Explanation:
When a fraction has a numerator larger than its denominator, the total value is more than one whole. Fractions
like 3/3,5/5, and 7/7 are all equal to one whole. Fractions with numerators less than their denominators represent
values that are less than one whole. 5/3,7/5, and 3/2 are all improper fractions representing total values larger than one whole.
Explanation:
90/3 = 30, and 30 + 6 = 36.
Explanation:
Total no. of balls = 10, number of yellow balls = 2, so, 2/10 X 100 = 20%
Answer:
The correct answer is D: 7/3.
Explanation:
2 1/3 is equivalent to 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3 + 1/3.
This represents seven groups of 1/3, or as an improper fraction, 7/3
Explanation:
Each element of the series is a multiple of 3 less than the previous element. Starting with 116, the next element
is 1 × 3 less, or 116 – (1 × 3) = 113. The next element is 2 × 3 less, or 113 – (2 × 3) = 107. The next element is 3 × 3
less, or 107 – (3 × 3) = 98. So the next element will be 4 × 3 less, or 98 – (4 × 3) = 86.
Explanation:
Area of the square = 12 x 12 = 144cm. Let x be the width so 2x will be
the length of rectangle. The area will be 2 x 2 and the perimeter will be
2(2x + x) = 6x. According to the condition 2 x 2 = 144 then x = 8.48 cm.
The perimeter will be 6 X 8.48 = 50.88
= 51 cm.
Explanation:
The correct answer is A: 1 2/3.
5/3 can be thought of as 1/3+1/3+1/3+1/3+1/3.
We can combine three groups of 1/3 in order to create 3/3, or one whole.
There are still two thirds left, so our mixed number is 1 2/3
Explanation:
The correct answer is c: 1 1/2 quarts of water.
If Kristina drinks 1/4 quart of water for every mile, she is essentially drinking 1/4+1/4+1/4+1/4+1/4+1/4 quarts of water.
The sum of this list of fractions is 1 2/4 or in simplest form, 1 1/2.
Explanation:
5000 X 4% = 200
5000 + 200 = $5200
Explanation:
Proportions are ratios that are equal to one another. We can solve
for the missing variable by using cross multiplication to develop
an equation.
8/3 x x/9 >br>
8x9 = x x 3
Simplify.
72 = 3x:
Divide both sides of the equation by 3.
72/3 = 3x/3
Solve.
x = 24
Explanation:
In order to solve this problem, we need to discuss probabilities. A
probability is generally defined as the chances or likelihood of an
event occurring. It is calculated by identifying two components:
the event and the sample space. The event is defined as the
favorable outcome or success that we wish to observe. On the
other hand, the sample space is defined as the set of all possible
outcomes for the event. Mathematically we calculate probabilities
by dividing the event by the sample space:
P _ event: particular phenomenon we Wish to observe
/sample space: total number of possible outcomes
Let's use a simple example: the rolling of a die. We want to know
the probability of rolling a one. We know that the sample space is
six because there are six sides or outcomes to the die. Also, we
know that there is only a single side with a value of one; therefore,
P = 1/6
Now, let's convert this into a percentage:
1
— = 0.1666
6
0.1666 x 100% = 16.6%
Explanation:
In order to solve this problem we need isolate the variable on the
left side 0 the equation. We will do this by performing the reverse
of the operations that were done to the variable. It is important to
note that what is done to one side of the equation needs to be
done on the other.
Let's start by writing the equation.
x
— + 12 = 22
4
Subtract 12 from both sides of the equation.
x
—+12—12 = 22—12
x
— = 10
4
Multiply both sides of the equation by 4.
x
— x 4 = 10 x 4
4
Solve.
x = 40
Explanation:
Perimeters can be calculated by adding together the side lengths
of a polygon. A square has four sides that are all the same length,
therefore, we can write the following formula to solve for the
perimeter.
P = s + s + s + s
We can rewrite this equation as the following:
P = 4s
In these equations the variable, .s, represents side length.
