Add the quotient of 4/7÷4/5 to the product of 4/7×5/8
To solve this problem, we need to find the quotient of 4/7 divided by 4/5 and then add it to the product of 4/7 multiplied by 5/8.
First, let's find the quotient of 4/7 divided by 4/5:
(4/7) ÷ (4/5) = (4/7) × (5/4) (invert the second fraction and multiply)
= (4 × 5) / (7 × 4) (multiply numerators and denominators separately)
= 20 / 28
= 5/7
Next, let's find the product of 4/7 multiplied by 5/8:
(4/7) × (5/8) = (4 × 5) / (7 × 8) (multiply numerators and denominators separately)
= 20 / 56
= 5/14
Now, we'll add the quotient (5/7) to the product (5/14):
(5/7) + (5/14) (both fractions have a common denominator of 14, so we can add them)
= (10/14) + (5/14) (rewrite both fractions having the same denominator)
= 15/14
Therefore, the sum of the quotient of 4/7 divided by 4/5 and the product of 4/7 multiplied by 5/8 is 15/14.
To solve the expression, we'll first find the quotient of 4/7 ÷ 4/5, then we'll find the product of 4/7 × 5/8, and finally, we'll add the two results together.
Step 1: Quotient of 4/7 ÷ 4/5
To divide two fractions, we need to multiply the first fraction by the reciprocal of the second fraction. So, the quotient can be found by multiplying 4/7 by 5/4:
(4/7) × (5/4) = (4 × 5) / (7 × 4) = 20/28
Step 2: Product of 4/7 × 5/8
To find the product, we simply multiply the numerators (4 × 5) and the denominators (7 × 8):
(4/7) × (5/8) = (4 × 5) / (7 × 8) = 20/56
Step 3: Add the results
To add the two fractions, we need to have a common denominator. The least common multiple of 28 and 56 is 56, so we'll rewrite both fractions with a denominator of 56:
20/28 = 20/28 × 2/2 = 40/56
20/56 + 40/56 = 60/56
Step 4: Simplify the result
The fraction 60/56 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 4:
60 ÷ 4 / 56 ÷ 4 = 15/14
Therefore, the sum of the quotient of 4/7 ÷ 4/5 and the product of 4/7 × 5/8 is 15/14.