15. QUESTION

Order the following fractions from least to greatest: – 5/6; 1/6; 1/2; -1/9

Drag the fractions into the correct order, with the least number being at the top and the greatest number being on the bottom.

View Answers:  

• -1/9
• -5/6
• 1/6
• 1/2

Incorrect

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Remember that when we are dealing with negative numbers, the greater its absolute value (a number’s distance from zero), the smaller the number itself.

Step 1: Organize and sort our numbers into groups
Since none of these numbers has any whole number in front, we will sort these numbers into positive and negative numbers.

Positive Numbers: 1/6 and 1/2
Both 1/6 and 1/2 are greater than any of the negative fractions. We will compare these fractions using common denominators. (Step 2)

Negative Numbers: -5/6 and – 1/9
These two we will also compare using common denominators. (Step 3)

Step 2: Compare positive fractions using Common Denominators & Equivalent Fractions
We are comparing the fractions 1/6 and 1/2

Let’s first find the Least Common Multiple of 6 and 2:
Multiples of 6: 6, 12, 18, 24
Multiples of 2: 2, 4, 6, 8, 10

LCM: 6
Now we create equivalent fractions with 6 as the new denominator.

Start with 1/2
Since 2 × 3 = 6, we also multiply the numerator by 3

(1×3)/(2×3) = 3/6

1/6 has already the denominator of 6

Now we can compare:
3/6 is larger than 1/6 therefore 1/2 is larger than 1/6

Step 3: Compare negative fractions using Common Denominators & Equivalent Fractions
We are comparing the fractions 5/6 and 1/9

Let’s first find the Least Common Multiple of 6 and 9:
Multiples of 6: 6, 12, 18, 24
Multiples of 9: 9, 18, 27, 36, 45

LCM: 18
Now we create equivalent fractions with 18 as the new denominator.

First Up: 5/6
Since 6 × 3 = 18, we also multiply the numerator by 3

(5×3)/(6×3)= 15/18

Second Up: 1/9
Since 9 × 2 = 18, we also multiply the numerator by 2

(1×2)/(9×2) = 2/18

Now we can compare:
15/18 is larger than 2/18 therefore -5/6 is further from zero than -1/9 which means -5/6 / is less than -1/9

Step 4: Organize our fractions from least to greatest.

-5/6 is smaller than -1/9
1/6 is smaller than 1/2

The order of the fractions from least to greatest is -5/6 ; – 1/9; 1/6 ; 1/2

14. QUESTION An event coordinator has a budget of $680. If she spent $75 on balloons and $65 on invitations, what percent of her budget does she have left?

 14. QUESTION

An event coordinator has a budget of $680. If she spent $75 on balloons and $65 on invitations, what percent of her budget does she have left?

•  20.6%
•  79.4%
•  9.6%
•  86.7%

Correct

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Step 1: Calculate Part (Non-100%)
In reading the prompt, the first step is to identify the amounts needed to be added to calculate the portion of the budget that has already been spent, which represents the part (non-100%).

75 + 65 = 140

Making 140 the part (non-100%).

Step 2: Divide the Part (Non-100%) by the Whole (100%)
In order to find the percentage, we have to divide the part of the total available amount by the total amount available. In this case, the non-100% part that we have, 140, will be divided by the total amount available that represents 100%, which is 680.

140÷ 680 = 0.2058823529

We can round this off to the third-place value. Check your answer choices to see if numbers were rounded to a different place value.

So let’s look at the third place value:

0.2058823529

We look to the right and see an 8. Since an 8 is 5 or more, that means the underlined digit goes up by one so the 5 becomes a 6.

0.206

Every other number to the right of the 5 would turn to 0, and since they would have no value, we can get rid of them.

Step 3: Multiply by 100
Now that we have our decimal, we have to turn it into a percent. Remember, we turn a decimal into a percent by multiplying it by 100, which is the same as moving the decimal point two spots to the right.

0.206 × 100 = 20.6%

This tells us how much of the budget has already been spent. Finally, we have to find the percentage of what she has left.

Step 4: Subtract Budget Spent from Total Budget

The event coordinator spent 20.6% of her budget. In order to find the percentage that is left we will subtract the percentage she spent from 100%.

