5/6 × -8/15
First, let's start off by changing the whole problem into a negative. To do so, we simplify move the negative sign and place it in front of the first fraction.
[tex]- \frac{5}{6} \times \frac{8}{15} [/tex]
Second, we can apply the multiplication rule to the fractions. If you do not know the rule of multiplication for fractions, the rule is: a/b × c/d = ac/bd. Let's use that for our own fractions.
[tex] -\frac{5 \times 8}{6 \times 15} [/tex]
Third, let's multiply now. (5 × 8 = 40) and (6 × 15 = 90). We now have a new fraction to work with, but it is not in its simplest form, so we can lower it.
[tex]- \frac{40}{90} [/tex]
Fourth, since we can simplify our new fraction, we start with having to find the GCF. To do this, we list the factors of both the numerator and the denominator, find the common factors and then the greatest one.
Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40
Factors of 90: 1, 2, 3, 5, 6, 9, 10, 15, 18, 30, 45, 90
Let's start by looking for our common factors. Which factors of 40 and 90 are common? I see that 1, 2, 5, and 10 are common factors of 40 and 90. Since we are looking for the greatest common factor, 10 is obviously the higher number, making it the greatest. The GCF is 10.
Fifth, we can now divide our numerator and denominator by the GCF we recently found which is 10.
[tex]40 \div 10 = 4 \\ 90 \div 10 = 9[/tex]
Sixth, collect our new numerator and denominator and make them into a fraction. That is the fraction in simplified form and it cannot be lowered down anymore.
Answer in fraction form: [tex]\fbox {-4/9}[/tex]
Answer in decimal form: [tex]\fbox {0.4444}[/tex]
