Evaluate the numerical expression.
1/2
− (−3/4
)
To evaluate the numerical expression 1/2 - (-3/4), we can simplify it step by step:
First, let's distribute the negative sign to (-3/4):
1/2 + 3/4
To add fractions, we need to have a common denominator. The least common multiple of 2 and 4 is 4. Therefore, we convert both fractions to have a denominator of 4:
1/2 = 2/4
3/4 = 3/4
Now we can add the fractions:
2/4 + 3/4 = 5/4
The final simplified expression is 5/4.
what is 5/4 as a mixed number?
To convert the improper fraction 5/4 into a mixed number, we divide the numerator (5) by the denominator (4):
5 ÷ 4 = 1 remainder 1
The quotient (whole number part) is 1, and the remainder is 1. Therefore, the mixed number equivalent of 5/4 is 1 1/4.
Evaluate this expression.
42.86 − 23.42
To evaluate the numerical expression 42.86 - 23.42, we can subtract the decimal numbers:
42.86 - 23.42 = 19.44
Therefore, the value of the expression 42.86 - 23.42 is 19.44.
Determine the value of the expression –5.45 + 4.12 –8.66.
To determine the value of the expression –5.45 + 4.12 – 8.66, let's simplify it step by step:
–5.45 + 4.12 - 8.66 = -5.45 + 4.12 - 8.66
When subtracting or adding decimals, it is important to line up the decimal points:
-5.45
+ 4.12
- 8.66
_______
-9.99
Therefore, the value of the expression –5.45 + 4.12 – 8.66 is -9.99.
Simplify.
7.829 − 3.21
To simplify the expression 7.829 - 3.21, we subtract the decimal numbers:
7.829 - 3.21 = 4.619
Therefore, the simplified expression is 4.619.
Divide and simplify.
−1/6
÷ 2/9
To divide the fractions -1/6 divided by 2/9, we will multiply by the reciprocal of the second fraction.
Reciprocal of 2/9 is 9/2:
-1/6 ÷ 2/9 = -1/6 x 9/2
To multiply fractions, we multiply the numerators and denominators:
(-1 x 9) / (6 x 2) = -9/12
To simplify the fraction -9/12, we can divide both the numerator and denominator by their greatest common divisor, which is 3:
(-9 ÷ 3) / (12 ÷ 3) = -3/4
Therefore, the simplified expression is -3/4.
5.36 x -3.1
To multiply the decimal numbers 5.36 and -3.1, we can multiply them as if they were whole numbers and then consider the sign:
5.36 x -3.1 = -16.616
Therefore, the product of 5.36 and -3.1 is -16.616.
−70.55 ÷ (0.5) =
To divide the decimal number -70.55 by 0.5, we can divide the absolute values and consider the sign:
|-70.55| ÷ |0.5| = 141.1
Since the dividend is negative and the divisor is positive, the quotient will be negative:
-70.55 ÷ 0.5 = -141.1
Therefore, -70.55 divided by 0.5 is -141.1.
Divide:
11.1÷3
Responses
To divide the decimal number 11.1 by 3, we divide as we would with whole numbers and then consider the decimal places:
11.1 ÷ 3 = 3.7
Therefore, 11.1 divided by 3 is 3.7.
-4.32 × -1.25
To multiply the decimal numbers -4.32 and -1.25, we can multiply them as if they were whole numbers and then consider the sign:
(-4.32) × (-1.25) = 5.4
Therefore, the product of -4.32 and -1.25 is 5.4.
4 1/3÷ −1 1/5
Find the quotient above.
To find the quotient of 4 1/3 divided by -1 1/5, we need to first convert the mixed numbers into improper fractions.
4 1/3 can be written as (4 * 3 + 1)/3 = 13/3
-1 1/5 can be written as (-1 * 5 + 1)/5 = -6/5
Now we can divide the two fractions:
(13/3) ÷ (-6/5)
To divide fractions, we multiply the first fraction by the reciprocal of the second fraction:
(13/3) * (5/-6) = (13 * 5) / (3 * -6)
Multiplying the numerators and denominators:
65 / -18
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor, which is 1:
65 / -18 = -65/18
Therefore, the quotient of 4 1/3 divided by -1 1/5 is -65/18.
what is -65/18 as a mixed number?
