How do you simplify 2 1/4 x+(4 1/3 x−7 4/5 )÷2 3/5

Answer 1

This is pretty complex, but no worries, it’s doable!

First, convert each mixed number to an improper fraction by multiplying the whole number by the denominator and adding the numerator.

Mixed Number	Numerator	Improper Fraction
2 1/4	2 * 4 = 8 + 1 = 9	9/4
4 1/3	4 * 3 = 12 + 1 = 13	13/3
7 4/5	7 * 5 = 35 + 4 = 39	39/5
2 3/5	2 * 5 = 10 + 3 = 13	13/5

Second, determine the least common multiple (LCM).

Number	Multiples
3	3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60...
4	4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60...
5	5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60...

Third, multiply each numerator and denominator by the same number.

Numerators	Denominators
9 * 15 = 135	4 * 15 = 60
13 * 20 = 260	3 * 20 = 60
39 * 12 = 468	5 * 12 = 60
13 * 12 = 156	5 * 12 = 60

Fourth, set up your new expression: (135/60)x + (260/60)x - (468/60) ÷ (156/60).

Fifth, divide the last two terms, (468/60) ÷ (156/60).

1. Multiply the reciprocal of the second term: (468/60) * (60/156).
2. Remove both occurrences of 60, since 60/60 equals 1, leaving 468 ÷ 156.
3. Divide 468 by 156, which equals 3, leaving (135/60)x + (260/60)x - 3.

Sixth, combine the first two terms, (135/60)x + (260/60)x.

1. Add the numerators: 135 + 260 = 395, leaving (395/60)x - 3.

Finally, simplify the first term, (395/60)x, by dividing both the numerator and denominator by the least common denominator (LCD), 5.

1. 395 ÷ 5 = 65
2. 60 ÷ 5 = 12
3. Simplified term: (65/12)x

Answer: The simplified expression is (65/12)x - 3.