solve; divide; then reduce to lowest terms 1 4/7 / 4/10

and

divide; then reduce to lowest terms 14/3 / 2 5/7

a. (4/7)/(4/10) = 4/7 * 10/4 = 10/7.

b. (14/3)/2 / (5/7) = 14/3*1/2 * 7/5 =
98/30 = 49/15.

reduce answers to their lowest terms

To solve the first problem, let's divide the fractions:

1 4/7 ÷ 4/10

Step 1: Convert the mixed numbers to improper fractions:
1 4/7 = (7*1 + 4)/7 = 11/7
4/10 = (10*0 + 4)/10 = 4/10

Step 2: Invert the second fraction and multiply:
11/7 ÷ 4/10 = 11/7 * 10/4

Step 3: Simplify by canceling out common factors:
11/7 * 10/4 = (11 * 10) / (7 * 4) = 110/28

To reduce the fraction to lowest terms, divide both the numerator and the denominator by their greatest common divisor:

110/28 = 55/14

Therefore, 1 4/7 ÷ 4/10 = 55/14, reduced to lowest terms.

Now let's solve the second problem:

14/3 ÷ 2 5/7

Step 1: Convert the mixed numbers to improper fractions:
2 5/7 = (7*2 + 5)/7 = 19/7

Step 2: Invert the second fraction and multiply:
14/3 ÷ 19/7 = 14/3 * 7/19

Step 3: Simplify by canceling out common factors:
14/3 * 7/19 = (14 * 7) / (3 * 19) = 98/57

To reduce the fraction to lowest terms, divide both the numerator and the denominator by their greatest common divisor:

98/57 cannot be reduced further, as 98 and 57 do not share any common factors other than 1.

Therefore, 14/3 ÷ 2 5/7 = 98/57, reduced to lowest terms.

To divide fractions and reduce the result to its lowest terms, you can follow these steps:

1. Convert mixed numbers to improper fractions. To convert a mixed number to an improper fraction, multiply the whole number by the denominator of the fraction, then add the numerator. The result becomes the new numerator, and the denominator stays the same.

Now let's solve the provided examples:

1) Divide and reduce to lowest terms: 1 4/7 / 4/10.

Step 1: Convert mixed numbers to improper fractions:
1 4/7 = ((1 * 7) + 4) / 7 = 11/7
4/10 = 4/10 (already in fraction form)

Step 2: Invert the divisor and multiply:
11/7 ÷ 4/10 = 11/7 * 10/4

Step 3: Simplify multiplication:
11/7 * 10/4 = (11 * 10) / (7 * 4) = 110/28

2) Divide and reduce to lowest terms: 14/3 / 2 5/7.

Step 1: Convert mixed numbers to improper fractions:
2 5/7 = ((2 * 7) + 5) / 7 = 19/7
14/3 = 14/3 (already in fraction form)

Step 2: Invert the divisor and multiply:
14/3 ÷ 19/7 = 14/3 * 7/19

Step 3: Simplify multiplication:
14/3 * 7/19 = (14 * 7) / (3 * 19) = 98/57

To simplify the resulting fraction to its lowest terms, find the greatest common divisor (GCD) of the numerator and denominator and divide them both by the GCD.

In the first example, 110/28 can be simplified. The GCD of 110 and 28 is 2. Divide both the numerator and denominator by 2:
110/2 ÷ 28/2 = 55/14. This is the result in lowest terms.

In the second example, 98/57 is already in its lowest terms since there are no common factors other than 1.

So the final results are:
- 1 4/7 / 4/10 = 55/14
- 14/3 / 2 5/7 = 98/57