Use the properties of operations and rules for multiplying and dividing to solve:
(−3)÷(34)×(27)×(−516)÷(57)
To solve the expression (-3) ÷ (34) × (27) × (-516) ÷ (57), we can apply the properties of operations and the rules for multiplying and dividing:
First, let's start with the division part of the expression: (-3) ÷ (34).
Dividing a negative number by a positive number results in a negative quotient.
So, (-3) ÷ (34) = -3/34.
Next, let's move on to the multiplication part: (-3/34) × (27) × (-516) ÷ (57).
When multiplying or dividing negative and positive numbers, we follow these rules:
- A negative number times a positive number is negative.
- A positive number times a negative number is negative.
- A negative number divided by a negative number is positive.
- A positive number divided by a negative number is negative.
Applying these rules, we can simplify the expression step by step:
(-3/34) × (27) × (-516) ÷ (57)
= (-3/34) × (-516) × (27) ÷ (57) (Rearranging the terms)
= ((-3) × (-516) × (27)) ÷ (34 × 57) (Remember that division takes precedence over multiplication)
Now, let's calculate each part separately:
(-3) × (-516) × (27) = 39,816 (Multiplying the numbers)
(34 × 57) = 1,938 (Multiplying the numbers)
Substituting these values back into the expression, we have:
39,816 ÷ 1,938
= 20.53 (Dividing the numbers)
Therefore, (-3) ÷ (34) × (27) × (-516) ÷ (57) simplifies to 20.53.
Use the properties of operations 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), we can apply the properties of operations and the rules for multiplying and dividing:
First, let's start with the division part of the expression: (-3) ÷ (3/4).
Dividing by a fraction is the same as multiplying by its reciprocal.
So, (-3) ÷ (3/4) = (-3) × (4/3) = (-12/3) = -4.
Next, let's move on to the multiplication part: -4 × (2/7) × (-5/16) ÷ (5/7).
When multiplying or dividing negative and positive numbers, we follow these rules:
- A negative number times a positive number is negative.
- A positive number times a negative number is negative.
- A negative number divided by a negative number is positive.
- A positive number divided by a negative number is negative.
Applying these rules, we can simplify the expression step by step:
-4 × (2/7) × (-5/16) ÷ (5/7)
= -4 × 2/7 × (-5/16) × 7/5 (Rearranging and multiplying the terms)
Now, let's calculate each part separately:
-4 × 2/7 × (-5/16) × 7/5
= -8/7 × (-5/16) × 7/5 (Multiplying the numbers)
= -40/112 × 7/5 (Simplifying fractions)
= -280/560 (Multiplying the numbers)
= -1/2 (Simplifying the fraction)
Therefore, (-3) ÷ (3/4) × (2/7) × (-5/16) ÷ (5/7) simplifies to -1/2.
Use the properties of operations and rules for multiplying and dividing to solve:
(8/9)×(−3/4)÷(1/9)×(−4/5)÷(3/5)
To solve the expression (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5), we can apply the properties of operations and the rules for multiplying and dividing:
First, let's start with the multiplication and division parts of the expression:
(8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5)
Multiplying fractions is done by multiplying the numerators together and the denominators together:
= (8 × -3) / (9 × 4) ÷ (1 × -4) / (9 × 5) ÷ (3 × 5)
Simplifying the numerators and denominators, we have:
= (-24) / (36) ÷ (-4) / (45) ÷ (15)
Dividing fractions is done by multiplying the first fraction by the reciprocal of the second fraction:
= (-24) / (36) × (45) / (-4) × (15)
= (-1) / (1) × (15)
= -15
Therefore, (8/9) × (-3/4) ÷ (1/9) × (-4/5) ÷ (3/5) simplifies to -15.
Use the properties of operations and rules for multiplying and dividing to solve:
(−3/5)×(5 1/6)×(7 1/2)÷(−3 1/6)×(−5/7)
To solve the expression (-3/5) × (5 1/6) × (7 1/2) ÷ (-3 1/6) × (-5/7), we can apply the properties of operations and the rules for multiplying and dividing:
Let's begin by converting the mixed numbers to improper fractions:
5 1/6 = (5 * 6 + 1) / 6 = 31/6
7 1/2 = (7 * 2 + 1) / 2 = 15/2
-3 1/6 = (-3 * 6 + 1) / 6 = -19/6
Now, let's simplify the expression using the rules for multiplication and division:
(-3/5) × (31/6) × (15/2) ÷ (-19/6) × (-5/7)
Multiplying fractions is done by multiplying the numerators together and the denominators together:
= (-3 * 31 * 15 * -5) / (5 * 6 * 2 * 19 * 7 * 6)
= 1395 / 99720
Simplifying this fraction is not possible since there are no common factors between the numerator and denominator.
Therefore, the expression (-3/5) × (5 1/6) × (7 1/2) ÷ (-3 1/6) × (-5/7) remains as 1395/99720.
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How many ounces are in 12 of 15 of a 10-ounce block of cheese?(1 point)
To find out how many ounces are in 12 of 15 of a 10-ounce block of cheese, we can set up a proportion:
Let x be the number of ounces we need to find.
