Howard made cards for the fractions 3/9,4/8, 1/7, 6/5,and 3/10. He set them out in a row, putting 1/7 first.The fraction equivalent to 1/2 went after the one equivalent to a mixed number. A fraction that is half of 3/5 went between the fraction equivalent to a mixed number and the one equivalent to 1/3. Fing the order of the cards.

Question

Howard made cards for the fractions 3/9,4/8, 1/7, 6/5,and 3/10. He set them out in a row, putting 1/7 first.The fraction equivalent to 1/2 went after the one equivalent to a mixed number. A fraction that is half of 3/5 went between the fraction equivalent to a mixed number and the one equivalent to 1/3. Fing the order of the cards.

Answer 1

so your saying that 1/7 went first, then half of 1/7 went next? i'm confused, could you put it another way?

Answer 2

1/7 went first

cards: 1/7 ? ? ? ?

the only mixed number is 6/5, so we will have 6/5 4/8

half of 3/5 is 3/10. It goes between 6/5 and 3/9. It can't go after 6/5, because 4/8 goes there. It must go before: 3/9 3/10 6/5

So, the cards are in the order

1/7 3/9 3/10 6/5 4/8

You just have to piece it together, one fact at a time.

Answer 3

To find the order of the cards, we need to analyze the given information and follow the given conditions step by step. Let's break it down:

Step 1: Howard set 1/7 first.
So the first card is 1/7.

Step 2: The fraction equivalent to 1/2 goes after the one equivalent to a mixed number.
This means the card equivalent to 1/2 comes after the mixed number card. Now, let's check the options:
- 3/9 is equivalent to 1/3, not 1/2.
- 4/8 is equivalent to 1/2.

So, the second card is 4/8.

Step 3: A fraction that is half of 3/5 goes between the fraction equivalent to a mixed number and the one equivalent to 1/3.
This means we need to find a fraction that is half of 3/5 and place it between the mixed number card (4/8) and the card equivalent to 1/3. Now, let's find the fraction that is half of 3/5:
3/5 ÷ 2 = (3/5) × (1/2) = 3/10

So, the third card is 3/10.

Step 4: Now, we have three cards placed:
1/7, 4/8, 3/10

Step 5: The fraction equivalent to 1/2 is already placed (4/8 is equivalent to 1/2). Therefore, we need to place the remaining fractions, namely 3/9 and 6/5.

Let's compare 3/9 and 6/5 with the cards already placed:
- 3/9 is not between 1/2 and 1/3.
- 6/5 is not between 1/2 and 1/3.

Hence, the fourth card is 3/9.

Finally, the last card is 6/5.

The order of the cards is:
1/7, 4/8, 3/10, 3/9, 6/5.