Simplify : 9 3/4 ÷ ( 2 1/2 + { 4 1/3:- 3 ( 1 1/2 ÷ 1 3/4 } step by step please
Answers
Answer:
the answer is 7 77/106
Step-by-step explanation:
Here is the step-by-step explanation:
Conversion a mixed number 4 1/
3
to a improper fraction: 4 1/3 = 4 1/
3
= 4 · 3 + 1/
3
= 12 + 1/
3
= 13/
3
To find new numerator:
a) Multiply the whole number 4 by the denominator 3. Whole number 4 equally 4 * 3/
3
= 12/
3
b) Add the answer from previous step 12 to the numerator 1. New numerator is 12 + 1 = 13
c) Write a previous answer (new numerator 13) over the denominator 3.
Four and one third is thirteen thirds
Divide: 13/
3
: (-3) = 13/
3
· -1/
3
= 13 · (-1)/
3 · 3
= -13/
9
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of -3/
1
is 1/
-3
) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - thirteen thirds divided by minus three = minus thirteen ninths.
Conversion a mixed number 1 1/
2
to a improper fraction: 1 1/2 = 1 1/
2
= 1 · 2 + 1/
2
= 2 + 1/
2
= 3/
2
To find new numerator:
a) Multiply the whole number 1 by the denominator 2. Whole number 1 equally 1 * 2/
2
= 2/
2
b) Add the answer from previous step 2 to the numerator 1. New numerator is 2 + 1 = 3
c) Write a previous answer (new numerator 3) over the denominator 2.
One and one half is three halfs
Conversion a mixed number 1 3/
4
to a improper fraction: 1 3/4 = 1 3/
4
= 1 · 4 + 3/
4
= 4 + 3/
4
= 7/
4
To find new numerator:
a) Multiply the whole number 1 by the denominator 4. Whole number 1 equally 1 * 4/
4
= 4/
4
b) Add the answer from previous step 4 to the numerator 3. New numerator is 4 + 3 = 7
c) Write a previous answer (new numerator 7) over the denominator 4.
One and three quarters is seven quarters
Divide: 3/
2
: 7/
4
= 3/
2
· 4/
7
= 3 · 4/
2 · 7
= 12/
14
= 2 · 6/
2 · 7
= 6/
7
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 7/
4
is 4/
7
) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 2 gives 6/
7
.
In words - three halfs divided by seven quarters = six sevenths.
Multiple: the result of step No. 2 * the result of step No. 5 = -13/
9
* 6/
7
= -13 · 6/
9 · 7
= -78/
63
= -26 · 3/
21 · 3
= -26/
21
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(-78, 63) = 3. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - minus thirteen ninths multiplied by six sevenths = minus twenty-six twenty-firsts.
Conversion a mixed number 2 1/
2
to a improper fraction: 2 1/2 = 2 1/
2
= 2 · 2 + 1/
2
= 4 + 1/
2
= 5/
2
To find new numerator:
a) Multiply the whole number 2 by the denominator 2. Whole number 2 equally 2 * 2/
2
= 4/
2
b) Add the answer from previous step 4 to the numerator 1. New numerator is 4 + 1 = 5
c) Write a previous answer (new numerator 5) over the denominator 2.
Two and one half is five halfs
Add: 5/
2
+ the result of step No. 6 = 5/
2
+ (-26/
21
) = 5 · 21/
2 · 21
+ (-26) · 2/
21 · 2
= 105/
42
+ (-52/
42
) = 105 + (-52)/
42
= 53/
42
For adding, subtracting, and comparing fractions, it is suitable to adjust both fractions to a common (equal, identical) denominator. The common denominator you can calculate as the least common multiple of both denominators - LCM(2, 21) = 42. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 2 × 21 = 42. In the next intermediate step, the fraction result cannot be further simplified by canceling.
In words - five halfs plus minus twenty-six twenty-firsts = fifty-three forty-seconds.
Conversion a mixed number 9 3/
4
to a improper fraction: 9 3/4 = 9 3/
4
= 9 · 4 + 3/
4
= 36 + 3/
4
= 39/
4
To find new numerator:
a) Multiply the whole number 9 by the denominator 4. Whole number 9 equally 9 * 4/
4
= 36/
4
b) Add the answer from previous step 36 to the numerator 3. New numerator is 36 + 3 = 39
c) Write a previous answer (new numerator 39) over the denominator 4.
Nine and three quarters is thirty-nine quarters
Divide: 39/
4
: the result of step No. 8 = 39/
4
: 53/
42
= 39/
4
· 42/
53
= 39 · 42/
4 · 53
= 1638/
212
= 2 · 819/
2 · 106
= 819/
106
Dividing two fractions is the same as multiplying the first fraction by the reciprocal value of the second fraction. The first sub-step is to find the reciprocal (reverse the numerator and denominator, reciprocal of 53/
42
is 42/
53
) of the second fraction. Next, multiply the two numerators. Then, multiply the two denominators. In the next intermediate step, , cancel by a common factor of 2 gives 819/
106
.
In words - thirty-nine quarters divided by fifty-three forty-seconds = eight hundred nineteen one-hundred sixths.