12/15 = x/10
To solve for x, we can cross-multiply:
12 * 10 = 15 * x
120 = 15x
Dividing both sides by 15:
120/15 = x
x = 8
Therefore, there are 8 ounces in 12 of 15 of a 10-ounce block of cheese.
How many ounces are in 1/2 of 1/5 of a 10-ounce block of cheese?(1 point)
To find out how many ounces are in 1/2 of 1/5 of a 10-ounce block of cheese, we can multiply the fractions:
1/2 * 1/5 = 1/10
Next, we multiply the resulting fraction by 10 ounces:
1/10 * 10 = 1
Therefore, there are 1 ounce in 1/2 of 1/5 of a 10-ounce block of cheese.
A group of 9 people won 15 of a $4,500 prize. How much money did each person in the group win?(1 point)
To find out how much money each person in the group won, we can divide the total prize amount by the number of people in the group.
The total prize amount won is 15 of $4,500, which is (15/100) * $4,500 = $675.
Since there are 9 people in the group, each person won $675 divided by 9:
$675 / 9 = $75.
Therefore, each person in the group won $75.
A group of 9 people won 1/5 of a $4,500 prize. How much money did each person in the group win?(1 point)
To find out how much money each person in the group won, we can multiply the total prize amount by the fraction won by the group.
The group won 1/5 of the $4,500 prize, which is (1/5) * $4,500.
To calculate this, we multiply the fraction by the whole number:
(1/5) * $4,500 = $900.
Therefore, each person in the group won $900.
Use the properties of operations and rules for multiplying and dividing to solve:
(−2)×(1/5)÷(2/3)×(−5/6)÷(3/4)
(1 point)
Responses
23
Start Fraction 2 over 3 End Fraction
−16
negative Start Fraction 1 over 6 End Fraction
−23
negative Start Fraction 2 over 3 End Fraction
16
To solve the expression (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4), we can apply the properties of operations and the rules for multiplying and dividing:
First, let's rearrange the expression by combining multiplication and division operations:
(-2) × (1/5) × (3/2) × (-5/6) ÷ (3/4)
To simplify multiplication, we multiply the numerators together and the denominators together:
= (-2 * 1 * 3 * -5) / (5 * 2 * 6 * 3) ÷ (3/4)
= (30 / 180) ÷ (3/4)
To divide two fractions, we multiply the first fraction by the reciprocal of the second fraction:
= (30 / 180) * (4/3)
= (30 * 4) / (180 * 3)
= 120 / 540
= 2/9
Therefore, (-2) × (1/5) ÷ (2/3) × (-5/6) ÷ (3/4) simplifies to 2/9.
Multiply & Divide Rational Numbers Quick Check
2 of 52 of 5 Items
Question
Use the properties of operations and rules for multiplying and dividing to solve:
(9)÷(5/4)×(7/9)×(−5)÷(7/2)
(1 point)
Responses
1,2258
Start Fraction 1,225 over 8 End Fraction
−8
negative 8
−1,2258
negative Start Fraction 1,225 over 8 End Fraction
8
To solve the expression (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2), we can apply the properties of operations and the rules for multiplying and dividing:
First, let's rearrange the expression by combining multiplication and division operations:
(9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2)
To simplify division, we multiply the first number by the reciprocal of the second number:
= (9) * (4/5) * (7/9) * (-5) * (2/7)
Next, we can simplify the multiplication by multiplying the numerators together and the denominators together:
= (9 * 4 * 7 * -5 * 2) / (5 * 9 * 7 * 2)
= (-2520) / (630)
Simplifying further, we can divide both the numerator and denominator by their greatest common divisor, which is 630:
= (-4)
Therefore, (9) ÷ (5/4) × (7/9) × (-5) ÷ (7/2) simplifies to -4.
Multiply & Divide Rational Numbers Quick Check
3 of 53 of 5 Items
Question
Solve this multi-step problem. A runner completes 1/4 of a 5-mile race every 8 minutes. At the same pace, how far can the runner go in 16 minutes?(1 point)
Responses
18 mile
Start Fraction 1 over 8 End Fraction mile
212 miles
2 Start Fraction 1 over 2 End Fraction miles
160 miles
160 miles
110 mile
Start Fraction 1 over 10 End Fraction mile
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page 13 of 13
To solve this multi-step problem, we can use the given information to determine the runner's pace and then calculate how far the runner can go in 16 minutes.
The runner completes 1/4 of a 5-mile race every 8 minutes.
First, let's determine the runner's pace:
1/4 of a 5-mile race is (1/4) * 5 = 5/4 miles.
The runner covers this distance in 8 minutes.
Next, let's find the runner's pace per minute:
To find the pace per minute, we divide the distance covered (5/4 miles) by the time taken (8 minutes):
(5/4) miles / 8 minutes = 5/32 miles per minute.
Now, let's calculate how far the runner can go in 16 minutes at the same pace:
To find the distance, we multiply the pace per minute (5/32 miles per minute) by the time (16 minutes):
(5/32) miles per minute * 16 minutes = 80/32 miles = 2.5 miles.
Therefore, at the same pace, the runner can go 2.5 miles in 16 minutes.