Mathematics, 18.07.2019 08:50 ari313

Add or subtract fractions write each sum or difference in simplest form. show work 1. 5/14 + 1/6 2. 5/12 - 3/20 3. 5/12 - 3/8 4. 1 3/10 + 1/4 5. 2/3 + 6 1/5 6. 3 1/6 - 1/7 7. 3/8 + 5/24 8. 1/20 + 5/12 9. 9/20 - 1/4 10. 9/10 - 3/14 11. 3 3/8 + 5/12 12. 5 7/10 - 5/18 multiply fractions. write each product in simplest form. show work 1. 1/2 x 5/8 2. 3/5 x 5/9 3. 3/8 x 2/5 4. 2 3/8 x 16 5. 1 4/5 x 5/12 6. 1 2/10 x 5 find each amount. show work 1. 1/4 of 12 bottles of water = bottles 2. 2/3 of 24 bananas = bananas 3. 3/5 of $40 restaurant bill = $ 4. 5/6 of 18 pencils = pencils

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Here are the solutions and answers for each question:

Addition and Subtraction - Find the common denominator then add or subtract the numerator and retain the common denominator. Finally, simplify into its lowest terms.

1. 5/14 + 1/6

(3/3)(5/14) + (7/7)(1/6) = 15/42 + 7/42 = 22/42 = 11/21

2. 5/12 - 3/20

(5/5)(5/12) - (3/3)(3/20) = 25/60 - 9/60 = 16/60 = 4/15

3. 5/12 - 3/8

(2/2)(5/12) - (3/3)(3/8) = 10/24 -9/24 = 1/24

4. 1 3/10 + 1/4

1 3/10 = ((1x10) + 3)/10 = 13/10

(4/4)(13/10) +(10/10)(1/4) = 52/40 + 10/40 = 62/40 = 31/20

5. 2/3 + 6 1/5

6 1/5 = ((6x5)+1)/5 = 31/5

(5/5)(2/3) +(3/3)(31/5) = 10/15 + 93/15 = 103/15

6. 3 1/6 - 1/7

3 1/6 = ((3x6)+1)/6 =19/6

(7/7)(19/6) - (6/6)(1/7) = 133/42 - 6/42 = 127/42

7. 3/8 + 5/24

(3/3)(3/8) + (1/1)(5/24) = 9/24 + 5/24 = 14/24 = 7/12

8. 1/20 + 5/12

(3/3)(1/20) + (5/5)(5/12) = 3/60 + 25/60 = 28/60 = 7/15

9. 9/20 - 1/4

(1/1)(9/20) - (5/5)(1/4) = 9/20 - 5/20 = 4/20 = 1/5

10. 9/10 - 3/14

(7/7)(9/10) - (5/5)(3/14) = 63/70 - 15/70 = 48/70 = 24/35

11. 3 3/8 + 5/12

3 3/8 = ((3x8)+3)/8 = 27/8

(3/3)(27/8) + (2/2)(5/12) = 81/24 + 10/24 = 91/ 24

12. 5 7/10 - 5/18

5 7/10 = ((5x10)+7)/10 = 57/10

(9/9)(57/10) - (5/5)(5/18) = 513/90 - 25/90 = 488/90 = 244/45

Multiplication - simply multiply the numerator by the numerator of the other fraction and the denominator by the denominator of the other fraction

1. 1/2 x 5/8 = 5/16

2. 3/5 x 5/9 = 15/45 = 1/3

3. 3/8 x 2/5 = 6/40 = 3/20

4. 2 3/8 x 16

2 3/8 = ((2x8)+3)/8 = 19/8

19/8 x 16 = 304/8 = 38

5. 1 4/5 x 5/12

1 4/5 = ((1x5)+4)/5 = 9/5

9/4 x 5/12 = 45/48 = 15/16

6. 1 2/10 x 5

1 2/10 = ((1x10)+2)/10 = 12/10

12/10 x 5 = 60/10 = 6

Find each amount - Simply multiply the two given values.

1. 1/4 of 12 bottles of water = 3 bottles

1/4 x 12 = 12/4 = 3

2. 2/3 of 24 bananas = 16 bananas

2/3 x 24 = 48/3 = 16

3. 3/5 of $40 restaurant bill = $ 24

3/5 x 40 = 120/5 = 24

4. 5/6 of 18 pencils = 15 pencils

5/6 x 18 = 90/6 = 15

Answer from: Quest

a 360 degree rotation

step-by-step explanation:

Answer from: Quest

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

step-by-step explanation:

step 1

find the equation of the dashed line

we have the points

(0,0) and (3,1)

the line passes through the origin, so, is a direct variation

find the slope

$m=y/x=1/3$

the equation of the dashed line is

$y=(1/3)x$

the solution of the inequality a s the shaded area above the dashed line

therefore

the equation of the inequality a is

$y> (1/3)x$

step 2

find the equation of the solid line

we have the points

(4,0) and (0,4)

find the slope

$m=(4-0)/(0-4)=-1$

the equation of the solid line is

$y=-x+4$

the solution of the inequality b s the shaded area below the solid line

therefore

the equation of the inequality b is

$y\leq-x+4$

step 3

the system of inequalities is

$y> (1/3)x$

$y\leq-x+4$

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