To convert the improper fraction -65/18 into a mixed number, we divide the numerator (-65) by the denominator (18):
-65 ÷ 18 = -3 remainder -11
The quotient (whole number part) is -3, and the remainder is -11. Therefore, the mixed number equivalent of -65/18 is -3 11/18.
Divide and simplify.
−2/17 ÷ −1/2
To divide the fractions -2/17 divided by -1/2, we will multiply by the reciprocal of the second fraction.
Reciprocal of -1/2 is -2/1:
-2/17 ÷ -1/2 = -2/17 x -2/1
To multiply fractions, we multiply the numerators and denominators:
(-2 x -2) / (17 x 1) = 4/17
Therefore, the simplified expression is 4/17.
(2.5)(−1.3) =
To find the product of 2.5 and -1.3, we simply multiply them together:
2.5 × -1.3 = -3.25
Therefore, the product of 2.5 and -1.3 is -3.25.
−0.539 ÷ (−0.11) =
To divide -0.539 by -0.11, we can divide the absolute values and consider the sign:
|-0.539| ÷ |-0.11|
This division can be rewritten as a multiplication by the reciprocal:
-0.539 × (-1/0.11)
To simplify this expression, we multiply the numerators and denominators:
(-0.539) × (-1/0.11) = 0.539 × (1/0.11)
Now, we can further simplify by dividing 0.539 by 0.11:
0.539 ÷ 0.11 = 4.9
Since the dividend and divisor are both negative, the quotient will be positive:
-0.539 ÷ -0.11 = 4.9
Therefore, -0.539 divided by -0.11 is 4.9.
At West High School, 2/5
of the students play a sport. Of the students who play a sport, 1/4
play football. What fraction of the students at West High School play football?
Responses
To find the fraction of students at West High School who play football, we need to multiply the fractions for each group.
First, we multiply the fraction of students who play a sport (2/5) by the fraction of those who play football (1/4):
(2/5) * (1/4) = 2/20
To simplify the fraction further, we can divide both the numerator and denominator by their greatest common divisor, which is 2:
(2/5) * (1/4) = 1/10
Therefore, 1/10 of the students at West High School play football.
Landry took a survey of all the sixth-grade students at Irvine Park Middle School and discovered that 35% of sixth-graders play sports.
What fraction of sixth-graders play sports?
To determine the fraction of sixth-graders who play sports, we need to convert the percentage to a fraction.
If 35% of sixth-graders play sports, that means 35 out of 100 sixth-graders play sports.
To express this as a fraction, we can write 35/100.
However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5:
35/100 = (35 ÷ 5) / (100 ÷ 5) = 7/20
Therefore, the fraction of sixth-graders who play sports is 7/20.
2 of 102 of 10 Items
01:21
Question
Which set of numbers are equivalent?
Responses
A 0.4, 4%, 4/10
B 0.062, 62%, 62/1000
C 0.80, 80%, 4/5
D 0.84, 84%, 10/84
The set of numbers that is equivalent is C: 0.80, 80%, 4/5.
To show the equivalence:
- 0.80 is the decimal representation of 80% (80/100) and is equivalent to 4/5 (both fractions reduced to their simplest form).
Daniel ate 0.55 of a candy bar. Which fraction represents the part of the candy bar that Daniel ate?
To represent the fraction of the candy bar that Daniel ate, we can express 0.55 as a fraction.
Since 0.55 is a decimal, we can write it as 55/100. However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 5:
55/100 = (55 ÷ 5) / (100 ÷ 5) = 11/20
Therefore, the fraction that represents the part of the candy bar that Daniel ate is 11/20.
The Frisco Falcons Soccer Team won 3/5
of their soccer games.
