multiply the equation by a power of 10 to write an equivalent equation with integer coefficients:
1. 4.15x+3.01=10.9x+1.29
2. 1.596y-3.08=0.9y
An integer is a rational number that does not have a fraction. Your numbers all have fractions. 4.15 = 4 15/100, 1.596 = 1 596/1000, etc. If you multiply these numbers by a form of ten that is large enough, they will change into integers:
4.15 x 100 = 415 no fraction, so an integer!
If you multiply one part of an addition or subtraction equation, you must multiply ALL parts of the equation.
Therefore:
4.15(100)x +3.01(100) = 10.9(100)x + 1.29(100)
Don't forget to simplify when you are done multiplying :-)
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To write an equivalent equation with integer coefficients, you need to eliminate the decimal numbers by multiplying the entire equation by a power of 10. Here's how you can do it for each of the given equations:
1. 4.15x + 3.01 = 10.9x + 1.29
To eliminate the decimals, you need to consider the least common multiple (LCM) of the denominators of the decimal numbers. In this case, the decimals 4.15 and 3.01 have a common denominator of 100. So, you can multiply the entire equation by 100:
100 * (4.15x + 3.01) = 100 * (10.9x + 1.29)
This gives you:
415x + 301 = 1090x + 129
Now the equation has integer coefficients.
2. 1.596y - 3.08 = 0.9y
In this case, the decimals 1.596 and 3.08 have a common denominator of 1000. So, you can multiply the entire equation by 1000:
1000 * (1.596y - 3.08) = 1000 * (0.9y)
This gives you:
1596y - 3080 = 900y
Now the equation has integer coefficients.