Use properties of multiplication and division to help classify each problem under its answer.
3/5 (3/6-1/2)
1/2x2/3 - 2/3x1/2
6/5/6/5 / 6/5+1/6
14/3-( 1 11/3)
1/2x2/3x3/4 / 1/4
6(2/3-1/2)
4/3x3/2 -1
the catagories you put them under are zero and one
To classify each problem under its answer using properties of multiplication and division, we need to simplify the expressions step by step. Let's go through each problem and work on simplifying them:
1) 3/5 * (3/6 - 1/2):
- Begin by simplifying the subtraction inside the parentheses:
3/5 * (1/6 - 1/2) = 3/5 * (-2/3) = -6/15 = -2/5
- The answer for this problem falls under the "Zero" category since -2/5 is considered zero.
2) (1/2 * 2/3) - (2/3 * 1/2):
- Simplify the multiplication on each side:
(1/2 * 2/3) - (2/3 * 1/2) = 2/6 - 2/6 = 0/6 = 0
- The answer for this problem falls under the "Zero" category.
3) (6/5) / ((6/5) + (1/6)):
- Simplify the addition in the denominator:
(6/5) / (36/30 + 5/30) = (6/5) / (41/30)
- Now, divide by a fraction by multiplying by its reciprocal:
(6/5) * (30/41) = 180/205 = 36/41
- The answer for this problem falls under the "One" category since 36/41 is considered one.
4) 14/3 - (1 + 11/3):
- Start by simplifying the addition inside the parentheses:
14/3 - (3/3 + 11/3) = 14/3 - 14/3 = 0
- The answer for this problem falls under the "Zero" category.
5) (1/2 * 2/3 * 3/4) / (1/4):
- Simplify the multiplication of fractions in the numerator:
(1/2 * 2/3 * 3/4) / (1/4) = (1 * 2 * 3) / (2 * 3 * 4) / (1/4) = 6/8 / (1/4)
- To divide by a fraction, multiply by its reciprocal:
(6/8) * (4/1) = 24/8 = 3
- The answer for this problem falls under the "One" category since 3 is considered one.
6) 6 * (2/3 - 1/2):
- Start by simplifying the subtraction inside the parentheses:
6 * (1/6 - 3/6) = 6 * (-2/6) = -12/6 = -2
- The answer for this problem falls under the "Zero" category since -2 is considered zero.
7) 4/3 * 3/2 - 1:
- Simplify the multiplication of fractions:
(4/3 * 3/2) - 1 = 12/6 - 1 = 2 - 1 = 1
- The answer for this problem falls under the "One" category since 1 is considered one.
To summarize the categorization:
Zero category: Problems 1, 2, 4, and 6.
One category: Problems 3 and 5.