Question

1. solve each of the following and write your answers in simplest fraction form. if necessary, convert any improper fractions into mixed numbers.

(a) $6y = 35$ (b) $12x = 3$ (c) $8n = 34$

1. solve each of the following equations. show the work that leads to your answers.

(a) $\frac{x}{3} = 10$ (b) $\frac{n}{8} = 4$ (c) $\frac{y}{6} = 10$
(d) $\frac{c}{18} = \frac{1}{2}$ (e) $\frac{x}{9} = \frac{5}{3}$ (f) $\frac{n}{8} = \frac{11}{4}$

Explanation:

For Question 2:

(a) Step1: Isolate $y$ by dividing by 6

$y = \frac{35}{6}$

(a) Step2: Convert to mixed number

$\frac{35}{6} = 5\frac{5}{6}$

(b) Step1: Isolate $x$ by dividing by 12

$x = \frac{3}{12}$

(b) Step2: Simplify the fraction

$x = \frac{1}{4}$

(c) Step1: Isolate $n$ by dividing by 8

$n = \frac{34}{8}$

(c) Step2: Simplify the fraction

$n = \frac{17}{4}$

(c) Step3: Convert to mixed number

$\frac{17}{4} = 4\frac{1}{4}$

(a) Step1: Isolate $x$ by multiplying by 3

$x = 10 \times 3$

(a) Step2: Calculate the product

$x = 30$

(b) Step1: Isolate $n$ by multiplying by 8

$n = 4 \times 8$

(b) Step2: Calculate the product

$n = 32$

(c) Step1: Isolate $y$ by multiplying by 6

$y = 10 \times 6$

(c) Step2: Calculate the product

$y = 60$

(d) Step1: Isolate $c$ by multiplying by 18

$c = \frac{1}{2} \times 18$

(d) Step2: Calculate the product

$c = 9$

(e) Step1: Isolate $x$ by multiplying by 9

$x = \frac{5}{3} \times 9$

(e) Step2: Calculate the product

$x = 15$

(f) Step1: Isolate $n$ by multiplying by 8

$n = \frac{11}{4} \times 8$

(f) Step2: Calculate the product

$n = 22$

Answer:

(a) $5\frac{5}{6}$
(b) $\frac{1}{4}$
(c) $4\frac{1}{4}$

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For Question 3: