Question

1. 4 3/14-2 11/42=2. 1 3/7×3 1/2=3. 2 8/17×1 20/21=4. 5-4 14/17=

Answer 1

1. 1/3
2. 9/14
3. 320/357
4. 29/17

Answer 2

Sure! Let's solve each of these equations step by step:

1. 1 + 4/3 - 2 + 11/42 = ?

To start, let's simplify the fractions first: - 4/3 can be rewritten as 1 1/3 (since 4 divided by 3 equals 1 with a remainder of 1). - 11/42 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 1. This gives us 11/42.

Now, let's replace the fractions with their simplified forms in the equation: 1 + 1 1/3 - 2 + 11/42

Next, let's convert the mixed number (1 1/3) into an improper fraction: 1 1/3 = (1 * 3 + 1)/3 = 4/3

Now, substitute the values back into the equation: 1 + 4/3 - 2 + 11/42

To add or subtract fractions, we need to have a common denominator. In this case, the common denominator is 42 (the least common multiple of 3 and 42).

Now, let's convert the fractions into fractions with a denominator of 42: 1 = 42/42 4/3 = (4 * 14)/(3 * 14) = 56/42 2 = 2 * (42/42) = 84/42 11/42 remains the same

Substituting the new fractions into the equation: 42/42 + 56/42 - 84/42 + 11/42

Now, let's add or subtract the fractions: (42 + 56 - 84 + 11)/42 = 25/42

So, the solution to the first equation is 25/42.

2. 1 + 3/7 × 3 + 1/2 = ?

First, let's simplify the fractions: - 3/7 remains the same. - 1/2 remains the same.

Now, let's substitute the values into the equation: 1 + 3/7 × 3 + 1/2

To multiply fractions, we simply multiply the numerators and denominators: 3/7 × 3 = (3 * 3)/(7 * 1) = 9/7

Now, substitute the new fraction into the equation: 1 + 9/7 + 1/2

To add fractions, we need a common denominator. In this case, the common denominator is 14 (the least common multiple of 7 and 2).

Now, let's convert the fractions into fractions with a denominator of 14: 1 = 14/14 9/7 = (9 * 2)/(7 * 2) = 18/14 1/2 = (1 * 7)/(2 * 7) = 7/14

Substituting the new fractions into the equation: 14/14 + 18/14 + 7/14

Now, let's add the fractions: (14 + 18 + 7)/14 = 39/14

So, the solution to the second equation is 39/14.

3. 2 + 8/17 × 1 + 20/21 = ?

Let's simplify the fractions first: - 8/17 remains the same. - 20/21 remains the same.

Now, let's substitute the values into the equation: 2 + 8/17 × 1 + 20/21

To multiply fractions, we simply multiply the numerators and denominators: 8/17 × 1 = 8/17

Now, substitute the new fraction into the equation: 2 + 8/17 + 20/21

To add fractions, we need a common denominator. In this case, the common denominator is 357 (the least common multiple of 17 and 21).

Now, let's convert the fractions into fractions with a denominator of 357: 2 = 2 * (357/357) = 714/357 8/17 remains the same. 20/21 = (20 * 17)/(21 * 17) = 340/357

Substituting the new fractions into the equation: 714/357 + 8/17 + 340/357

Now, let's add the fractions: (714 + 8 + 340)/357 = 1062/357

Simplifying the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 3: (1062/3) / (357/3) = 354/119

So, the solution to the third equation is 354/119.

4. 5 - 4 + 14/17 = ?

Let's simplify the fraction first: - 14/17 remains the same.

Now, let's substitute the values into the equation: 5 - 4 + 14/17

To subtract fractions, we need a common denominator. In this case, the common denominator is 17.

Now, let's convert the fractions into fractions with a denominator of 17: 5 = 5 * (17/17) = 85/17 4 = 4 * (17/17) = 68/17 14/17 remains the same

Substituting the new fractions into the equation: 85/17 - 68/17 + 14/17

Now, let's subtract the fractions: (85 - 68 + 14)/17 = 31/17

So, the solution to the fourth equation is 31/17.

I hope this helps! Let me know if you have any other questions.