Question

Lesson 7: Solving Equations with Fractions 6th Grade Practice

1. 2 1/4r=10


A. R= 4 3/4


B. R= 4 2/5


C. R= 4 4/9



2. h/26=5


A. H=120


B. H=123


C. H=140



3. 6/7k=6


A. K=7


B. K=6 6/7


C. K=6


4. 4/5 x for x= 5/8


A.2


B.1/2


C.1/4


5. h÷4/9 for h = 5 1/3

A. 2 10/27


B.10


C.12

Answer 1

1.C

2. 130, answer not listed

3. A

4. B

5.C

Explanation:

To solve equations with fractions, convert from a mixed number to an improper fraction then use the inverse. The inverse of a fraction is multiplying by the reciprocal of the fraction on both sides.

1.

`2(1)/(4)r=10\\\\(9)/(4)r=10\\\\(4)/(9) *(9)/(4)r=10*(4)/(9)\\\\r=(40)/(9) \\\\r=4(4)/(9)`

2.

`(h)/(26)=5\\\\(26)/(1) *(h)/(26)=5*(26)/(1)\\\\h=130`

3.

`(6)/(7)k=6\\\\(7)/(6) *(6)/(7)k=6*(7)/(6)\\\\k=(42)/(6) \\\\k=7`

4.

`(4)/(5)x\\\\(4)/(5)*(5)/(8)\\\\(20)/(40) \\\\(1)/(2)`

5.

`(h)/(4/9) \\\\((16)/(3) )/((4)/(9) ) \\\\\\((16)/(3) *(9)/(4))/((4)/(9)*(9)/(4))\\\\(16)/(3) *(9)/(4)\\\\\\(144)/(12) \\\\12`