Substitute the known side length and solve.
P = 4 x 5
P = 20
Explanation:
In algebra an inequality is a relationship that holds through
different values of a variable. An inequality is considered to be
solved when the variable is isolated to one side of the
inequality. We will do this by performing the reverse of the
operations that were done to the variable. It is important to note
that what is done to one side of the inequality needs to be done
on the other.
Let's start by writing the inequality.
10x + 44 > 84
Subtract 44 from both sides of the inequality.
10x + 44—44 > 84—44
10x > 40
Divide each side of the inequality by 10.
10x/10 > 40/10
Solve.
x > 4
The variable is greater than four.
Explanation:
Start by finding out how much Jack makes. Since he makes
15% less than Sarah, we can write the following to find Jack's
weekly salary:
1500 — 0.15(1500) = 1275
Jack must make $1275 each week. Now, add together their
salaries to find the sum.
1500 + 1275 = 2775
Explanation:
Start by finding how much weight Steve lost after the first month.
Since he lost 1/12 of his starting weight of 240, he must have lost
20 pounds.
This means that at the end of his first month, he weighed
220 pounds.
Since he lost 10% of his remaining weight in the second month,
he must have lost 22 pounds from his 220 pounds.
Thus, Sam must weigh 198 pounds now.
Explanation:
5x + 12 = 7x + 2
Start by subtracting both sides by 5x.
12 = 2x + 2
Next, subtract both sides by 2.
2x = 10
Finally, divide both sides by 2.
x = 5
Explanation:
Start by listing out multiples of 3:
3 : 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39,42
Next, list out multiples of 13:
13 : 13,26,39, 52
Now, find the smallest number that is found in both lists. In this
case, the least common multiple must be 39.
Explanation:
Since the question asks for the product, you will need to multiply
the two fractions. Recall that in multiplying two fractions, you will
multiply the numerators together and then multiply the
denominators together.
5/6 x 3/8 = 15/48 >br>
Next, reduce the fraction.
15/48 = 5/16
Explanation:
Start by finding out how many books the 20 full shelves can hold
by multiplying it by the number of books held per shelf.
20 X 325 = 6500
Next, find out how many books are held by the shelf that is not
completely full.
325 X 0.8 = 260
Now, add the two together to find how many books total are in
the library.
6500 + 260 = 6760
Explanation:
Start by figuring out how much Rachel can earn in each week by
multiplying her hourly rate by the number of hours worked each
week.
Earning each week = 12.50 X 40 = 500
Now, divide the amount she needs to earn by the amount earned
each week to find how many weeks she will need to work to earn
that amount.
3000/500 = 6
Ruby must work for 6 weeks in order to earn enough for the car.
Explanation:
Start by finding out the total square footage of wallpaper needed.
Find the area of one wall. Recall that in order to find the area of a
rectangle, you must multiply the length by the width.
Area of One Wall = 15 x 12 = 180
Since we have four identical walls,
Total Area of Walls = 4 x 180 = 720
Now divide this by the amount of square feet covered by each roll
of wallpaper to find how many rolls are needed.
Rolls of wallpaper needed = 720/60 = 12
Explanation:
In the order of operations, in the absence of grouping symbols,
multiplication takes precedence over addition and subtraction.
Multiply 15 by 8 first:
15 X 8 — 12 + 25
= 120 — 12 + 25
Addition and subtraction have equal precedence and are worked
in Ieft-to-right order. Subtract 120 and 12 next:
= 108 + 25
Now add:
= 133
Explanation:
To find the median of a group of scores, first, arrange the scores
from least to greatest:
{82, 83, {\color{Red} 84, 87}, 90, 99}
There are an even number of scores, so the median is the mean of
the two scores that fall in the middle, which are noted in red
above. Add the scores and divide by two:
84 + 87/ 2 = 171/2 = 85.5
Explanation:
The sample in this scenario is selected from the population by
choosing obects that occur at regular intervals. That makes this
an example of systematic sampling.
