Simplify: (-\frac{1}{3} \times \frac{5}{4}) + [\frac{3}{5} \div (\frac{1}{2} - \frac{1}{4})]

a) 1\frac{18}{60}

b) 1\frac{59}{60}

c) 1\frac{49}{60}

d) 1\frac{58}{59}

Question

High School

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Answer :

RyanHarmon181 RyanHarmon181 · Answer 1 · 2023-07-26T20:31:29-04:00

Let's simplify the given expression step-by-step:

The expression is:

[tex](-\frac{1}{3} \times \frac{5}{4}) + \left[ \frac{3}{5} \div \left(\frac{1}{2} - \frac{1}{4}\right) \right][/tex]

Step 1: Simplify the multiplication part

First, simplify [tex]-\frac{1}{3} \times \frac{5}{4}[/tex]:

[tex]= -\frac{1 \times 5}{3 \times 4} = -\frac{5}{12}[/tex]

Step 2: Simplify the expression in the brackets

For the division part, start by simplifying the subtraction inside the parentheses:

[tex]\frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}[/tex]

Then divide [tex]\frac{3}{5}[/tex] by [tex]\frac{1}{4}[/tex]:

Remember that dividing by a fraction is the same as multiplying by its reciprocal, so:

[tex]\frac{3}{5} \div \frac{1}{4} = \frac{3}{5} \times 4 = \frac{3 \times 4}{5 \times 1} = \frac{12}{5}[/tex]

Step 3: Combine the results

Now, add the results from Steps 1 and 2:

[tex]-\frac{5}{12} + \frac{12}{5}[/tex]

To add these fractions, find a common denominator, which is 60:

Convert [tex]-\frac{5}{12}[/tex] to [tex]-\frac{25}{60}[/tex]:

[tex]-\frac{5}{12} = -\frac{5 \times 5}{12 \times 5} = -\frac{25}{60}[/tex]

Convert [tex]\frac{12}{5}[/tex] to [tex]\frac{144}{60}[/tex]:

[tex]\frac{12}{5} = \frac{12 \times 12}{5 \times 12} = \frac{144}{60}[/tex]

Therefore, the expression becomes:

[tex]-\frac{25}{60} + \frac{144}{60} = \frac{144 - 25}{60} = \frac{119}{60}[/tex]

Convert [tex]\frac{119}{60}[/tex] to a mixed number:

Since 119 divided by 60 equals 1 with a remainder of 59, the result is:

[tex]1\frac{59}{60}[/tex]

Thus, the simplified expression is [tex]1\frac{59}{60}[/tex].

Therefore, the correct answer is option b) [tex]1\frac{59}{60}[/tex].