Question

I'm looking for someone to just give me a push in the right direction on how to answer these questions.

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1)

On Monday, Ryan jogged 1 ½ miles in ¼ hour. On Wednesday he jogged 2 1/3 miles in 1/3 hour. How much farther did Ryan jog on Wednesday than on Monday?


2)

Josh is making three recipes. One requires 2/3 cup of flour, another requires 7/8 cup of flour, and the third requires ¾ cup of flour. How much flour will Josh use? Write your answer as a simplified mixed number.

Answer 1

1) 5/6 miles

2) 2 7/24 cups

Explanation:

1) Convert each mixed number into an improper fraction.

1 ½ = (2×1+1)/2 = 3/2

2 ⅓ = (3×2+1)/3 = 7/3

To add or subtract, find the common denominator.

3/2 = 9/6

7/3 = 14/6

The difference is:

14/6 − 9/6 = 5/6

2) To add the fractions, first find the common denominator (least common multiple of the denominators). To do that, write the prime factorizations:

3 = 3

8 = 2³

4 = 2²

LCM = 2³ × 3 = 24

2/3 = 16/24

7/8 = 21/24

3/4 = 18/24

The sum is:

(16 + 21 + 18) / 24

55/24

To convert to a mixed number, divide the numerator by the denominator. 24 goes into 55 two times with a remainder of 7.

55/24 = 2 7/24