4/5 x 1 1/6?

4/5 x 1 1/6?

To multiply 4/5 by 1 1/6, first convert the mixed number 1 1/6 to an improper fraction, which is 7/6. Then multiply:

(4/5) * (7/6) = (4 * 7) / (5 * 6) = 28/30.

Now, simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:

(28/2) / (30/2) = 14/15.

So, 4/5 multiplied by 1 1/6 equals 14/15.

Multiplying Fractions

When multiplying fractions, the main goal is to end up with a product that has a single fraction as the answer. To do this, we first multiply the numerators together to get a new numerator, then multiply the denominators together to get a new denominator.

For example:

2/3 x 3/5 Numerators: 2 x 3 = 6 Denominators: 3 x 5 = 15

So 2/3 x 3/5 = 6/15

We can simplify 6/15 further by dividing both the numerator and denominator by their greatest common factor, 3.

6/15 = 2/5

This provides the simplest form of the product.

Multiplying Mixed Numbers

Sometimes one or both of the fractions to be multiplied are mixed numbers, which contain a whole number and a fraction, like 1 1/6.

To multiply mixed numbers:

1. Ignore the whole number for now, just multiply the fractions.
2. After multiplying the fractions, multiply the whole numbers.
3. Add the whole number product to the fraction product.

For example, to multiply 4/5 x 1 1/6:

1. Multiply just the fractions: 4/5 x 1/6 = 4/30
2. Multiply the whole numbers: 4 x 1 = 4
3. Add the products: 4/30 + 4 = 19/30

Therefore, 4/5 x 1 1/6 = 19/30

We can double check this using a calculator to multiply 4/5 * 1 1/6, and we get the same result.

Converting Mixed Numbers

To make multiplying mixed numbers easier, we can convert them to improper fractions first:

4/5 = 16/20 (by multiplying 4 x 5)

1 1/6 = 7/6 (by converting 1 whole to 6/6 and adding the 1/6)

Then multiply as regular fractions:

16/20 x 7/6 = 112/120

Which reduces to 19/30, the same answer as before.

So converting to improper fractions before multiplying can help simplify the process while still arriving at the correct product.

In summary, multiplying fractions requires multiplying numerators, multiplying denominators, and simplifying. With mixed numbers, convert them or just multiply the fractions first before multiplying the whole numbers separately and combining the products.