Question

5. 42 07/17 - 13/05 (j) 9 Subtract the following fractions. 8 1 (a) 16 -58 g 1 1 (d) 34-6 1 (g) 3-6-1/2 3 (02-10-25 Simplify: 16 2 (b) 3 -7/7 1 (e) 33 w 3 4 3 16 (h) 2 10 25 4 2 (k) 103-69 (c) 4 (0)5 3 (1) 5 - / -​

Answer 1

The given expressions result in the following simplified values: (a)
`\(-(11)/(85)\)`, (b)
`\((54)/(7)\)`, (c)
`\(-(11)/(5)\)`, (d)
`\(28\)`, (e)
`\((21)/(4)\)`, (f) (7), (g) (0), (h)
`\(-(24)/(5)\)`, (i)
`\((103)/(69)\)`.

Let's address each subtraction and simplification:

(a)
`\( (42)/(17) - (13)/(5) \)`: To subtract these fractions, find a common denominator, which is 85. Then, subtract the numerators:

`\[ (42)/(17) - (13)/(5) = (42 \cdot 5 - 13 \cdot 17)/(17 \cdot 5) = (210 - 221)/(85) = -(11)/(85). \]`

(b)
`\( 16 - (58)/(7) \)`: Convert 16 to an equivalent fraction with denominator 7:

`\[ (112)/(7) - (58)/(7) = (54)/(7). \]`

(c)
`\( (4)/(5) - (3)/(1) \)`: Find a common denominator, which is 5:

`\[ (4)/(5) - (15)/(5) = -(11)/(5). \]`

(d)
`\( 34 - (6)/(1) \)`: Convert 34 to an equivalent fraction with denominator 1:

`\[ (34)/(1) - (6)/(1) = (28)/(1) = 28. \]`

(e)
`\( (33)/(4) - (3)/(3) \)`: Find a common denominator, which is 4:

`\[ (33)/(4) - (12)/(4) = (21)/(4). \]`

(f)
`\( (16)/(2) - (7)/(7) \)`: Simplify the fractions:

`\[ 8 - 1 = 7. \]`

(g)
`\( (3)/(6) - (1)/(2) \)`: Find a common denominator, which is 6:

`\[ (3)/(6) - (3)/(6) = 0. \]`

(h)
`\( (2)/(10) - (25)/(4) \)`: Find a common denominator, which is 20:

`\[ (4)/(20) - (100)/(20) = -(96)/(20) = -(24)/(5). \]`

(i)
`\( (103)/(69) \)`: This fraction is already in its simplest form.