Question

Fraction Path

Use the fraction in the treasure chest to fill the cards below. Following the indicated operations, the end result of the path must be 1.
Start:
⅚ - _ = 1/12 + ⅜ = _ × _= 11/46 ÷ _ = 11/16 + _ = 11/24 × _ = 11/36 ÷ _ = 1

Answer 1

To find the missing fractions in the given fraction path and ensure that the end result is 1, let's solve each step one by one:

Step 1:

Starting with ⅚, we need to subtract a fraction to get closer to 1. One option is to subtract 5/6, which gives us 1/6.

Step 2:

Now, we need to add a fraction to get to 1/12. Adding 1/12 to 1/6 gives us 1/4.

Step 3:

Next, we need to multiply two fractions to get 11/46. One possible pair of fractions that gives us 11/46 when multiplied is 1/2 and 11/23.

Step 4:

To get to 11/16, we need to divide by a fraction. Dividing 11/46 by 1/4 gives us 11/46 ÷ 1/4 = 11/46 × 4/1 = 11/11 = 1.

Step 5:

To reach 11/24, we need to add a fraction. Adding 1/8 to 1 gives us 9/8.

Step 6:

In order to get 11/36, we need to multiply by a fraction. Multiplying 9/8 by 1/4 gives us 9/32.

Step 7:

Finally, we need to divide by a fraction to get 1. Dividing 9/32 by 9/32 gives us 1.

Therefore, the missing fractions in the fraction path are:

- Step 1: Subtract 5/6

- Step 2: Add 1/12

- Step 3: Multiply 1/2 and 11/23

- Step 4: Divide by 1/4

- Step 5: Add 1/8

- Step 6: Multiply by 1/4

- Step 7: Divide by 9/32

Note: It is important to keep in mind that there may be multiple correct answers depending on the fractions chosen at each step. The above explanation provides one possible solution.

Answer 2

To fill the cards and reach a final result of 1, let's solve the fraction path step by step:

1. Start with the fraction ⅚. We need to subtract a fraction to get 1/12. To do this, we subtract 1/12 from ⅚:

⅚ - 1/12 = (6/6) - (1/12) = 72/72 - 6/72 = 66/72

2. Next, we add 3/8 to the result obtained in step 1. This will give us the fraction that will be multiplied with an unknown fraction to get 11/46:

66/72 + 3/8 = 88/96 + 27/96 = 115/96

3. Now, we need to find the value of the unknown fraction that, when multiplied by 115/96, will give us 11/46. To solve for this fraction, we can cross-multiply and solve for the numerator:

(115/96) × (numerator/1) = 11/46

Cross-multiplying gives us: (115 × numerator) = (96 × 11)

Solving for the numerator: numerator = (96 × 11) / 115 = 9.4087

4. Moving on to the next card, we need to divide 11/46 by an unknown fraction to get 11/16. To solve for this fraction, we can set up a division equation:

(11/46) ÷ (unknown fraction) = 11/16

Cross-multiplying gives us: (11 × 16) = (46 × unknown fraction)

Solving for the unknown fraction: unknown fraction = (11 × 16) / 46 = 3.8261

5. Now, we need to add an unknown fraction to 11/16 to get 11/24. To find this fraction, we can subtract 11/16 from 11/24:

11/24 - 11/16 = (11 × 2) / (24 × 2) - (11 × 3) / (16 × 3)

Simplifying gives us: 22/48 - 33/48 = -11/48

6. Moving forward, we need to multiply 11/24 by an unknown fraction to get 11/36. To solve for this fraction, we can set up a multiplication equation:

(11/24) × (unknown fraction) = 11/36

Cross-multiplying gives us: (11 × 36) = (24 × unknown fraction)

Solving for the unknown fraction: unknown fraction = (11 × 36) / 24 = 16.5

7. Finally, we need to divide 11/36 by an unknown fraction to get 1. To find this fraction, we can set up a division equation:

(11/36) ÷ (unknown fraction) = 1

Cross-multiplying gives us: (11 × 1) = (36 × unknown fraction)

Solving for the unknown fraction: unknown fraction = (11 × 1) / 36 = 0.3056

By filling the cards with the respective fractions obtained in each step, following the indicated operations, we can achieve a path where the end result is 1.