To multiply fractions, you multiply the numerators (top numbers) together and then multiply the denominators (bottom numbers) together.
For 3/10 ⋅ 4/9, the product is (3⋅4)/(10⋅9), which simplifies to 12/90.
To further simplify the fraction, you can divide both the numerator and denominator by their greatest common divisor, which is 6.
So, the simplified product of 3/10 ⋅ 4/9 is 2/15.
Multiply.
3/10⋅4/9
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Simplify using the distributive property.
7/6(30−18)
7/6(30−18)
To simplify using the distributive property, you need to multiply each term inside the parentheses by the fraction.
So, 7/6(30 - 18) = 7/6 * 30 - 7/6 * 18.
To multiply a fraction by a whole number, you multiply the numerator by the whole number.
7/6 * 30 = (7 * 30)/6 = 210/6.
Similarly,
7/6 * 18 = (7 * 18)/6 = 126/6.
Now you can subtract the two fractions:
210/6 - 126/6 = (210 - 126)/6 = 84/6.
Finally, you can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 6.
84/6 = (6 * 14)/(6 * 1) = 14/1.
Therefore, the simplified expression is 14.
So, 7/6(30 - 18) = 7/6 * 30 - 7/6 * 18.
To multiply a fraction by a whole number, you multiply the numerator by the whole number.
7/6 * 30 = (7 * 30)/6 = 210/6.
Similarly,
7/6 * 18 = (7 * 18)/6 = 126/6.
Now you can subtract the two fractions:
210/6 - 126/6 = (210 - 126)/6 = 84/6.
Finally, you can simplify the fraction by dividing both the numerator and denominator by their greatest common divisor, which is 6.
84/6 = (6 * 14)/(6 * 1) = 14/1.
Therefore, the simplified expression is 14.
Multiply.
9/4⋅14
9/4⋅14
To multiply a fraction by a whole number, you simply multiply the numerator of the fraction by the whole number.
So, 9/4 ⋅ 14 = (9 ⋅ 14)/4.
Multiplying 9 by 14 gives us 126:
(9 ⋅ 14)/4 = 126/4.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
126/4 = (2 ⋅ 63)/(2 ⋅ 2).
Canceling out the common factor of 2:
(2 ⋅ 63)/(2 ⋅ 2) = 63/2.
Therefore, the product of 9/4 ⋅ 14 is 63/2.
So, 9/4 ⋅ 14 = (9 ⋅ 14)/4.
Multiplying 9 by 14 gives us 126:
(9 ⋅ 14)/4 = 126/4.
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
126/4 = (2 ⋅ 63)/(2 ⋅ 2).
Canceling out the common factor of 2:
(2 ⋅ 63)/(2 ⋅ 2) = 63/2.
Therefore, the product of 9/4 ⋅ 14 is 63/2.
Simplify using the distributive property.
1.2(20+0.5)
1.2(20+0.5)
To simplify using the distributive property, you need to multiply each term inside the parentheses by the number outside the parentheses.
So, 1.2(20 + 0.5) = 1.2 * 20 + 1.2 * 0.5.
Multiplying 1.2 by 20 gives us 24:
1.2 * 20 = 24.
Multiplying 1.2 by 0.5 gives us 0.6:
1.2 * 0.5 = 0.6.
Now, you can add the two products together:
24 + 0.6 = 24.6.
Therefore, the simplified expression is 24.6.
So, 1.2(20 + 0.5) = 1.2 * 20 + 1.2 * 0.5.
Multiplying 1.2 by 20 gives us 24:
1.2 * 20 = 24.
Multiplying 1.2 by 0.5 gives us 0.6:
1.2 * 0.5 = 0.6.
Now, you can add the two products together:
24 + 0.6 = 24.6.
Therefore, the simplified expression is 24.6.
What is the sum of 2 3/4 and −2 3/4 ?
To find the sum of two mixed numbers, you first need to add the whole numbers and then add the fractions separately.
For the whole numbers, 2 and -2 sum to 0.
For the fractions, you add the numerators together if the denominators are the same. In this case, the denominators are both 4, so we add the numerators, which gives us 3 + (-3) = 0.
Therefore, the sum of 2 3/4 and -2 3/4 is 0 + 0 = 0.
For the whole numbers, 2 and -2 sum to 0.
For the fractions, you add the numerators together if the denominators are the same. In this case, the denominators are both 4, so we add the numerators, which gives us 3 + (-3) = 0.
Therefore, the sum of 2 3/4 and -2 3/4 is 0 + 0 = 0.
Solve 14−2x=28 using the replacement set {−21, −7, 7} .
To solve the equation 14 - 2x = 28, we can substitute each value in the replacement set {-21, -7, 7} for x and see which values satisfy the equation.
1. Substitute x = -21:
14 - 2(-21) = 14 + 42 = 56, which is not equal to 28.
2. Substitute x = -7:
14 - 2(-7) = 14 + 14 = 28, which equals 28.
Therefore, x = -7 satisfies the equation.
3. Substitute x = 7:
14 - 2(7) = 14 - 14 = 0, which is not equal to 28.
So, the only value in the replacement set that satisfies the equation is x = -7.
1. Substitute x = -21:
14 - 2(-21) = 14 + 42 = 56, which is not equal to 28.
2. Substitute x = -7:
14 - 2(-7) = 14 + 14 = 28, which equals 28.
Therefore, x = -7 satisfies the equation.
3. Substitute x = 7:
14 - 2(7) = 14 - 14 = 0, which is not equal to 28.
So, the only value in the replacement set that satisfies the equation is x = -7.
What is the value of x in the equation x + 5.1 = 0?
To solve for x in the equation x + 5.1 = 0, you need to isolate x on one side of the equation.
To do this, you can subtract 5.1 from both sides of the equation:
x + 5.1 - 5.1 = 0 - 5.1.
This simplifies to:
x = -5.1
Therefore, the value of x in the equation x + 5.1 = 0 is -5.1.
To do this, you can subtract 5.1 from both sides of the equation:
x + 5.1 - 5.1 = 0 - 5.1.
This simplifies to:
x = -5.1
Therefore, the value of x in the equation x + 5.1 = 0 is -5.1.
What is the coefficient in the expression −5x+8?
The coefficient in the expression -5x + 8 is -5.
Simplify.
5/7x+2/7y−2−1/7x+7
5/7x+2/7y−2−1/7x+7
To simplify the expression, we combine like terms and perform operations according to the rules of arithmetic:
5/7x - 1/7x + 2/7y - 2 + 7
(5/7 - 1/7)x + 2/7y + 5
(4/7)x + 2/7y + 5
Therefore, the simplified expression is (4/7)x + (2/7)y + 5.
5/7x - 1/7x + 2/7y - 2 + 7
(5/7 - 1/7)x + 2/7y + 5
(4/7)x + 2/7y + 5
Therefore, the simplified expression is (4/7)x + (2/7)y + 5.
What is the constant in the expression 3x−7+6y ?
Responses
Responses
The constant in the expression 3x - 7 + 6y is -7.
Divide.
−112÷8
−112÷8
To divide -112 by 8, we perform the division:
-112 ÷ 8 = -14
Therefore, -112 divided by 8 is equal to -14.
-112 ÷ 8 = -14
Therefore, -112 divided by 8 is equal to -14.
1 answer