-2 2/3 * 6/7
First, we can start out by turning 2 2/3 into an improper fraction. To do this, we will have to use the improper fraction rule which is: a b/c = ac+b/c. Let's use that rule to create our improper fraction.
[tex]- \frac{2 \times 3 + 2}{3} \times \frac{6}{7} [/tex]
Second, let's simplify the numerator. We can begin with 2 × 3 (equals 6). We can then move onto 6 + 2 (equals 8).
[tex]- \frac{8}{3} \times \frac{6}{7} [/tex]
Third, our next step will be to apply another rule to our problem. This is our last rule, don't worry. If you have never learned these rules, you could always look them up and see what they are for. Basically, we need the rules to get the correct answer. The rule for this step is: a/b × c/d = ac/bd. Let's continue to use that for our problem.
[tex]- \frac{8 \times 6}{3 \times 7} [/tex]
Fourth, let's simplify the numerator and denominator. 8 × 6 (equals 48) and then 3 × 7 (equals 21).
[tex] -\frac{48}{21} [/tex]
Fifth, we can simplify our fraction now down to lower terms. To do this, we have to find the greatest common factor (GCF) of both the numerator and denominator.
Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
Factors of 21: 1, 3, 7, 21
The common factors between the two numbers are 1 and 3. Since 3 is the greatest, it is considered the GCF.
Sixth, our next step to simplifying the fraction is to divide the numerator (48) and the denominator (21) by the greatest common factor we just found which was 3.
[tex]48 \div 3 = 16 \\ 21 \div 3 = 7 [/tex]
Our new fraction is now -16/7.
Seventh, we now have to convert the fraction we recently found to a mixed fraction. 16 ÷ 7 = 2 with a remainder of 2. One of those 2's will be the whole number and the second will be our new numerator. After doing this, we will have our answer.
[tex]-2 \frac{2}{7} [/tex]
Answer in fraction form: [tex]\fbox {-2 2/7} [/tex]
Answer in decimal form: [tex]\fbox {-2.2857} [/tex]
