Simplify 3/10x + 1/6y + 3/10x + 3/6y. Be sure to reduce any fractions to the lowest terms.(1 point)
Combining like terms, we have the sum (3/10)x + (1/6)y + (3/10)x + (3/6)y.
We can simplify this expression by adding the coefficients of like terms together.
The coefficients of the x terms are (3/10) and (3/10), so their sum is (3/10) + (3/10) = 6/10.
The coefficients of the y terms are (1/6) and (3/6), so their sum is (1/6) + (3/6) = 4/6.
Putting it all together, we have the simplified expression (6/10)x + (4/6)y.
To reduce this fraction to its lowest terms, we can simplify the coefficients. Both 6 and 10 are divisible by 2, so we can divide both by 2 to get 3/5.
Both 4 and 6 are divisible by 2, so we can divide both by 2 to get 2/3.
Thus, the simplified expression is (3/5)x + (2/3)y.
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Simplify 4x + 8x using the properties of operations.
To simplify the expression 3/10x + 1/6y + 3/10x + 3/6y, we can combine like terms.
The terms 3/10x and 3/10x have the same coefficient (3/10) and the same variable (x), so we can combine them by adding their coefficients together:
3/10x + 3/10x = (3/10 + 3/10)x = 6/10x
Similarly, the terms 1/6y and 3/6y have the same coefficient (1/6) and the same variable (y), so we can combine them:
1/6y + 3/6y = (1/6 + 3/6)y = 4/6y
Now, the expression becomes:
6/10x + 4/6y
To reduce the fractions to the lowest terms, we can simplify each fraction further.
The fraction 6/10 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:
(6/10)/(2/2) = 3/5
Similarly, the fraction 4/6 can be simplified by dividing both the numerator and denominator by their greatest common divisor, which is 2:
(4/6)/(2/2) = 2/3
Therefore, the simplified expression is:
3/5x + 2/3y
To simplify the expression 3/10x + 1/6y + 3/10x + 3/6y, we can combine like terms by grouping them together.
First, let's group the terms with 'x' and 'y' separately:
Grouping the terms with 'x':
3/10x + 3/10x = 6/10x
Grouping the terms with 'y':
1/6y + 3/6y = 4/6y
Now, let's combine the simplified expressions for 'x' and 'y':
6/10x + 4/6y
To further simplify this expression, we need to find a common denominator for the fractions involved. The least common multiple (LCM) of 10 and 6 is 30, so we can multiply the numerators and denominators by appropriate factors to obtain fractions with a common denominator of 30:
(6/10)*(3/3)x + (4/6)*(5/5)y
= 18/30x + 20/30y
Now, we can add the fractions:
18/30x + 20/30y = (18x + 20y)/30
Finally, we can further simplify this fraction by dividing both the numerator and denominator by their greatest common divisor (GCD) of 2:
(18/2x + 20/2y)/30
= (9x + 10y)/30
Therefore, the simplified form of the expression 3/10x + 1/6y + 3/10x + 3/6y is (9x + 10y)/30.