What percentage is equivalent to the fraction of games the Falcons won?
To determine the percentage equivalent to the fraction of games the Frisco Falcons Soccer Team won, we can convert the fraction to a percentage.
The fraction 3/5 can be expressed as a decimal by dividing the numerator (3) by the denominator (5):
3 ÷ 5 = 0.6
To convert this decimal to a percentage, we can multiply it by 100:
0.6 × 100 = 60
Therefore, the percentage equivalent to the fraction 3/5 is 60%.
Elizabeth read 19/20
of her book.
What percentage is equivalent to the fraction of the book that Elizabeth read?
To determine the percentage equivalent to the fraction of the book that Elizabeth read, we can convert the fraction to a percentage.
The fraction 19/20 can be expressed as a decimal by dividing the numerator (19) by the denominator (20):
19 ÷ 20 = 0.95
To convert this decimal to a percentage, we can multiply it by 100:
0.95 × 100 = 95
Therefore, the percentage equivalent to the fraction 19/20 is 95%.
In Jamie's class, 1/5
of the students are boys. What percent of the students in Jamie’s class are boys?
To find the percentage of students in Jamie's class that are boys, we can convert the fraction to a percentage.
The fraction 1/5 can be expressed as a decimal by dividing the numerator (1) by the denominator (5):
1 ÷ 5 = 0.2
To convert this decimal to a percentage, we can multiply it by 100:
0.2 × 100 = 20
Therefore, 20% of the students in Jamie's class are boys.
Which set of numbers are equivalent?
Responses
A 3%, 0.3, 3/100
B 20%, 0.2, 2/10
C 40%, 0.4, 4/100
D 50%, 0.05, 5/10
The set of numbers that are equivalent is A: 3%, 0.3, 3/100.
To show the equivalence:
- 3% is the percentage representation of 3/100 (both fractions representing 3 out of 100 parts).
- 0.3 is the decimal representation of 3/10 (both fractions having a numerator of 3 and a denominator of 10).
Reynold has 3/10
of the race left to run.
Which value is equivalent to 3/10
?
To find the equivalent value for 3/10, we need to express it in a different form, such as a decimal or a percentage.
3/10 as a decimal is 0.3.
Therefore, the value equivalent to 3/10 is 0.3.
Which set of numbers are equivalent?
Responses
A 33/10
, 0.33, 33%
B 1/47
, 0.47, 47%
C 1/4
, 0.25, 25%
D 1/200
, 0.20, 20%
The set of numbers that are equivalent is C: 1/4, 0.25, 25%.
To show the equivalence:
- 1/4 is a fraction representing one out of four equal parts.
- 0.25 is the decimal representation of 1/4 (both fractions having a numerator of 1 and a denominator of 4).
- 25% is the percentage representation of 1/4 (both fractions representing one-fourth or 25 out of 100 parts).
Wade walked 0.58 mile to school.
Which value is equivalent to 0.58?
Responses
To identify the equivalent value for 0.58, we can express it as a fraction.
0.58 can be written as 58/100.
However, we can simplify this fraction by dividing both the numerator and denominator by their greatest common divisor, which is 2:
58/100 = (58 ÷ 2) / (100 ÷ 2) = 29/50
Therefore, the value equivalent to 0.58 is 29/50.
Wade walked 0.58 mile to school.
Which value is equivalent to 0.58?
Responses
A 5.8%
B 5/8
C 58/50
D 58%
To determine the equivalent value for 0.58, we can analyze the given options.
A. 5.8% - This represents 5.8 out of 100, but it is not equivalent to 0.58.
B. 5/8 - This fraction does not equal 0.58.
C. 58/50 - This fraction can be further simplified and evaluated.
D. 58% - This represents 58 out of 100, but it is not equivalent to 0.58.
By further simplifying option C, we have:
58/50 = (58 ÷ 2) / (50 ÷ 2) = 29/25
Thus, the value that is equivalent to 0.58 is option C: 58/50 or 29/25.