Simplify.
7 2/3 + −5 1/4
To simplify the expression 7 2/3 - 5 1/4, we first need to convert the mixed numbers into improper fractions.
7 2/3 = (7*3 + 2)/3 = 23/3
5 1/4 = (5*4 + 1)/4 = 21/4
Now, we can substitute these improper fractions into the expression:
23/3 - 21/4
To subtract fractions, we need to have a common denominator. The least common multiple (LCM) of 3 and 4 is 12.
Multiplying the first fraction by 4/4 and the second fraction by 3/3, we get:
(23/3)*(4/4) - (21/4)*(3/3)
= 92/12 - 63/12
Now, we can subtract the fractions:
(92 - 63)/12
= 29/12
The simplified expression is 29/12.
what is 29/12 as a mixed number?
To convert the improper fraction 29/12 to a mixed number, we need to divide the numerator (29) by the denominator (12).
29 ÷ 12 = 2 remainder 5
The quotient (whole number part) is 2, and the remainder is 5. So the mixed number representation of 29/12 is 2 5/12.
Consider this expression:
1/4
− 0.5 + 1/2
− 0.25 + 3/5
+ 0.4
To simplify this expression, we can add up all the terms:
1/4 - 0.5 + 1/2 - 0.25 + 3/5 + 0.4
First, we need to find a common denominator for the fractions to add or subtract them. The least common denominator (LCD) in this case is 20.
Converting each fraction to have a denominator of 20:
1/4 = (1*5)/(4*5) = 5/20
1/2 = (1*10)/(2*10) = 10/20
3/5 = (3*4)/(5*4) = 12/20
Now, we substitute the fractions back into the expression:
5/20 - 0.5 + 10/20 - 0.25 + 12/20 + 0.4
Combining the like terms:
(5/20 + 10/20 + 12/20) - 0.5 - 0.25 + 0.4
= 27/20 - 0.50 - 0.25 + 0.4
To perform the subtraction and addition:
27/20 - 0.50 - 0.25 + 0.4
= 27/20 - 11/20 + 8/20
= (27 - 11 + 8)/20
= 24/20
Simplifying the fraction:
24/20 = (24/4) / (20/4) = 6/5
So, the simplified expression is 6/5.
Consider this expression:
1/4
− 0.5 + 1/2
− 0.25 + 3/5
+ 0.4
You are asked to find the sum by using fractions. Which expression could you use?
Responses
To find the sum of the given expression using fractions, we can use the expression:
(1/4) + (1/2) + (3/5) + (0.4)
This expression adds up all the given terms using fractions.
Consider this expression as a mixed fraction:
1/4
− 0.5 + 1/2
− 0.25 + 3/5
+ 0.4
To express the given expression as a mixed fraction, we need to perform the calculations and simplify the result.
(1/4) - 0.5 + (1/2) - 0.25 + (3/5) + 0.4
First, let's convert the decimal numbers to fractions:
0.5 = 5/10 = 1/2 (by dividing the numerator and denominator by 5)
0.25 = 25/100 = 1/4 (by dividing the numerator and denominator by 25)
0.4 = 4/10 = 2/5 (by dividing the numerator and denominator by 2)
Now we can substitute these fractions back into the expression:
(1/4) - (1/2) + (1/2) - (1/4) + (3/5) + (2/5)
The fractions with the same denominator can be combined:
(1/4 - 1/4) + (1/2 + 1/2) + (3/5 + 2/5)
These fractions simplify to:
0 + 1 + 5/5
Simplifying further:
1 + 5/5 = 1 + 1 = 2
So, the given expression as a mixed fraction is 2.
Consider this expression:
1/4
− 0.5 + 1/2
− 0.25 + 3/5
+ 0.4
Find the sum.
Responses
A 0
B 1
C 1 1/2
D 1/2
1 2