Evaluate the expression shown below and write your answer as a fraction in simplest form.
start fraction, 7, divided by, 8, end fraction, minus, one tenth
8
7
−
10
1
To evaluate the expression, we need to first divide 7 by 8, and then subtract one tenth.
7 divided by 8 can be written as 7/8.
So, the expression becomes:
7/8 - 1/10
To subtract the fractions, we need to find a common denominator. In this case, the common denominator is 40.
Converting both fractions to have a denominator of 40, we get:
(35/40) - (4/40)
Now, we can subtract the fractions:
(35 - 4)/40 = 31/40
Therefore, the expression 7/8 - 1/10 evaluates to 31/40 in simplest form.
Perform the operation below. Express your answer as a mixed number in simplest form.
4, one half, plus, 3, start fraction, 3, divided by, 5, end fraction
4
2
1
+3
5
3
To perform the operation, we first need to add the whole numbers and the fractions separately.
Adding the whole numbers, we have:
4 + 3 = 7
Next, we add the fractions separately.
First, we need to find a common denominator for 1/2 and 3/5. In this case, the least common denominator (LCD) is 10.
Converting 1/2 and 3/5 to have a denominator of 10, we get:
5/10 + 6/10
Now, we can add the fractions:
5/10 + 6/10 = 11/10
Next, we simplify the fraction by dividing the numerator (11) by the denominator (10). The quotient is the whole number, and the remainder is the numerator of the proper fraction.
11 divided by 10 equals 1 with a remainder of 1.
So, the fraction 11/10 can be written as the mixed number 1 and 1/10.
Combining the whole numbers and the fractions, we have:
7 + 1 and 1/10 = 8 and 1/10
Therefore, the expression 4 1/2 + 3 3/5 evaluates to 8 1/10 as a mixed number in simplest form.
Gabriel plans to repaint some classroom bookcases. All of the bookcases are the same size and each requires start fraction, 3, divided by, 4, end fraction
4
3
gallon of paint. If he's going to paint 6 bookcases, how many gallons of paint does he need?
Answer
Attempt 1 out of 2
To solve, we'll need to
, because we know the SIZE of the groups and the
, but we don't know the
.
To find how many gallons of paint Gabriel needs, we can multiply the number of bookcases by the amount of paint needed for each bookcase.
First, we need to find the total amount of paint needed for one bookcase:
3/4 gallon of paint for each bookcase
Next, we multiply the amount of paint needed for one bookcase by the number of bookcases:
(3/4) * 6
To multiply fractions, we simply multiply the numerators together and the denominators together:
(3 * 6)/(4 * 1) = 18/4
Next, we simplify the fraction by dividing the numerator (18) by the denominator (4). The quotient is the whole number, and the remainder is the numerator of the proper fraction.
18 divided by 4 equals 4 with a remainder of 2.
So, the fraction 18/4 can be written as the mixed number 4 and 2/4.
However, we can simplify the fraction 2/4 by dividing the numerator and the denominator by their greatest common factor, which is 2:
2/4 divided by 2/2 equals 1/2.
Therefore, the expression (3/4) * 6 evaluates to 4 1/2 gallons of paint.
Gabriel needs 4 1/2 gallons of paint to paint 6 bookcases.
Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
one quarter, times, start fraction, 2, divided by, 3, end fraction
4
1
×
3
2
To perform the operation, we need to multiply one quarter by 2/3.
Multiplying fractions is done by multiplying the numerators together and the denominators together:
(1 * 2) / (4 * 3)
Simplifying the numerator and denominator:
2/12
Since both the numerator and denominator are divisible by 2, we can simplify further:
1/6
Therefore, one quarter times 2/3 equals 1/6 as a simplified fraction.
Perform the operation and reduce the answer fully. Make sure to express your answer as a simplified fraction.
one half, divided by, start fraction, 3, divided by, 4, end fraction
2
1
÷
4
3
To perform the operation, we need to divide one half by 3/4.
Dividing fractions is done by multiplying the first fraction by the reciprocal of the second fraction:
(1/2) * (4/3)
Multiplying the numerators and denominators:
(1 * 4) / (2 * 3)
Simplifying the numerator and denominator:
4/6
Since both the numerator and denominator are divisible by 2, we can simplify further:
2/3
Therefore, one half divided by 3/4 equals 2/3 as a simplified fraction.
Simplify to a single power of 5:
5, to the power 5 , times, 5, squared
5
5
×5
2
To simplify the expression, we need to multiply 5 raised to the power of 5 by 5 squared.
