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Evaluate (−1/6+0.6(−1/3)+1)2 What is the value of the expression? Enter your answer as a simplified fraction in the box.

Sagot :

Conversion a decimal number to a fraction: 0.6 = 6/10 = 3/5

A) Write down the decimal 0.6 divided by 1: 0.6 = 0.6/1

B) Multiply both top and bottom by 10 for every number after the decimal point. (For example, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, etc.)

0.6/1 = 6/10

Note: 6/10 is called a decimal fraction.

C) Simplify and reduce the fraction

6/10 = 3 * 2/5 * 2 = 3 * 2/5 * 2 = 3/5

Multiple: 0.6 * (-1/3) = 3 · (-1)/5 · 3 = -3/15 = -1 · 3/5 · 3 = -1/5

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-3, 15) = 3. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - three fifths multiplied by minus one third = minus one fifth.

Add: -1/6 + the result of step No. 2 = -1/6 + (-1/5) = -1 · 5/6 · 5 + (-1) · 6/5 · 6 = -5/30 + (-6/30) = -5 + (-6)/30 = -11/30

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(6, 5) = 30. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 6 × 5 = 30. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - minus one sixth plus minus one fifth = minus eleven thirtieths.

Add: the result of step No. 3 + 1 = -11/30 + 1 = -11/30 + 1/1 = -11/30 + 1 · 30/1 · 30 = -11/30 + 30/30 = -11 + 30/30 = 19/30

For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(30, 1) = 30. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 30 × 1 = 30. In the following intermediate step, the fraction result cannot be further simplified by canceling.

In other words - minus eleven thirtieths plus one = nineteen thirtieths.

Exponentiation: the result of step No. 4 ^ 2 = 19/30^2 = 192/302 = 361/900

In other words - nineteen thirtieths raised to the power of squared = three hundred sixty-one nine-hundredths.

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