Answer with Explanation:
1) Multiply: 3 x 3/4 =
Before we multiply, we must make the whole number 3 a improper fraction before we can multiply the fractions.
3 -> 3/1 as improper fraction
3/1 * 3/4 =
Then, we just multiply the numerators and denominators of both fractions.
3/1 * 3/4 = 9/4
9/4 is an improper fraction. It needs to be an mixed number as a proper answer.
9/4 = 2 1/4
Answer to Question I:
2 ¼
2) Divide 2 3/4 ÷ 1 1/4
Before we do anything else, we must make both fractions improper so we can do our operations easily.
2 ¾ as improper is: 11/4
1 ¼ as improper is: 5/4
Now the fractions has been made to improper, the divisor's must be in it's reciprocal form and the operation used is multiplication.
11/4 * 4/5 (4/5 is the reciprocal of 5/4)
Now, the following fractions can be just multiplied.
11/4 * 4/5 = 44/20
44/20 is an improper fraction. It needs to be a mixed number for a proper answer.
44/20 = 2 4/20 -> 2 1/5 (4/20 was turned into lowest form.)
Answer to Question II:
2 ⅕
3) Subtract 1 ¼ - ⅓
Before we do anything else, notice 1/4 is too small to be subtracted to 1/3. For that, we must make 1/4 bigger to 1/3 by giving in the value of the whole number with it, 1.
Adding in 1 and 1/4 together would give: 5/4.
5/4 - 1/3 = N.
Now our fractions is applicable for subtraction, we must subtract now.
To subtract dissimilar fractions, we must find it's LCD (Least Common Denominator) so we can subtract our fractions without any trouble.
The LCD of 4 and 3 is 12 according to the calculation below.
LCD(4,3) = 3 -> (3,4)
= 4 -> (1,4)
= -> (1,1)
LCD(4,3) = 3*4 = 12.
Now we have the LCD of both fractions, we also need to convert the numerator related to its denominator.
[tex] \frac{5}{4} - \frac{1}{3} = \frac{15 - 4 }{12} = \frac{11}{12} [/tex]
To convert the numerator of both fractions, divide the LCD to the original denominator of a fraction then multiply it to the numerator.
After converting both fractions, we get the fraction "15-4/12". We simply subtract our fraction to get 11/12.
Answer to Question III:
[tex] \frac{11}{12} [/tex]
4) Add 1 ⅖ + ⅓
Before we add, let's first ignore the whole 1 in the mixed 1 ⅖. We will add the 1 later.
We have the fractions: ⅖ + ⅓.
To add dissimilar fractions, we first need to find the LCD of the fractions ⅖ and ⅓.
The LCD of 5 and 3 is 15 according to the calculation below.
LCD(5,3) = (3) => (3,5)
= (5) => (1,5)
= => (1,1)
LCD (5,3) = 3 x 5 = 15
Now we have the LCD of both fractions, we also need to convert the numerator related to its denominator.
[tex] \frac{2}{5} + \frac{1}{3} = \frac{6 + 5}{15} = \frac{11}{15} [/tex]
To convert the numerator of both fractions, divide the LCD to the original denominator of a fraction then multiply it to the numerator.
After converting both fractions, we get to the fraction "6+5/15". We simply add the numerator to get 11/15.
Then this is where our 1 from earlier comes in.
We add 1 to the fraction 11/15 to get 1 11/15.
Answer to Question IV:
[tex]1 \frac{11}{15} [/tex]
End of answer. Hope it helps. Correct me if there's wrong with the statements.
