Fractions · Ages 10–11
Three fractions added and subtracted worksheet
Part of: Fractions with different denominators
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Three fractions added and subtracted worksheet
Fractions · Ages 10–11
Numsprite
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Name:Date:Score:／48
Write each answer in the space. For word problems, show your working and write a sentence answer.
Part A: Working out and filling in (2 marks each)
1.56 − 13 − 112 = ?
Answer in simplest form
Answer:
2.13 + 112 + 16 = ?
Answer in simplest form
Answer:
3.56 − 13 − 18 = ?
Answer in simplest form
Answer:
4.18 + 112 + 13 = ?
Answer in simplest form
Answer:
5.34 + 12 − 45 = ?
Answer in simplest form
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6.712 − 12 + 34 = ?
Answer in simplest form
Answer:
7.34 + 78 − 23 = ?
Answer in simplest form
Answer:
8.25 − (12 − 38) = ?
Answer in simplest form
Answer:
9.5 12 − 14 + 710 =
Fill in each blank
Answer:
10.2 112 − 13 + 12 =
Fill in each blank
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Part B: Choose, or true or false (2 marks each)
11.Working out 12 + 16 − 18, which is the smallest common denominator?
- A. 96
- B. 8
- C. 16
- D. 24
Choose the right answer
Answer:
12.Working out 13 + 14 − 16, which is the smallest common denominator?
- A. 72
- B. 6
- C. 13
- D. 12
Choose the right answer
Answer:
Part C: Word problems (4 marks each)
13.Of one pizza, Ming eats 14, Ka-yee eats 112 and May eats 12. What fraction of the pizza is left?
Answer in simplest form
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14.A tank is 35 full. 13 of a tank is used, then 12 of a tank is poured in. What fraction of the tank is full now?
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15.On day one a crew mends 12 of a road; on day two, 13 of the road less than day one. What fraction of the road do they mend in the two days?
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16.Ming spends 23 hour on homework, 12 hour revising and 14 hour playing. How many hours more do homework and revising take together than playing?
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17.Of one pizza, Ming eats 14, Chi-keung eats 15 and Ka-lok eats 12. What fraction of the pizza is left?
Answer in simplest form
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18.Tsz-ching spends 14 hour on homework, 110 hour revising and 16 hour playing. How many hours more do homework and revising take together than playing?
Answer in simplest form
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Show the answers and working
Three fractions added and subtracted worksheet: Answers and working
Part A: Working out and filling in
1. 512
Find the L.C.M. of 6, 3 and 12 as the common denominator, then subtract one at a time, left to right.
Over a common denominator of 12, subtract left to right: 512.
2. 712
Find the L.C.M. of 3, 12 and 6 as the common denominator, and rewrite all three fractions over it.
The L.C.M. of the three denominators is 12; add the numerators over 12 and simplify: 712.
3. 38
Find the L.C.M. of 6, 3 and 8 as the common denominator, then subtract one at a time, left to right.
Over a common denominator of 24, subtract left to right: 38.
4. 1324
Find the L.C.M. of 8, 12 and 3 as the common denominator, and rewrite all three fractions over it.
The L.C.M. of the three denominators is 24; add the numerators over 24 and simplify: 1324.
5. 920
Rewrite all three over the L.C.M. of 4, 2 and 5, then add and subtract left to right.
Common denominator 20; add then subtract, left to right, and simplify: 920.
6. 56
No brackets, so go left to right: 712 − 12 first, then add 34.
Left to right: subtract first, then add; don't work out 12 + 34 first. Over 12: 56.
7. 2324
Rewrite all three over the L.C.M. of 4, 8 and 3, then add and subtract left to right.
Common denominator 24; add then subtract, left to right, and simplify: 2324.
8. 1140
Work out 12 − 38 in the brackets first, or open them, remembering the minus in front flips the signs.
Brackets first, or open them and flip the signs: 25 − 12 + 38 = 1140.
9. 5, 19, 20
Put the three fractions over a common denominator and go left to right; if 12 falls short, borrow 1 from the 5.
Over 20, left to right, borrowing 1 from the whole when a fraction falls short: 5 1920.
10. 2, 1, 4
Put the three fractions over a common denominator and go left to right; if 112 falls short, borrow 1 from the 2.
Over 12, left to right, borrowing 1 from the whole when a fraction falls short: 2 14.
Part B: Choose, or true or false
11. D. 24
List the multiples of 8 and check each one for whether 2 and 6 divide it.
The L.C.M. of 2, 6 and 8 is 24.
12. D. 12
List the multiples of 6 and check each one for whether 3 and 4 divide it.
The L.C.M. of 3, 4 and 6 is 12.
Part C: Word problems
Marking: 2 for the working, 1 for the answer, 1 for the sentence.
13. 16
The whole pizza is 1, and all three shares come off it. Find a common denominator for 4, 12 and 2 first.
The whole pizza is 1: 1 − 14 − 112 − 12 = 16.
14. 2330
Used means subtract, poured in means add. Write the calculation, then find a common denominator and go left to right.
Used is minus, poured in is plus, left to right: 35 − 13 + 12 = 2330.
15. 23
Find day two first: 13 less than day one's 12.
Day two is 12 − 13 = 16; both days 12 + 16 = 23.
16. 1112 hours
Add the homework and revision times, then subtract the play time. Put all three fractions over a common denominator first.
23 + 12 − 14 = 1112 hours.
17. 120
The whole pizza is 1, and all three shares come off it. Find a common denominator for 4, 5 and 2 first.
The whole pizza is 1: 1 − 14 − 15 − 12 = 120.
18. 1160 hours
Add the homework and revision times, then subtract the play time. Put all three fractions over a common denominator first.
14 + 110 − 16 = 1160 hours.
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