Question

section 3.5
pg 81
peanut butter
39/14 = 2 11/14 = 2.79
14 longdiv 39
28
11
14 longdiv 112
28*4=112
112-112=0
14*8=112
112/14=8
39/14=2 11/14≈2.79
24/14=1 10/14=1 5/7≈1.71
14 longdiv 24
14
10
14 longdiv 24
14
10
10.5/14=3/4=0.75
14 longdiv 10.5
10.5-10.5=0
14*0.75=10.5
195/14=13 13/14≈13.93
14 longdiv 195
182
13
14*13=182
195-182=13
195/14=13 13/14≈13.93
decimal

Explanation:

Step1: Analyze the first fraction $\frac{77}{14}$

Simplify the fraction by dividing numerator and denominator by their greatest common divisor (GCD). The GCD of 77 and 14 is 7. So, $\frac{77\div7}{14\div7}=\frac{11}{2} = 5.5$.

Step2: Analyze the fraction $\frac{39}{14}$

Convert the improper fraction to a mixed number: $39\div14 = 2$ with a remainder of 11, so $\frac{39}{14}=2\frac{11}{14}\approx2.79$.

Step3: Analyze the fraction $\frac{24}{14}$

Simplify by dividing numerator and denominator by 2: $\frac{24}{14}=\frac{12}{7}\approx1.71$ (or as a mixed number $1\frac{5}{7}$).

Step4: Analyze the fraction $\frac{10.5}{14}$

Divide 10.5 by 14: $10.5\div14 = 0.75=\frac{3}{4}$.

Step5: Analyze the fraction $\frac{195}{14}$

Convert to a mixed number: $195\div14 = 13$ with a remainder of 13, so $\frac{195}{14}=13\frac{13}{14}\approx13.93$.

Answer:

The simplified or converted forms are: $\frac{77}{14}=5.5$, $\frac{39}{14}=2\frac{11}{14}\approx2.79$, $\frac{24}{14}=\frac{12}{7}\approx1.71$, $\frac{10.5}{14}=0.75$, $\frac{195}{14}=13\frac{13}{14}\approx13.93$ (depending on the required form for each).