How do I answer this

Question

When Sofie looked at her cell phone bill for the month, she saw that she had spent 1/2 of her minutes talking to her mother and 2/5 of her minutes talking to her best friend. What fraction of the minutes did Sofie spend talking to either her mom or her best friend?

Answer 1

Since we are trying to find the total amount of time that she spent talking to either her mom or her best friend, we add the fractions from each.

Total = 1/2 + 2/5

To add fractions we need to find a common denominator, which is 10. So

Total = 5/10 + 4/10 = 9/10

Then reduce if possible. Since the fraction does not reduce, the final answer is 9/10

Answer 2

Well, half of the time Sophie talked to her mom. That is 50% of time.

2/5 parts of the time, Sophie talked to her best friend. That is 2/5 = 40% of the time.

Talking to both: 50% + 40% = 90%.

Going back to fractions: 90% = 90/100 = 9/10!

With other words, percents, fractions are just different names for the same ratios.

Answer 3

1/2 + 2/5

To add or subtract, we have to have the same denominator. We need to find the LCM of 2 and 5.

2,4,6,8,10

5,10

Hey, it's 10.

How many twos make 10? Five! We have to multiply the numerator and the denominator by 5 (because 5/5 = 1 and anything times 1 is itself). When multiplying or dividing, the denominators do not have to be the same; we just multiply straight across.

How many fives make 10? Well, 2, we just decided in reverse.

(1/2)(5/5) + (2/5)(2/2) = 5/10 + 4/10 = 9/10

Do 9 and 10 have any common factors besides 1? Nope, so we are done!