Question

1)|-32/48|:|-5 1/16|2)|-4 2/9|-|-3 7/8|​

Answer 1

1)|-32/48|:|-5 1/16| =
= 32/48 : 5 1:16 =
= 32/48 : 81/16 =
= 32/48 • 16/81 = 32/243

2)|-4 2/9|-|-3 7/8|
= 4 2/9 - 3 7/8 =
= 38/9 - 31/8 =
= 3049/72 - 279/72 = 25/72

Answer 2

To simplify the expressions, let's start by converting the mixed numbers to improper fractions.

1. |-32/48| : |-5 1/16| To convert -32/48 to an improper fraction, we divide the numerator (-32) by the denominator (48), which gives us -2/3. Similarly, to convert -5 1/16 to an improper fraction, we multiply the whole number (-5) by the denominator (16) and add the numerator (1) to get -81/16.

So the expression becomes: |-2/3| : |-81/16|

2. |-4 2/9| - |-3 7/8| Converting -4 2/9 to an improper fraction, we get -38/9. Converting -3 7/8 to an improper fraction, we get -31/8.

So the expression becomes: |-38/9| - |-31/8|

Now let's simplify each expression.

1. |-2/3| : |-81/16| To simplify the division of fractions, we multiply the first fraction by the reciprocal of the second fraction.

|-2/3| : |-81/16| = |-2/3| * |16/-81|

Simplifying the absolute values and multiplying: 2/3 * 16/81 = (2 * 16) / (3 * 81) = 32/243

The result is 32/243.

2. |-38/9| - |-31/8| To subtract fractions, we need to find a common denominator. The common denominator for 9 and 8 is 72.

|-38/9| - |-31/8| = |-38/9| - |-31/8| * (9/9)

Simplifying the absolute values and performing the subtraction: 38/9 - 31/8 * (9/9) = 38/9 - 31/8 * 9/9 = 38/9 - 31/8 = (304 - 279) / 72 = 25/72

The result is 25/72.

Therefore, the simplified expressions are:

1. |-32/48| : |-5 1/16| = 32/243
2. |-4 2/9| - |-3 7/8| = 25/72