order these fraction from least to greatest 3/4,-2/3,7/10,-5/6

Change the fractions to their equivalents with 60 as the common denominator. Then they'll be easy to put in order.

To order these fractions from least to greatest, we can convert them to have a common denominator. The common denominator we can use is 12.

Converting the fractions:

3/4 = (3/4) * (3/3) = 9/12
-2/3 = (-2/3) * (4/4) = -8/12
7/10 = (7/10) * (6/6) = 42/60
-5/6 = (-5/6) * (10/10) = -50/60

Now, we can order the fractions:

-50/60, -8/12, 9/12, 42/60

Simplifying the fractions:

-50/60 reduces to -5/6
-8/12 reduces to -2/3
9/12 reduces to 3/4
42/60 reduces to 7/10

Ordering the simplified fractions:

-5/6, -2/3, 3/4, 7/10

Therefore, the fractions ordered from least to greatest are: -5/6, -2/3, 3/4, 7/10.

To order fractions from least to greatest, you can follow these steps:

1. Find a common denominator for all the fractions. In this case, the common denominator for 4, 3, 10, and 6 is 12.

2. Convert each fraction to have the common denominator of 12. Multiply the numerator and denominator of each fraction by the appropriate factor to achieve this.

Let's go through the process step by step:

The first fraction, 3/4, already has 4 as its denominator, so there is no need to modify it.

For the second fraction, -2/3, we need to multiply the numerator and denominator by 4 to get a denominator of 12:
-2/3 * 4/4 = -8/12

The third fraction, 7/10, requires multiplying the numerator and denominator by 6 to get a denominator of 12:
7/10 * 6/6 = 42/60

Lastly, the fourth fraction, -5/6, demands multiplying the numerator and denominator by 2 to get a denominator of 12:
-5/6 * 2/2 = -10/12

Now, we have the fractions with a common denominator:

3/4, -8/12, 42/60, -10/12

3. Start comparing the fractions from least to greatest:

-10/12 < -8/12 < 3/4 < 42/60

4. If necessary, simplify the fractions to their simplest form:

-10/12 simplifies to -5/6, and 42/60 simplifies to 7/10

The final order from least to greatest is:

-5/6, -8/12, 3/4, 7/10