Question

dividing fractions word problems - maze #3
start
a dylan is a computer programmer who works freelance, if she intends to work at least 100\frac{1}{4} hours this month & works 6\frac{1}{2} hours per day, how many days does she need to work?
b wooden dowels for deck railing come in 5 ft long sections. if mike needs 2\frac{1}{3} ft per rail, how many rails can he get out of each 5 ft section?
c roberto relies on firewood to heat his house during the winter. if he bought 4\frac{1}{2} cords of wood and burns \frac{1}{3} of a cord per week, does he have enough firewood for 12 weeks of winter?
d patrick has a roll of 60\frac{3}{5} m of ribbon to bind the edges of the blankets he makes and sells on etsy. if each blanket needs 9\frac{3}{5} m of ribbon for the edges, how many blankets can he make?
e there is 1\frac{4}{5} oz of black pepper in a small spice jar. if there is \frac{81}{300} oz (1 tsp) in each serving of pepper, how many servings are in a jar?
f neecy is in training for soccer camp and can eat 60\frac{9}{10} grams of fat per day. if her favorite frozen meals have 5\frac{5}{8} grams of fat each, how many can she eat each day?
g alicia measured 6\frac{1}{9} cups of ice cream in her quart bucket. if she eats \frac{2}{3} cup per day, how much of a serving will be left after she eats the full servings up?
h together, yondles hopper & buster eat \frac{1}{2} cup of kibble each day. simone has 3\frac{7}{8} cups of food left. how many full days of kibble does she have before she needs to buy more food?
finish
16\frac{2}{3}, 12\frac{1}{2}, 18\frac{1}{6}, 7\frac{1}{2}, 2, 6\frac{2}{3}, 11\frac{1}{9}, \frac{62}{75}, \frac{1}{6}, 58\frac{119}{25}, 6\frac{5}{16}, \frac{819}{2500}, 10, 7
greatest common factor - maze #11
name:
start
a what is the greatest common factor of 100 & 80?
b what is the greatest common factor of 72 & 96?
c what is the greatest common factor of 40 & 32?
d what is the greatest common factor of 12 & 16?
e what is the greatest common factor of 45 & 63?
f what is the greatest common factor of 32 & 48?
g what is the greatest common factor of 12 & 10?
h what is the greatest common factor of 98 & 72?
i what is the greatest common factor of 24 & 36?
j what is the greatest common factor of 96 & 49?
k what is the greatest common factor of 54 & 90?
l what is the greatest common factor of 90 & 100?
m what is the greatest common factor of 15 & 20?
n what is the greatest common factor of 48 & 52?
o what is the greatest common factor of 75 & 60?
finish
10, 24, 8, 5, 20, 14, 2, 4, 3, 6, 3, 16, 8, 12, 2, 5, 1, 18, 9, 10, 7, 3, 12, 10, 4, 5

Explanation:

First Maze (Least Common Multiple)

Step1: Find LCM of 4 & 8

Prime factors: $4=2^2$, $8=2^3$. LCM is $2^3=8$. Wait, the given path is 4, so solve the next:

Step2: Find LCM of 10 & 11

10 and 11 are coprime, so $\text{LCM}(10,11)=10\times11=110$.

Step3: Find LCM of 8 & 12

Prime factors: $8=2^3$, $12=2^2\times3$. LCM is $2^3\times3=24$.

Step4: Find LCM of 7 & 9

7 and 9 are coprime, so $\text{LCM}(7,9)=7\times9=63$.

Step1: Solve Problem B

Total length = 5 ft, per roll = $2\frac{1}{2}=\frac{5}{2}$ ft. Number of rolls: $5\div\frac{5}{2}=5\times\frac{2}{5}=2$. Follow path to H.

Step2: Solve Problem H

Total kibble = $3\frac{7}{8}=\frac{31}{8}$ cups, daily use = $\frac{1}{2}$ cup. Days: $\frac{31}{8}\div\frac{1}{2}=\frac{31}{8}\times2=\frac{31}{4}=7\frac{3}{4}$, full days = 7. Follow path to G.

Step3: Solve Problem G

Total ice cream = $6\frac{1}{9}=\frac{55}{9}$ cups, daily serving = $\frac{2}{3}$ cup. Number of full servings: $\frac{55}{9}\div\frac{2}{3}=\frac{55}{9}\times\frac{3}{2}=\frac{55}{6}=9\frac{1}{6}$, so 9 full servings. Remaining: $\frac{55}{9}-9\times\frac{2}{3}=\frac{55}{9}-\frac{54}{9}=\frac{1}{9}$. Wait, no—wait, the path from G is $\frac{1}{6}$ to C.

Step4: Solve Problem C

Total wood = $4\frac{1}{2}=\frac{9}{2}$ cords, weekly use = $\frac{1}{3}$ cord. Total weeks: $\frac{9}{2}\div\frac{1}{3}=\frac{27}{2}=13.5$ weeks. 13.5 > 12, so answer is "yes". Follow path to FINISH.

Step1: Solve Problem A

GCF of 100 & 80: Prime factors $100=2^2\times5^2$, $80=2^4\times5$. GCF is $2^2\times5=20$. Follow path to F.

Step2: Solve Problem F

GCF of 32 & 48: $32=2^5$, $48=2^4\times3$. GCF is $2^4=16$. Wait, no—path from F is 8 to J.

Step3: Solve Problem J

GCF of 96 & 49: 96=$2^5\times3$, 49=$7^2$. GCF is 1. Follow path to I.

Step4: Solve Problem I

GCF of 24 & 36: $24=2^3\times3$, $36=2^2\times3^2$. GCF is $2^2\times3=12$. Follow path to N.

Step5: Solve Problem N

GCF of 48 & 52: $48=2^4\times3$, $52=2^2\times13$. GCF is $2^2=4$. Follow path to K.

Step6: Solve Problem K

GCF of 54 & 90: $54=2\times3^3$, $90=2\times3^2\times5$. GCF is $2\times3^2=18$. Wait, no—path from K is 10 to O.

Step7: Solve Problem O

GCF of 75 & 60: $75=3\times5^2$, $60=2^2\times3\times5$. GCF is $3\times5=15$. Follow path to L.

Step8: Solve Problem L

GCF of 90 & 100: $90=2\times3^2\times5$, $100=2^2\times5^2$. GCF is $2\times5=10$. Follow path to FINISH.

Answer:

The path is: Start $
ightarrow$ A (4) $
ightarrow$ B (110) $
ightarrow$ C (24) $
ightarrow$ Final answer $\boldsymbol{63}$

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Second Maze (Dividing Fractions Word Problems)