Question

а) 4 1/12 + 1 1/6 б) 2 3/5 + 3 1/3 в) 5 14/25 + 2 7/15 г) 7 3/10 - 2 4/15 д) 4 5/8 - 2 1/3 ё) 5 3/4 - 2 4/5 ​

Answer 1

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а) 4 1/12 + 1 1/6⁽²= 4 1/12 + 1 2/12 = 5 3/12 = 5 1/4

б) 2 3/5⁽³ + 3 1/3⁽⁵ = 2 9/15 + 3 5/15 = 5 14/15

в) 5 14/25⁽³ + 2 7/15⁽⁵ = 5 42/75 + 2 35/75 = 7 77/75 = 8 2/75

г) 7 3/10⁽³ - 2 4/15⁽² = 7 9/30 - 2 8/30 = 5 1/30

д) 4 5/8⁽³ - 2 1/3⁽⁸ = 4 15/24 - 2 8/24 = 2 7/24

ё) 5 3/4⁽⁵ - 2 4/5⁽⁴ = 5 15/20 - 2 16/20 = 115/20 - 56/20 = 59/20 = 2 19/20

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Answer 2

To solve the given expressions involving mixed numbers, you'll need to perform addition or subtraction of fractions and simplify the results. Here are the solutions:

а) 4 1/12 + 1 1/6 To add these mixed numbers, convert them into improper fractions first: 4 1/12 = (4 * 12 + 1) / 12 = 49 / 12 1 1/6 = (1 * 6 + 1) / 6 = 7 / 6

Now, find a common denominator, which is 12: 49 / 12 + 7 / 6 = (49 + 2 * 7) / 12 = 49 / 12 + 14 / 12 = (49 + 14) / 12 = 63 / 12

Simplify the fraction if possible: 63 / 12 = 5 3/12

But we can reduce it further: 5 3/12 = 5 1/4

So, the result is 5 1/4.

б) 2 3/5 + 3 1/3 Using the same approach, convert the mixed numbers to improper fractions: 2 3/5 = (2 * 5 + 3) / 5 = 13 / 5 3 1/3 = (3 * 3 + 1) / 3 = 10 / 3

Find a common denominator, which is 15: 13 / 5 + 10 / 3 = (39 + 50) / 15 = 89 / 15

The fraction cannot be simplified further, so the result is 5 14/15.

в) 5 14/25 + 2 7/15 Convert to improper fractions: 5 14/25 = (5 * 25 + 14) / 25 = 139 / 25 2 7/15 = (2 * 15 + 7) / 15 = 37 / 15

Find a common denominator, which is 75: 139 / 25 + 37 / 15 = (3 * 139 + 5 * 37) / 75 = (417 + 185) / 75 = 602 / 75

Simplify the fraction if possible: 602 / 75 = 8 2/75

The fraction cannot be further reduced, so the result is 8 2/75.

г) 7 3/10 - 2 4/15 Convert to improper fractions: 7 3/10 = (7 * 10 + 3) / 10 = 73 / 10 2 4/15 = (2 * 15 + 4) / 15 = 34 / 15

Find a common denominator, which is 30: 73 / 10 - 34 / 15 = (3 * 73 - 2 * 34) / 30 = (219 - 68) / 30 = 151 / 30

Simplify the fraction if possible: 151 / 30 = 5 1/30

The result is 5 1/30.

д) 4 5/8 - 2 1/3 Convert to improper fractions: 4 5/8 = (4 * 8 + 5) / 8 = 37 / 8 2 1/3 = (2 * 3 + 1) / 3 = 7 / 3

Find a common denominator, which is 24: 37 / 8 - 7 / 3 = (3 * 37 - 8 * 7) / 24 = (111 - 56) / 24 = 55 / 24

The fraction cannot be simplified further, so the result is 2 7/24, or you can write it as 2 7/8.

ё) 5 3/4 - 2 4/5 Convert to improper fractions: 5 3/4 = (5 * 4 + 3) / 4 = 23 / 4 2 4/5 = (2 * 5 + 4) / 5 = 14 / 5

Find a common denominator, which is 20: 23 / 4 - 14 / 5 = (5 * 23 - 4 * 14) / 20 = (115 - 56) / 20 = 59 / 20

The fraction cannot be simplified further, so the result is 2 19/20.

So, the solutions are:

а) 5 1/4 б) 5 14/15 в) 8 2/75 г) 5 1/30 д) 2 7/24 (or 2 7/8) ё) 2 19/20