- 3/8 x -1 2/3

To multiply a fraction by a whole number, we multiply the numerator of the fraction by the whole number and keep the denominator the same.

To multiply a fraction by a fraction, we multiply the numerators together and the denominators together.

First, let's simplify the mixed number -1 2/3.

To convert -1 2/3 to an improper fraction, we multiply the whole number (-1) by the denominator of the fraction (3) and add the numerator (2). This gives us -5/3.

Now we can multiply:

(-3/8) * (-5/3)

Multiplying the numerators and denominators:

(-3 * -5) / (8 * 3)

This simplifies to:

15/24

To reduce this fraction, we divide the numerator and denominator by their greatest common divisor, which in this case is 3:

15/24 ÷ 3/3

This gives us:

5/8

Therefore, - 3/8 x -1 2/3 is equal to -5/8.

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-4 1/2 x 1 2/5

To multiply mixed numbers, we first convert them to improper fractions.

Starting with -4 1/2, we convert it to an improper fraction:

-4 1/2 = -9/2

Next, we convert 1 2/5 to an improper fraction:

1 2/5 = 7/5

Now, we can multiply the two fractions:

(-9/2) * (7/5)

Multiplying the numerators and denominators:

(-9 * 7) / (2 * 5)

This simplifies to:

-63/10

Therefore, -4 1/2 x 1 2/5 is equal to -63/10.

To solve the expression -3/8 multiplied by -1 2/3, follow these steps:

Step 1: Convert the mixed number -1 2/3 to an improper fraction:
-1 2/3 = -1 * 3 + 2 = -5/3

Step 2: Multiply the fractions together:
-3/8 * -5/3 = (-3 * -5) / (8 * 3)

Step 3: Simplify the fraction:
= 15 / 24
= 5/8

Therefore, -3/8 multiplied by -1 2/3 is equal to 5/8.

To solve the expression -3/8 x -1 2/3, we need to perform the operations in the correct order. Here are the steps:

1. Start by converting the mixed number, -1 2/3, into an improper fraction. To do this, multiply the whole number (-1) by the denominator of the fraction (3), and then add the numerator (2) to get -5/3.

2. Now we have: -3/8 x -5/3.

3. To multiply fractions, multiply the numerators (top numbers) together to get the new numerator, and multiply the denominators (bottom numbers) together to get the new denominator.

-3 x -5 = 15
8 x 3 = 24

4. The expression becomes 15/24.

5. To simplify the fraction, find the greatest common divisor (GCD) of the numerator and denominator, then divide both by the GCD.

The GCD of 15 and 24 is 3.

Divide 15 by 3: 15 ÷ 3 = 5
Divide 24 by 3: 24 ÷ 3 = 8

6. The simplified fraction is 5/8. Therefore, the final answer to the expression -3/8 x -1 2/3 is 5/8.