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How Do You Find a Missing Factor in a Monomial Equation?

Find the monomial to multiply 3x3y by to get 48x7y3

Summary

  1. We want to figure out what to multiply 3x3y by to get 48x7y3
  2. Divide 48x7y3 by 3x3y
  3. 48÷3=16
  4. x7÷x3=x7-3=x4
  5. y3÷y=y3-1=y2
  6. 16x4y2 is the missing factor
  7. Check our result by multiplying it by 3x3y

Notes

    1. We want to figure out what to multiply 3x3y by to get 48x7y3
    2. So to do that, we need to divide 48x7y3 by 3x3y
    1. The left hand side is 48x7y3
    2. On the right we know we have 3x3y times some missing factor
    1. Think of it kind of like a multiplication equation, where the missing factor is the variable
    2. To solve a multiplication equation, we would divide both sides by what we know to get the variable by itself
    3. So here we divide 48x7y3 by 3x3y
    1. 48x7y3 is the dividend, so it goes under the division sign
    2. 3x3y is the divisor, so it goes out in front of the division sign
    1. 48÷3=16
    2. So the 16 goes up top above the 48
    1. Remember, when we're dividing powers that have the same base we can just subtract their exponents
    2. So here we can subtract 7 and 3 to get the exponent for the result
    3. x7÷x3=x7-3=x4
    1. x7÷x3=x7-3=x4
    1. Here we can subtract 3 and 1 to get the exponent for the result
    2. Remember, a number or variable without an exponent has a hidden exponent of 1
    3. y3÷y=y3-1=y2
    1. y3÷y=y3-1=y2
    1. The result we got was 16x4y2
    1. This is the number we need to multiply 3x3y by to get 48x7y3
    1. We can check our answer by multiplying it by 3x3y to see if we get 48x7y3
    1. We can check our answer by multiplying it by 3x3y to see if we get 48x7y3
    1. We can check our answer by multiplying it by 3x3y to see if we get 48x7y3
    1. Multiply the numbers first
    2. 3•16=48
    1. Remember, when we're multiplying two powers with the same base we can just add the exponents
    2. So here we can add 3 and 4 to get the exponent for the result
    3. x3•x4=x3+4=x7
    1. Here we can add 3 and 4 to get the exponent for the result
    2. x3•x4=x3+4=x7
    1. Here we can add 1 and 2 to get the exponent for the result
    2. Remember, a number or variable without an exponent has a hidden exponent of 1
    3. y•y2=y1+2=y3
    1. So that must mean our result was correct!
    1. 16x4y2 is what we need to multiply 3x3y by to get 48x7y3