Question

1 an electric eel has a length of 0.95 meters. what fraction is equivalent to the length of this electric eel in meters? dont forget to simplify! 2 order the integers from greatest to least: 42, -38, -56, 85, -23 3 what is 14% as a fraction in simplest form? solve each problem. 4 -4 - 2 = 5 6 - 9 = 6 -12(-8) = 7 -4 + -7 = 8 -2 - -3 = 9 10(-3) = 10 -66 ÷ -11 = 11 30 ÷ -5 =

Explanation:

Step1: Convert decimal to fraction

To convert \(0.95\) to a fraction, we write it as \(\frac{95}{100}\) because \(0.95=\frac{95}{100}\) (since \(0.95 = 95\times0.01=\frac{95}{100}\)).

Step2: Simplify the fraction

Find the greatest common divisor (GCD) of \(95\) and \(100\). The factors of \(95\) are \(1,5,19,95\) and the factors of \(100\) are \(1,2,4,5,10,20,25,50,100\). The GCD of \(95\) and \(100\) is \(5\).
Divide both the numerator and denominator by \(5\): \(\frac{95\div5}{100\div5}=\frac{19}{20}\).

Step3: Order the integers

Positive integers are greater than negative integers. Among positive integers \(85>42\). Among negative integers, the one with a smaller absolute - value is greater. \(\vert - 23\vert=23\), \(\vert - 38\vert = 38\), \(\vert - 56\vert=56\). So, \(-23>-38>-56\).
The order from greatest to least is \(85,42,-23,-38,-56\).

Step4: Convert percentage to fraction

\(14\%=\frac{14}{100}\) (since \(x\%=\frac{x}{100}\)).
Find the GCD of \(14\) and \(100\). The factors of \(14\) are \(1,2,7,14\) and the factors of \(100\) are \(1,2,4,5,10,20,25,50,100\). The GCD of \(14\) and \(100\) is \(2\).
Divide both the numerator and denominator by \(2\): \(\frac{14\div2}{100\div2}=\frac{7}{50}\).

Step5: Calculate \(-4 - 2\)

\(-4-2=-(4 + 2)=-6\) (using the rule \(a-b=-(b - a)\) when \(b>a\) for \(a=-4\) and \(b = 2\), or \(-4-2=-4+(-2)\) and adding two negative numbers: \(\vert - 4\vert+\vert - 2\vert=4 + 2\) and the result is negative).

Step6: Calculate \(6-9\)

\(6-9=-(9 - 6)=-3\) (using the rule \(a-b=-(b - a)\) when \(b>a\) for \(a = 6\) and \(b=9\)).

Step7: Calculate \(-12\times(-8)\)

The product of two negative numbers is positive. So, \(-12\times(-8)=12\times8 = 96\).

Step8: Calculate \(-4+(-7)\)

Adding two negative numbers: \(\vert - 4\vert+\vert - 7\vert=4 + 7\) and the result is negative. So, \(-4+(-7)=-(4 + 7)=-11\).

Step9: Calculate \(-2-(-3)\)

\(-2-(-3)=-2 + 3\) (since \(a-(-b)=a + b\)). Then \(3-2 = 1\).

Step10: Calculate \(10\times(-3)\)

The product of a positive and a negative number is negative. So, \(10\times(-3)=-(10\times3)=-30\).

Step11: Calculate \(-66\div(-11)\)

The quotient of two negative numbers is positive. So, \(-66\div(-11)=\frac{66}{11}=6\).

Step12: Calculate \(30\div(-5)\)

The quotient of a positive and a negative number is negative. So, \(30\div(-5)=-(30\div5)=-6\).

Answer:

1. \(\frac{19}{20}\)
2. \(85,42,-23,-38,-56\)
3. \(\frac{7}{50}\)
4. \(-6\)
5. \(-3\)
6. \(96\)
7. \(-11\)
8. \(1\)
9. \(-30\)
10. \(6\)
11. \(-6\)