Question

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unit 6 lesson 4 homework
fluency

1. solve each of the following equations. show the work you used to find your answer. place your answers in simplest form. convert any improper fractions into mixed numbers.

(a) $n + \frac{2}{5} = \frac{3}{2}$
(b) $y - \frac{4}{3} = \frac{11}{6}$
(c) $x + 3\frac{1}{2} = 7\frac{1}{3}$

1. solve each of the following equations. show the work you used to find your answer. place your answers in simplest form. convert any improper fractions into mixed numbers.

(a) $\frac{3}{8}x = 21$
(b) $\frac{4}{7}n = \frac{2}{3}$
(c) $\frac{5}{2}y = \frac{20}{9}$

1. solve each of the following equations. show the work you used to find your answer. place your answers in simplest form. convert any improper fractions into mixed numbers.

(a) $\frac{n}{8} = \frac{11}{4}$
(b) $\frac{c}{10} = \frac{3}{4}$
(c) $\frac{x}{12} = \frac{7}{10}$

Explanation:

Problem 1(a)

Step1: Isolate $n$ by subtracting $\frac{2}{5}$

$n = \frac{3}{2} - \frac{2}{5}$

Step2: Find common denominator (10)

$n = \frac{15}{10} - \frac{4}{10}$

Step3: Subtract fractions

$n = \frac{11}{10} = 1\frac{1}{10}$

Problem 1(b)

Step1: Isolate $y$ by adding $\frac{4}{3}$

$y = \frac{11}{6} + \frac{4}{3}$

Step2: Find common denominator (6)

$y = \frac{11}{6} + \frac{8}{6}$

Step3: Add fractions

$y = \frac{19}{6} = 3\frac{1}{6}$

Problem 1(c)

Step1: Convert mixed numbers to fractions

$x + \frac{7}{2} = \frac{22}{3}$

Step2: Isolate $x$ by subtracting $\frac{7}{2}$

$x = \frac{22}{3} - \frac{7}{2}$

Step3: Find common denominator (6)

$x = \frac{44}{6} - \frac{21}{6}$

Step4: Subtract fractions

$x = \frac{23}{6} = 3\frac{5}{6}$

Problem 2(a)

Step1: Isolate $x$ by multiplying by $\frac{8}{3}$

$x = 21 \times \frac{8}{3}$

Step2: Simplify the product

$x = 7 \times 8 = 56$

Problem 2(b)

Step1: Isolate $n$ by multiplying by $\frac{7}{4}$

$n = \frac{2}{3} \times \frac{7}{4}$

Step2: Simplify the product

$n = \frac{14}{12} = \frac{7}{6} = 1\frac{1}{6}$

Problem 2(c)

Step1: Isolate $y$ by multiplying by $\frac{2}{5}$

$y = \frac{20}{9} \times \frac{2}{5}$

Step2: Simplify the product

$y = \frac{40}{45} = \frac{8}{9}$

Problem 3(a)

Step1: Isolate $n$ by multiplying by 8

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

Step2: Simplify the product

$n = 11 \times 2 = 22$

Problem 3(b)

Step1: Isolate $c$ by multiplying by 10

$c = \frac{3}{4} \times 10$

Step2: Simplify the product

$c = \frac{30}{4} = \frac{15}{2} = 7\frac{1}{2}$

Problem 3(c)

Step1: Isolate $x$ by multiplying by 12

$x = \frac{7}{10} \times 12$

Step2: Simplify the product

$x = \frac{84}{10} = \frac{42}{5} = 8\frac{2}{5}$

Answer:

1. (a) $1\frac{1}{10}$

(b) $3\frac{1}{6}$
(c) $3\frac{5}{6}$

1. (a) $56$

(b) $1\frac{1}{6}$
(c) $\frac{8}{9}$

1. (a) $22$

(b) $7\frac{1}{2}$
(c) $8\frac{2}{5}$