100% – 20.6% = 79.4%

The event coordinator has 79.4% of her budget left.

13. QUESTION An emergency room patient’s heart rate dropped 30% to 63 beats per minute. What was the patient’s heart rate prior to the drop in beats per minute?

 13. QUESTION

An emergency room patient’s heart rate dropped 30% to 63 beats per minute. What was the patient’s heart rate prior to the drop in beats per minute?

•  90
•  210
•  19
•  44

Correct

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Step 1: Interpret the Problem

Calculating the patient’s original heart rate before the drop requires some manipulation of the percentages. We need to consider that the original heart rate represents 100%. If the original heart rate represents 100% we must calculate how much of the original heart rate is remaining after a percent drop.
Given the heart rate dropped by 30%, we know,

100% – 30% = 70%

Therefore, the remaining heart rate percent is 70%.

Step 2: Turn The Percent Into a Decimal
We never use percentages in our actual math problems, so we first must turn our percentages into a decimal.
To turn a percentage into a decimal, we divide by 100, which is the same as moving the decimal point two spaces to the left.

                70% = 70.%
70.% ÷ 100 = .70

70% as a decimal is .70. Remember, zeros at the end of a number after a decimal do not add any value, so we can just write it as .70.

.70 = .7

Step 3: Determine the Original Heart Rate
We know 63= 70%, and that we are looking for the value that represents 100%. This means whatever 100% is, will be more than 63.
Once you calculate the percent paid and turn that to a decimal, we can use the rule below to calculate the original price of an item by using division.

Current Heart Rate ÷ Decimal = Original Heart Rate
63 ÷ .7 = 90

The patient’s heart rate before the drop was 90 beats per minute.

12. QUESTION Oscar ordered food delivery for his family dinner. The total of the order was $122.19. If he was charged a 7% service fee and gave a 15% tip on the bill after the service fee, what was the final total of his order?

 12. QUESTION

Oscar ordered food delivery for his family dinner. The total of the order was $122.19. If he was charged a 7% service fee and gave a 15% tip on the bill after the service fee, what was the final total of his order?

•  $144.74
•  $150.35
•  $125.86
•  $62.33

Correct

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Step 1: Interpret the Problem
In this problem we are given a monetary value that incurs a fee percentage and a tip percentage, to find a final cost amount.
We will do this in two parts. First, we will determine the fee percentage amount and add that to the initial monetary value. When calculating a percentage amount, we multiply the percentage by the given total.

Fee Percentage x Initial Total = Fee Percentage Amount

Step 2: Convert the fee percent to a decimal
We do not use actual percentages when solving math problems so we have to change 7% into a decimal.
In order to change a percent into a decimal, we divide the percent by 100, which is the same as moving the decimal two spots to the left. Since there is no decimal in 7, we assume it is to the right of the ones place, so:

7% = 7. %

Now we can slide the decimal point two spaces left. Note, there will be an empty space between the decimal and the 7 which is filled by a 0.

7.% → 0.07

7% as a decimal is 0.07

Step 3: Determine the fee percentage amount and find the first total
Now that our percent has been turned into a decimal we can multiply:

0.07 × 122.19 = 8.5533

*Note: We will not be rounding here, we round at the end of the problem.
To determine our first total, we add the percentage fee amount to our initial amount.

122.19 + 8.5533 = 130.7433

Step 4: Convert the tip percent to a decimal
We do not use actual percentages when solving math problems so we have to change 15% into a decimal.
In order to change a percent into a decimal, we divide the percent by 100, which is the same as moving the decimal two spots to the left. Since there is no decimal in 15, we assume it is to the right of the ones place, so:

15% = 15. %

Now we can slide the decimal point two spaces left.

15.% → 0.15

15% as a decimal is 0.15.

Step 5: Determine the tip percentage amount and find the final total

Remember that we are finding the tip based on the bill after the service fee, so we will use the total amount calculated in step 3 here.

Now that our percent has been turned into a decimal we can multiply it with our first total:

0.15 × 130.7433 = 19.611495

*Note: We will not be rounding here, we round at the end of the problem.
To determine our final total, we add the tip percentage amount to our first total.

