Use the properties of operations and rules for multiplying and dividing to solve: (−3/5)×(5/16)×(7/12)÷(−3/16)×(−5/7)
To solve this expression, we can follow the order of operations and the rules for multiplying and dividing fractions.
Step 1: Multiply all the fractions together from left to right.
(-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
Multiplying the first two fractions:
((-3) × (5))/((5) × (16)) × (7/12) ÷ (-3/16) × (-5/7)
(-15)/(80) × (7/12) ÷ (-3/16) × (-5/7)
Multiplying the result by the next fraction:
((-15) × (7))/((80) × (12)) ÷ (-3/16) × (-5/7)
(-105)/(960) ÷ (-3/16) × (-5/7)
Multiplying the last two fractions together:
(-105)/(960) ÷ ((-3) × (16))/((1) × (7))
(-105)/(960) ÷ (-48)/(7)
Step 2: Invert the dividing fraction and multiply.
(-105)/(960) × (7)/( -48)
-735/- 46080
Step 3: Simplify the fraction.
Divide both the numerator and denominator by the Greatest Common Divisor (GCD) of 735 and 46080, which is 15.
(-735 ÷ 15)/(-46080 ÷ 15)
(-49)/(3072)
So, (-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7) simplifies to (-49)/(3072).
To solve this problem, we will use the rules of multiplying and dividing fractions:
1. To multiply fractions, multiply the numerators together and multiply the denominators together.
2. To divide fractions, multiply the first fraction by the reciprocal of the second fraction.
Let's simplify the expression step by step:
Start with (-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7)
Step 1: Multiply the numerators and denominators together:
(-3 × 5 × 7) / (5 × 16 × 12) ÷ (-3 × -5) / (16 × 7)
Step 2: Simplify the numerator:
(-105) / (5 × 16 × 12) ÷ (15) / (16 × 7)
Step 3: Simplify the denominator:
(-105) / (960) ÷ (15) / (112)
Step 4: Divide by multiplying by the reciprocal:
(-105) / (960) × (112) / (15)
Step 5: Simplify the expression:
(-105 × 112) / (960 × 15)
Step 6: Simplify the numerator and denominator:
-11760 / 14400
Step 7: Reduce the fraction:
-49 / 60
Therefore, (-3/5) × (5/16) × (7/12) ÷ (-3/16) × (-5/7) simplifies to -49/60.