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