First, let's calculate 5 raised to the power of 5:
5^5 = 5 * 5 * 5 * 5 * 5 = 3125
Next, let's calculate 5 squared:
5^2 = 5 * 5 = 25
Now, we can multiply 3125 by 25:
3125 * 25 = 78125
Therefore, 5 to the power of 5 times 5 squared simplifies to 78125.
can you tell me what the answer is Simplify to a single power of 5:
5, to the power 5 , times, 5, squared
5
5
×5
2
To simplify the expression, we can add the exponents when multiplying the same base:
5^5 × 5^2 = 5^(5+2) = 5^7.
Therefore, the expression simplifies to 5^7.
can you tell me what the answer is Simplify to a single power of 3:
start fraction, 3, to the power 5 , divided by, 3, cubed, end fraction
3
3
3
5
To simplify the expression, we subtract the exponents when dividing the same base:
3^5 ÷ 3^3 = 3^(5-3) = 3^2.
Therefore, the expression simplifies to 3^2.
Write the number 5, point, 8, times, 10, to the power 55.8×10
5
in standard form.
To write the number in standard form, we need to multiply 5.8 by 10 to the power of 55.
5.8 * 10^55
Since 10 to the power of 1 is simply 10, we can rewrite this as:
5.8 * 10^(10 * 5 + 5)
5.8 * 10^55
So, the number 5.8 times 10 to the power of 55 in standard form is 5.8 × 10^55.
Write the number 6, point, 2, times, 10, squared6.2×10
2
in standard form.
To write the number in standard form, we need to multiply 6.2 by 10 squared.
6.2 * 10^2
Since 10 squared is 100, we can rewrite this as:
6.2 * 100
Multiplying 6.2 by 100, we get:
620
So, the number 6.2 times 10 squared in standard form is 620.
Write the number 5, times, 10, to the power minus 65×10
−6
in standard form.
To write the number in standard form, we need to multiply 5 by 10 to the power of -6.
5 * 10^(-6)
Since 10 to the power of -6 is equivalent to 1 divided by 10 to the power of 6, we can rewrite this as:
5 * 1/(10^6)
Calculating 10 to the power of 6, we get:
10^6 = 1,000,000
So, the expression simplifies to:
5 * 1/1,000,000
Dividing 5 by 1,000,000 gives us:
0.000005
Therefore, the number 5 times 10 to the power of -6 in standard form is 0.000005.
Write the number 97,000 in scientific notation.
times, 10×10
To write the number 97,000 in scientific notation, we first need to determine the decimal place.
Starting from the last non-zero digit in the number, we count 5 digits to the left to place the decimal point.
So, 97,000 can be written as 9.7 × 10^4 in scientific notation.
Write the number 0.000022 in scientific notation.
times, 10×10
To write the number 0.000022 in scientific notation, we need to determine the decimal place.
Starting from the first non-zero digit in the number, we count 5 digits to the right to place the decimal point.
So, 0.000022 can be written as 2.2 × 10^(-5) in scientific notation.
Evaluate. Express your answer in scientific notation.
3, point, 3, times, 10, to the power 6 , plus, 4, point, 2, times, 10, to the power 5
3.3×10
6
+4.2×10
5
times, 10×10
To evaluate the expression, we need to add 3.3 times 10 to the power 6 to 4.2 times 10 to the power 5.
First, let's add the numbers without considering the exponent:
3.3 + 4.2 = 7.5
Next, we determine the exponent.
Since both terms have different exponents, we need to adjust them so they have the same exponent.
The exponent of 10 for 3.3 times 10 to the power 6 is 6.
The exponent of 10 for 4.2 times 10 to the power 5 is 5.
To have the same exponent, we can adjust the second term:
4.2 times 10 to the power 5 can be rewritten as 0.42 times 10 to the power 6 (since multiplying by 10 increases the exponent by 1).
Now, we can add the adjusted terms:
7.5 + 0.42 = 7.92
Finally, we put the result in scientific notation:
7.92 times 10 to the power 6.
Therefore, the expression simplifies to 7.92 times 10 to the power 6 in scientific notation.
its wrong
Apologies for the mistake. Let's reevaluate the expression correctly.
To evaluate the expression, we need to add 3.3 times 10 to the power 6 to 4.2 times 10 to the power 5.
First, let's convert both numbers to scientific notation:
3.3 times 10^6 can be expressed as 3.3e6.
4.2 times 10^5 can be expressed as 4.2e5.
Next, we can add the numbers:
3.3e6 + 4.2e5 = 3.3e6 + 0.42e6 = 3.72e6.
Therefore, the expression simplifies to 3.72 times 10 to the power 6 in scientific notation.
Evaluate. Express your answer in scientific notation.