130.7433 + 19.611495 = 150.354795

When a math problem has a final answer that represents a monetary quantity, the final answer must be rounded to the nearest hundredth, unless otherwise directed.

150.354795 = $150.35

The final total of Oscar’s order was $150.35.

If two even numbers are added to an odd number and the result is multiplied by an odd number, which of the following could be the result?

 9. QUESTION

If two even numbers are added to an odd number and the result is multiplied by an odd number, which of the following could be the result?

Please select all that apply.

•  62
•  175
•  110
•  78
•  297

Incorrect

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Step 1: Remember Addition Rules for Odd/Even Numbers

Firstly, we can look at the odd and even rules involving addition.

 

Odd Number + Odd Number = Even Number

Even Number + Even Number = Even Number

Odd Number + Even Number = Odd Number

 

Step 2: Try an Example Problem Or Interpret The Situation

The situation above says we are adding two even numbers to an odd number and then multiplying the result by an odd number. Let’s take this step by step.

 

Even Integer + Even Integer = Even Integer (New Sum 1)

 

Since two even integers added together got us an even integer, we can add this new even integer to the odd number. 

 

Even Integer (New Sum 1) + Odd Integer = Odd Integer(New Sum 2)

 

Step 3: Multiply the Result from Step 2 by an Odd Number

We can look at the odd and even rules involving multiplication.

 

Odd Number × Odd Number = Odd Number

Even Number × Even Number = Even Number

Odd Number × Even Number = Even Number

 

Odd Integer(New Sum 2) × Odd Integer = Odd Integer 

 

We expect the result to be an odd integer

 

Step 4: Interpret the Information

Since we know that our answer has to be an odd integer, which means a whole number ending in a 1, 3, 5, 7, or 9. Therefore, the correct answer choices that could potentially be the answer to this problem would be 175 and 193

The city’s population has grown by 1/6 in 2020, and in 2021 it has grown by another 2/5 from 2020. If in 2019 the population was 155,880 people, what has it become in 2021? 181,860

 The city’s population has grown by 1/6 in 2020, and in 2021 it has grown by another 2/5 from 2020. If in 2019 the population was 155,880 people, what has it become in 2021?

•  181,860
•  72,744
•  254,604
•  25,980

Correct

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Step 1: Determine the population growth in 2020.
We need to find what is 1/6of 155,880. This is the population growth in 2020. The key words “has grown by 1/6” point to multiplication.

155,880×(1/6) = (155,880/1)×(1/6)
= (155,880×1)/(1×6)
= (155,880)/(6)
= 155,880÷6
= 25,980

Step 2: Find the total population in 2020.
The total population in 2020 is the population in 2019 plus the population growth in 2020.

155,880 + 25,980 = 181,860

Step 3: Determine the population growth in 2021.
We need to find what is 2/5 of 181,860. Again, we find the key words “has grown by 2/5” to be sure that we should use multiplication.

181,860 × (2/5) = (181,860/1) × (2/5)
= (181,860×2)/(1×5)
= (363,720/5)
= 363,720 ÷5

         = 72,744

Step 4: Find the total population in 2021.
The total population in 2021 is the population in 2020 plus the population growth in 2021.

181,860 + 72,744 = 254,604

The city’s population in 2021 is 254,604 people.

7. QUESTION 3 5/8 × 2 2/5 =

QUESTION 7 OF 38

7. QUESTION

3 5/8 × 2 2/5 =

•  6 1/4
•  7 9/16
•  8 7/10
•  10/87

 Step 1: Convert the mixed numbers into improper fractions

3 5/8 = (3×8+5)/8
 = 29/8

2 2/5 = (2×5+2)/5
 = 12/5

3 5/8 × 2 2/5 now becomes 29/8 × 12/5

Step 2: Cross Simplify [If Applicable] and multiply
When we look at the fractions to cross simplify, we find that 12 and 8 have a common factor of 4. We can now reduce the fraction by 4.

    29/8× 12/5= 29×(12÷4)/(8÷4)×5
       = 29×3/2×5
= 87/10

Step 3: Simplify [If Possible] and convert into a mixed number
Convert the improper fraction into a mixed number.

87/10 = 87 ÷ 10
= 8 7/10