Is confidence of operation and rules for multiplying and dividing to solve -3÷3/4×2/7×-5/16÷5/7
To solve the expression -3÷3/4×2/7×-5/16÷5/7, you need to follow the order of operations (also known as PEMDAS or BODMAS) and apply the rules for multiplying and dividing fractions.
First, let's calculate the division operation (-3 ÷ 3/4):
-3 ÷ 3/4 = -3 * 4/3 = -12/3 = -4
Next, let's perform the multiplication operations:
-4 × 2/7 × -5/16 ÷ 5/7
-4 × (2/7) × (-5/16) ÷ (5/7)
Now, cancel out the common factors and simplify the expression:
= -4 × 1/1 × 1/8 ÷ 1/1
= -4/8
= -1/2
Therefore, the solution to the given expression is -1/2.
To solve the expression -3 ÷ 3/4 × 2/7 × -5/16 ÷ 5/7, you need to follow the order of operations and apply the rules for multiplying and dividing fractions. Here are the steps:
Step 1: Simplify each fraction if possible:
-3 can be written as -3/1.
3/4 is already in its simplest form.
2/7 is already in its simplest form.
-5/16 is already in its simplest form.
5/7 is already in its simplest form.
Step 2: Perform the divisions from left to right:
-3/1 ÷ 3/4 = (-3/1) × (4/3) = -12/3 = -4.
Step 3: Perform the multiplications from left to right:
-4 × 2/7 = (-4) × (2/7) = -8/7.
Step 4: Perform the next division:
-8/7 ÷ 5/16 = (-8/7) × (16/5) = -128/35.
So, the result of the expression -3 ÷ 3/4 × 2/7 × -5/16 ÷ 5/7 is -128/35.
To solve the expression -3 ÷ 3/4 × 2/7 × -5/16 ÷ 5/7, you need to apply the rules of multiplying and dividing fractions while also considering the order of operations.
First, let's break down the expression step by step:
Step 1: Simplify the division
Start by simplifying the division expressions separately. In this case, we have two divisions: -3 ÷ 3/4 and -5/16 ÷ 5/7.
-3 ÷ 3/4 = -3 × 4/3 = -12/3 = -4
Similarly,
-5/16 ÷ 5/7 = -5/16 × 7/5 = -35/80
Step 2: Multiply the simplified expressions
Now that we have simplified the division expressions, we can move on to the multiplication.
Multiply the results obtained in Step 1:
(-4) × ( -35/80) = 140/80
Step 3: Simplify the fraction
To simplify the fraction obtained in Step 2, you can find the greatest common divisor (GCD) of the numerator and denominator.
The GCD of 140 and 80 is 20, so divide numerator and denominator by 20:
140/80 = 7/4
Therefore, the result of -3 ÷ 3/4 × 2/7 × -5/16 ÷ 5/7 is 7/4.
To summarize the steps:
-3 ÷ 3/4 × 2/7 × -5/16 ÷ 5/7
= -3 × 4/3 × 2/7 × (-5/16) × 7/5 (simplifying division separately)
= -12/3 × 2/7 × (-5/16) × 7/5 (multiplying simplified expressions)
= 140/80 (multiplying fractions)
= 7/4 (simplifying the fraction)
Remember to follow the order of operations (multiplication and division from left to right) and simplify the fractions as needed.