9, point, 9, 6, times, 10, to the power 7 , minus, 9, point, 7, 7, times, 10, to the power 7
9.96×10
7
−9.77×10
7
times, 10×10
To evaluate the expression, we need to subtract 9.96 times 10 to the power 7 from 9.77 times 10 to the power 7.
First, let's convert both numbers to regular decimal form:
9.96 times 10^7 = 99600000
9.77 times 10^7 = 97700000
Next, we can subtract the numbers:
97700000 - 99600000 = -1900000
Lastly, we convert the result back into scientific notation:
-1.90 times 10 to the power 6.
Therefore, the expression simplifies to -1.90 times 10 to the power 6 in scientific notation.
Evaluate. Express your answer in scientific notation.
9, point, 8, times, 10, cubed, minus, 9, point, 2, times, 10, cubed
9.8×10
3
−9.2×10
3
To evaluate the expression, we need to subtract 9.8 times 10 cubed from 9.2 times 10 cubed.
Let's start by converting both numbers to regular decimal form:
9.8 times 10^3 = 9800
9.2 times 10^3 = 9200
Next, we can subtract the numbers:
9200 - 9800 = -600
Lastly, we convert the result back into scientific notation:
-6 times 10 to the power 2.
Therefore, the expression simplifies to -6 times 10 to the power 2 in scientific notation.
What is the product of 5, point, 5, times, 10, cubed5.5×10
3
and 6, point, 3, times, 10, to the power 46.3×10
4
expressed in scientific notation?
To find the product of 5.5 times 10 cubed and 6.3 times 10 to the power 4, we need to multiply the numbers and add the exponents:
(5.5 * 6.3) * (10^3 * 10^4)
Multiplying the decimal numbers:
5.5 * 6.3 = 34.65
Adding the exponents:
10^3 * 10^4 = 10^(3+4) = 10^7
Finally, we can express the result in scientific notation:
34.65 times 10 to the power 7.
Therefore, the product of 5.5 times 10 cubed and 6.3 times 10 to the power 4 expressed in scientific notation is 34.65 times 10 to the power 7.
What is the product of 8, point, 2, times, 10, squared8.2×10
2
and 3, point, 4, times, 10, to the power 53.4×10
5
expressed in scientific notation?
To find the product of 8.2 times 10 squared and 3.4 times 10 to the power 5, we need to multiply the numbers and add the exponents:
(8.2 * 3.4) * (10^2 * 10^5)
Multiplying the decimal numbers:
8.2 * 3.4 = 27.88
Adding the exponents:
10^2 * 10^5 = 10^(2+5) = 10^7
Finally, we can express the result in scientific notation:
27.88 times 10 to the power 7.
Therefore, the product of 8.2 times 10 squared and 3.4 times 10 to the power 5 expressed in scientific notation is 27.88 times 10 to the power 7.
what is the answerWhat is the product of 8, point, 2, times, 10, squared8.2×10
2
and 3, point, 4, times, 10, to the power 53.4×10
5
expressed in scientific notation?
To find the product of 8.2 times 10 squared and 3.4 times 10 to the power 5, we need to multiply the decimal parts and add the exponents:
8.2 * 3.4 = 27.88
The exponents can be added since the bases are both 10:
10^2 * 10^5 = 10^(2+5) = 10^7
Finally, we can express the result in scientific notation:
27.88 times 10 to the power 7.
Therefore, the product of 8.2 times 10 squared and 3.4 times 10 to the power 5 expressed in scientific notation is 2.788 x 10^8.
what is the answer What is the quotient of 8, point, 8, 3, 2, times, 10, to the power 68.832×10
6
and 9, point, 6, times, 10, squared9.6×10
2
expressed in scientific notation?
To find the quotient of 68.832 times 10 to the power 6 and 9.6 times 10 squared, we need to divide the decimal parts and subtract the exponents:
68.832 / 9.
What is the quotient of 3, point, 1, 6, 8, times, 10, to the power 93.168×10
9
and 4, point, 8, times, 10, squared4.8×10
2
expressed in scientific notation?
What is the quotient of 3, point, 4, 9, 6, times, 10, to the power 93.496×10
9
and 3, point, 8, times, 10, to the power 53.8×10
5
expressed in scientific notation?
What is the quotient of 7, point, 5, 8, 4, times, 10, to the power 67.584×10
6
and 7, point, 9, times, 10, squared7.9×10
2
expressed in scientific notation?
what is the answer What is the quotient of 5, point, 6, 8, 8, times, 10, to the power 95.688×10
9
and 7, point, 9, times, 10, squared7.9×10
2
expressed in scientific notation?