Use the properties of operations and rules for multiplying and dividing to solve
(-3)÷(3/4)×(2/7)×(- 5/26)÷(5/7)
To solve this problem, we will simplify the expression using the properties of operations and rules for multiplying and dividing.
First, we can simplify the division of (-3) by (3/4):
(-3) ÷ (3/4) = (-3) × (4/3) = -12/3 = -4
Next, we can multiply the result by (2/7):
-4 × (2/7) = (-4/1) × (2/7) = (-4 × 2) / (1 × 7) = -8/7
After that, we can multiply the result by (- 5/26):
-8/7 × (- 5/26) = (-8/7) × (5/26) = (-8 × 5) / (7 × 26) = -40/182 = -20/91
Finally, we divide the result by (5/7):
-20/91 ÷ (5/7) = (-20/91) × (7/5) = (-20 × 7) / (91 × 5) = -140/455 = -28/91
Therefore, the solution is -28/91.
To solve the expression (-3)÷(3/4)×(2/7)×(- 5/26)÷(5/7), we can simplify each operation step by step.
Step 1: Divide (-3) by (3/4).
Dividing by a fraction is equivalent to multiplying by its reciprocal. So, (-3)÷(3/4) can be rewritten as (-3) × (4/3).
Step 2: Multiply the result from Step 1 by (2/7).
Multiplying (-3) × (4/3) by (2/7) can be done by multiplying the numerators and multiplying the denominators. We get: (-3) × (4/3) × (2/7) = -24/21.
Step 3: Divide the result from Step 2 by (5/26).
Dividing by a fraction is equivalent to multiplying by its reciprocal. So, -24/21 ÷ (5/26) can be rewritten as -24/21 × (26/5).
Step 4: Multiply the result from Step 3 by (5/7).
Multiplying -24/21 × (26/5) by (5/7) can be done by multiplying the numerators and multiplying the denominators. We get: -24/21 × (26/5) × (5/7) = -24/21 × 26/1 × 1/7.
Step 5: Simplify the fraction.
Multiplying the numerators and denominators, we have -24 × 26 × 1 / 21 × 1 × 7.
Simplifying the numerator, we get -24 × 26 × 1 = -624.
Simplifying the denominator, we get 21 × 1 × 7 = 147.
So, the final result is: -624/147, which cannot be simplified further.
To solve the expression (-3)÷(3/4)×(2/7)×(-5/26)÷(5/7), we need to simplify each operation step by step using the properties of operations and rules for multiplying and dividing. Let's break it down:
Step 1: Simplify the division:
To divide a number by a fraction, we can multiply the number by the reciprocal (flipped fraction) of the fraction.
(-3)÷(3/4) simplifies to (-3) × (4/3)
Step 2: Simplify the multiplication:
To multiply fractions, we multiply the numerators together and the denominators together.
(-3) × (4/3) × (2/7) × (-5/26) ÷ (5/7) simplifies to (-3 * 4 * 2 * -5) / (3 * 7 * 26) ÷ (5/7)
Step 3: Simplify the numerator and denominator:
Multiply the values in the numerator together, and multiply the values in the denominator together.
(-3 * 4 * 2 * -5) / (3 * 7 * 26) ÷ (5/7) simplifies to 120 / 5460 ÷ (5/7)
Step 4: Simplify the division:
To divide by a fraction, we multiply by the reciprocal (flipped fraction) of the fraction.
120 / 5460 ÷ (5/7) simplifies to 120 / 5460 * (7/5)
Step 5: Simplify the multiplication:
To multiply fractions, multiply the numerators together and the denominators together.
120 / 5460 * (7/5) simplifies to (120 * 7) / (5460 * 5)
Step 6: Simplify the numerator and denominator:
Multiply the values in the numerator together, and multiply the values in the denominator together.
(120 * 7) / (5460 * 5) simplifies to 840 / 27300
Step 7: Simplify the fraction:
If possible, reduce the fraction to its simplest form. In this case, we can divide both the numerator and the denominator by 60.
840 ÷ 27300 simplifies to 14 / 455
Therefore, the expression (-3)÷(3/4)×(2/7)×(-5/26)÷(5/7) simplifies to 14/455.