Explain an error problem in each of the following:
a) 13/35=1/5, 27/73 = 2/3, 16/64 = ¼
b) 4/5+2/3=6/8, 2/5+3/4=5/9, 7/8+1/3=8/11
c) 8 3/8-6 ¼=2 2/4, 5 3/8-2 2/3=3 1/5, 2 2/7-1 1/3=1 ¼
d) 2/3*3=6/9, ¼*6=6/24, 4/5*2=8/10
This has been posted elsewhere, and is answered there.
a) In each of the given equations, there is an error in the calculation of the fractions. The fractions on the left sides of the equations are not equal to the fractions on the right sides. This error occurred because the fractions were not simplified properly before comparing them. To solve this problem, we need to simplify the fractions and then compare them.
For example,
- 13/35 should be simplified to 1/5, so the equation is correct.
- 27/73 can be simplified to 9/24, not 2/3, so the equation is incorrect.
- 16/64 can be simplified to 1/4, not 1/4, so the equation is correct.
b) In each of the given equations, there is an error in the addition of the fractions. The sum on the left side of the equation is not equal to the sum on the right side. This error occurred because the fractions were not added correctly. To solve this problem, we need to find a common denominator for the fractions and then add them.
For example,
- 4/5 + 2/3 can be simplified by finding a common denominator, which is 15. So, the equation is incorrect.
- 2/5 + 3/4 can be simplified by finding a common denominator, which is 20. So, the equation is incorrect.
- 7/8 + 1/3 can be simplified by finding a common denominator, which is 24. So, the equation is incorrect.
c) In each of the given equations, there is an error in the subtraction of the mixed numbers. The difference on the left side of the equation is not equal to the difference on the right side. This error occurred because the mixed numbers were not subtracted correctly. To solve this problem, we need to regroup the mixed numbers and subtract them.
For example,
- 8 3/8 - 6 1/4 can be simplified by regrouping and finding a common denominator, which is 8. So, the equation is incorrect.
- 5 3/8 - 2 2/3 can be simplified by regrouping and finding a common denominator, which is 24. So, the equation is incorrect.
- 2 2/7 - 1 1/3 can be simplified by regrouping and finding a common denominator, which is 21. So, the equation is incorrect.
d) In each of the given equations, there is an error in the multiplication of the fractions. The product on the left side of the equation is not equal to the product on the right side. This error occurred because the fractions were not multiplied correctly. To solve this problem, we need to multiply the numerators and denominators separately.
For example,
- 2/3 * 3 can be simplified by multiplying the numerator and the whole number separately. So, the equation is incorrect.
- 1/4 * 6 can be simplified by multiplying the numerator and the whole number separately. So, the equation is incorrect.
- 4/5 * 2 can be simplified by multiplying the numerator and the whole number separately. So, the equation is incorrect.