To cancel is to simplify an expression using sums totaling 0 and common factors.^{[1]} Cancelation is the process of canceling.
Step | Expression | Explanation |
---|---|---|
1 | In order to get x by itself on the left side of the equation, the 3 will be canceled. | |
2 | The 3 will be canceled. Create a zero sum by subtracting 3 from both sides. This uses the subtractive property of equality. | |
3 | Group the numeric expressions. 3-3 is the zero sum on the left, and 5-3=2 on the right. The associative property of addition allows one to change the order of the terms, if necessary. | |
4 | Simplify the numeric expressions using the substitution property of equality. Use the additive property of zero to change x+0 to x. | |
5 | The solution to the equation is x=2. | |
Table 1 |
Step | Expression | Explanation |
---|---|---|
1 | In order to get x by itself on the left side of the equation, the y on the left side of the equation will be canceled. | |
2 | The y will be canceled. Create a zero sum by subtracting y from both sides. This uses the subtractive property of equality. | |
3 | Group the numeric expressions. y-y is the zero sum on the left, and 3y-y=2y on the right. The associative property of addition allows one to change the order of the terms, if necessary. | |
4 | Simplify the numeric expressions using the substitution property of equality. Use the additive property of zero to change x+0 to x. | |
5 | The solution set of the equation is x=2y. | |
Table 2 |
Step | Expression | Explanation |
---|---|---|
1 | The fraction 4x/6 will be simplified using cancellation. | |
2 | Factor the numerator and denominator of the fraction. 4x=2·2·x and 6 = 2·3. | |
3 | Find the common factors of the numerator and denominator. The common factor is 2. Use the associative property of multiplication to group the common factors together. | |
4 | Since anything divided by itself is 1, use the substitution property of equality to substitute 1 for 2/2. | |
5 | Use the multiplicative property of 1 to eliminate the 1 from the expression. | |
6 | The fraction 4x/6 can be simplified to 2x/3. | |
Table 3 |
Step | Expression | Explanation |
---|---|---|
1 | The fraction 6xy/10x will be simplified using cancellation. | |
2 | Factor the numerator and denominator of the fraction. 6xy=2·3·x·y and 10x=2·5·x. | |
3 | Find the common factors of the numerator and denominator. The common factor is 2x. Use the associative property of multiplication to group the common factors together. | |
4 | Since anything divided by itself is 1, use the substitution property of equality to substitute 1 for 2x/2x. | |
5 | Use the multiplicative property of 1 to eliminate the 1 from the expression. | |
6 | The fraction 6xy/10x can be simplified to 3y/5, assuming x is not 0. | |
Table 3 |
# | A | B | C | D |
E | F | G | H | I |
J | K | L | M | N |
O | P | Q | R | S |
T | U | V | W | X |
Y | Z |
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