Question

1 a piece of tape measuring 100 cm is divided into tape a measuring 40 cm and tape b measuring 60 cm. answer the questions below.
(1) show the ratio of tape a to tape b in as small an integer as possible. 40 : = :
(2) show the ratio of tape a to the original tape measuring 100 cm, then find the value of that ratio. 40 : = : the value of ratio
(3) show the ratio of tape b to the original tape measuring 100 cm, then find the value of that ratio. 60 : = : the value of ratio
(4) given the original tape measuring 100 cm is set to 1, show the ratio of tape a to tape b in fractions. □/□ : □/□
2 40 pieces of candy are divided into two bags, with 25 pieces in bag a and 15 pieces in bag b. answer the questions below.
(1) show the ratio of the candies in bag a to that in bag b in as small an integer as possible. the ratio :
(2) show the ratio of bag a to the original 40 candies, then find the value of that ratio. the ratio : 40 = : the value of ratio
(3) show the ratio of bag b to the original candies, then find the value of that ratio. the ratio : the value of ratio
(4) given the original number of candies is set to 1, show the ratio of bag a to bag b in fractions.

Explanation:

Step1: Find ratio of A to B

Original ratio: $40:60$. Divide by GCD(40,60)=20: $40\div20:60\div20=2:3$

Step2: Find ratio of A to original tape

Ratio: $40:100$. Divide by 20: $2:5$. Value: $2/5=0.4$

Step3: Find ratio of B to original tape

Ratio: $60:100$. Divide by 20: $3:5$. Value: $3/5=0.6$

Step4: Fraction ratio of A to B (original=1)

A=40/100=2/5, B=60/100=3/5. Ratio: $2/5:3/5$

Step5: Ratio of candies A to B

Original:25:15. Divide by GCD=5: $5:3$

Step6: Ratio of candy A to original

Ratio:25:40. Divide by 5: $5:8$. Value: $5/8=0.625$

Step7: Ratio of candy B to original

Ratio:15:40. Divide by 5: $3:8$. Value: $3/8=0.375$

Step8: Fraction ratio of candy A to B (original=1)

A=25/40=5/8, B=15/40=3/8. Ratio: $5/8:3/8$

Answer:

1(1) $40:60=2:3$
1(2) $40:100=2:5$, value=0.4
1(3) $60:100=3:5$, value=0.6
1(4) $2/5:3/5$
2(1) $5:3$
2(2) $25:40=5:8$, value=0.625
2(3) $15:40=3:8$, value=0.375
2(4) $5/8:3/8$