Answer:
Step-by-step explanation:
1) 4 2/3 - 3 1/4 = (4 -3) +(2/3 -1/4) = 1 + (8/12 -3/12) = 1 5/12
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2) (7 3/4)/(8/62) = (31/4)(62/8) = (31/4)(31/4) = 961/16 = 60 1/16
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3) (2 5/7 +3 2/3) -(4 2/3 +1 2/5) = (2 + 3 -4 -1) +(5/7 +2/3 -2/3 -2/5)
= 5/7 -2/5 = (25 -14)/35 = 11/35
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Notes on arithmetic with fractions
It can be helpful to make use of a common denominator when adding or subtracting fractions. Your knowledge of multiplication tables can help you find a suitable common denominator. Without too much effort, you can use the product of denominators as the common denominator, though doing that may require you to reduce the resulting fraction.
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If you need a formula for addition or subtraction of fractions, this is it:
a/b + c/d = (ad +bc)/(bd)
A sign can be attached to any of these numbers, so that ...
a/b - c/d = (ad -bc)/(bd)
Using this formula is how we worked problem 3. It is essentially the same as rewriting each fraction to use the common denominator bd:
a/b = ad/(bd)
c/d = bc/(bd)
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Of course, division of fractions (or any sort of division, actually) is the same as multiplying by the inverse (reciprocal) of the denominator. The mantra "invert and multiply" can be a useful reminder of this.
1. Subtract 3 1/4 from 4 2/3
This will be:
= 4 2/3 - 3 1/4
Note that the LCM of 3 and 4 is 12.
= 4 2/3 - 3 1/4
= 4 8/12 - 3 3/12
= 1 5/12
2. Simplify 7 3/4 divided by 8/62
This will be:
= 7 3/4 ÷ 8/62
Change 7 3/4 to improper fraction and this will be 31/4. Therefore,
= 7 3/4 ÷ 8/62
= 31/4 ÷ 8/62
= 31/4 × 62/8
= 1922/32
= 60 2/32 = 60 1/16
3. Subtract the sum of 4 2/3 and 1 2/5 from the sum of 2 5/7 and 3 2/3
= (2 5/7 + 3 2/3) - ( 4 2/3 + 1 2/5)
= (2 15/21 + 3 14/21) - (4 10/15 + 1 6/15)
= 5 29/21 - 5 16/15
= (5 + 1 8/21) - (5 + 1 1/15)
= 6 8/21 - 6 1/15
= 6 40/105 - 6 7/105
= 33/105
= 11/35
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