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Answers
Answer:
3/4 * 12/6 / 3/2 + 12/3 * 1/2 - 12/6 = 1/
1
= 1
Step-by-step explanation:
Multiple: 3/
4
* 12/
6
= 3 · 12/
4 · 6
= 36/
24
= 3 · 12/
2 · 12
= 3/
2
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(36, 24) = 12. In the next intermediate step, , cancel by a common factor of 12 gives 3/
2
.
In words - three quarters multiplied by twelve sixths = three halfs.
Divide: the result of step No. 1 : 3/
2
= 3/
2
: 3/
2
= 3/
2
· 2/
3
= 3 · 2/
2 · 3
= 6/
6
= 6 · 1/
6 · 1
= 1
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/
2
is 2/
3
) 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 6 gives 1/
1
.
In words - three halfs divided by three halfs = one.
Multiple: 12/
3
* 1/
2
= 12 · 1/
3 · 2
= 12/
6
= 2 · 6/
1 · 6
= 2
Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(12, 6) = 6. In the next intermediate step, , cancel by a common factor of 6 gives 2/
1
.
In words - twelve thirds multiplied by one half = two.
Add: the result of step No. 2 + the result of step No. 3 = 1 + 2 = 3
Subtract: the result of step No. 4 - 12/
6
= 3 - 12/
6
= 3/
1
- 12/
6
= 3 · 6/
1 · 6
- 12/
6
= 18/
6
- 12/
6
= 18 - 12/
6
= 6/
6
= 6 · 1/
6 · 1
= 1
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(1, 6) = 6. In practice, it is enough to find the common denominator (not necessarily the lowest) by multiplying the denominators: 1 × 6 = 6. In the next intermediate step, , cancel by a common factor of 6 gives 1/
1
.
In words - three minus twelve sixths = one.