Sunny has left with 718 gallons of paint.
Correct Answer is :   718
Q9Charlie and Frank ate 46 of a pizza. If Charlie ate 13 of the pizza, then how much did Frank eat?
A. 56
B. 17
C. 15
D. 26

Solutions
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Step: 1
46 - 13
  [Original expression.]
Step: 2
The denominators in the fractions are not the same. So, we change the fraction 13 to a fraction whose denominator is 6.
Step: 3
= 46 - 13 × 22
  [Multiply the fraction 13 by 22 .]
Step: 4
= 46 - 26
  [Simplify.]
Step: 5
= 4 - 26
  [Subtract the numerators.]
Step: 6
= 26
  [Simplify.]
Step: 7
So, Frank ate 26 of the pizza.
Correct Answer is :   26
Q10Emily found her water tank 78 full at 9:00 a.m. She measured the level of water in the evening, and it was 17 of the tank. What fraction of the water did she use by evening?
A. 4256
B. 4257
C. 157
D. 4156

Solutions
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Step: 1
The fraction of water Emily used = 78 - 17
  [Original expression.]
Step: 2
The denominators in the two fractions are not the same.
So, we change the fractions 78 and 17 to have a common denominator.
Step: 3
= 78 × 77 - 17 × 88
  [Multiply fraction 78 by 77 and the faction 17 by 88 .]
Step: 4
= 4956 - 856
  [Simplify.]
Step: 5
= 49 - 856
= 4156
  [Subtract the numerators.]
Correct Answer is :   4156
Q11Nancy bought 78 of a yard of a fabric. She used only 14 of a yard of the fabric. How much fabric is left?
A. 58 yd
B. 68 yd
C. 59 yd
D. 78 yd

Solutions
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Step: 1
The length of the fabric unused = the length of the fabric Nancy bought - the length of the fabric used.
Step: 2
= 78 - 14
  [Substitute the values.]
Step: 3
= 78 - 28
  [Rename 14 to 28 by multiplying 14 with 22.]
Step: 4
= 7 - 28
  [Write the difference over the common denominator.]
Step: 5
= 58
  [Subtract.]
Step: 6
So, 58 yd of fabric was unused.
Correct Answer is :   58 yd

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