Ques1- represent
numberline -7/3.
Ques2- divide the sum of3/8and -5/12by the reciprocal of -15/8 *16/27
(3/8 - 5/12) / 1/(-15/8 * 16/27)
= (9/24 - 10/24) * (-15/8 * 16/27)
= (-1/24) * (-10/9)
= 5/108
Ques1:
To represent -7/3 on a number line, follow these steps:
1. Draw a straight line horizontally.
2. Mark a point at the center of the line, and label it as zero.
3. Choose a unit length for each division on the line.
4. Count to the left from zero and mark seven equal divisions.
5. On the seventh division, mark a point and label it as -7/3.
Ques2:
To divide the sum of 3/8 and -5/12 by the reciprocal of -15/8 * 16/27, follow these steps:
1. Add 3/8 and -5/12 to find their sum:
3/8 + (-5/12) = (9/24) + (-10/24) = -1/24
2. Find the reciprocal of -15/8 * 16/27 by swapping the numerator and denominator:
Reciprocal: (-8/15) * (27/16)
3. Multiply the reciprocals:
(-8/15) * (27/16) = (-8 * 27) / (15 * 16) = -216/240 = -9/10
4. Divide the sum (-1/24) by the reciprocal (-9/10):
(-1/24) / (-9/10) = (-1/24) * (10/-9) = (1/24) * (10/9) = (1 * 10) / (24 * 9) = 10/216 = 5/108
Therefore, the result of dividing the sum of 3/8 and -5/12 by the reciprocal of -15/8 * 16/27 is 5/108.
To represent the number -7/3 on a number line, you would follow these steps:
Step 1: Draw a straight line horizontally.
Step 2: Choose a starting point on the line and label it as the zero point or origin.
Step 3: Mark off equal intervals on the line in both directions. For example, you can mark intervals of 1.
Step 4: Locate the point that represents -7/3. Since -7/3 is a negative fraction, it lies to the left of the origin. The point on the line that corresponds to -7/3 will be located between the intervals you marked off. To find the exact point, you can estimate the position between the intervals based on the numerator and denominator of -7/3.
Now, let's move on to the second question:
To divide the sum of 3/8 and -5/12 by the reciprocal of -15/8 * 16/27, you can follow these steps:
Step 1: Find the reciprocal of -15/8 * 16/27. To find the reciprocal, you simply need to invert the fraction. The reciprocal of a/b is b/a. Therefore, the reciprocal of -15/8 * 16/27 is 27/16 * 8/15.
Step 2: Add 3/8 and -5/12. To add fractions, you need to have a common denominator. In this case, the least common denominator between 8 and 12 is 24. Multiply each fraction by the appropriate value to make the denominators equal to 24: (3/8) * (3/3) = 9/24 and (-5/12) * (2/2) = -10/24. Adding these fractions together gives you 9/24 + (-10/24) = -1/24.
Step 3: Divide the sum (-1/24) by the reciprocal (27/16 * 8/15). When dividing fractions, you can multiply by the reciprocal of the second fraction. Therefore, you would multiply (-1/24) by (16/27 * 15/8).
To perform this calculation, you can multiply the numerators and denominators across:
(-1/24) * (16/27 * 15/8) = (-1 * 16)/(24 * 27 * 15/8).
Simplify the expression and perform the multiplication:
(-16)/(24 * 27 * 15/8) = (-16)/(9720/8) = (-16) * (8/9720) = -128/9720.
Further simplification is possible by dividing both the numerator and denominator by their greatest common divisor, which is 8.
(-128/9720) รท 8 = -16/1215.
Thus, the final answer to the division is -16/1215.