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Why does the method of dividing fractions work?
This is related to the fact that dividing by a number is the same as multiplying with the number's reciprocal.
Why do you have to switch the numerator and denominator when dividing fractions?
This is because dividing by a number is the same as multiplying by its reciprocal.
Why do people say that dividing is the same as multiplying by the reciprocal?
Dividing by a number is the same as multiplying by its reciprocal because of the fundamental property of fractions. When you divide by a number, you can rewrite it as multiplying by one over that number. For example, dividing by 2 (or 2/1) can be expressed as multiplying by 1/2, which effectively gives the same result. This relationship simplifies calculations and is a foundational concept in arithmetic and algebra.
Why is multiplying or dividing the numerator and the denominator by the same number the same as multiplying or dividing the fraction by 1?
Because multiplying or dividing them by the same NON-ZERO number does not alter their ratio.
How do you change 123.456 into a fraction?
123.456 is changed into fraction by multiplying and dividing it by a number such that both denominator and numerator don't contain decimal. Multiplying and dividing by 100, we get 123.456 as 123456/100.
Details about multiplying and dividing rational number?
Details about multiplying and dividing rational number involves modeling multiplying fractions by dividing squares to equal segments and then overlap the squares.
Why does the method of dividing fractions work?
This is related to the fact that dividing by a number is the same as multiplying with the number's reciprocal.
Why do you have to switch the numerator and denominator when dividing fractions?
This is because dividing by a number is the same as multiplying by its reciprocal.
How is dividing fractions similar to multiplying fractions?
It is similar because when you divide fractions you are technically multiplying the second number's reciprocal. (Turning the fraction the other way around)
Why is the number larger when you divide fractions?
Because it's the same as multiplying the inverse. Dividing something by one third is the same as multiplying it by three. The number will get larger.
Why is multiplying or dividing the numerator and denominator by the same nonzero number the same as multiplying or dividing the fraction by 1?
because of mathematical equivalence: it doesn't change the result
When dividing fractions it is most helpful to change a mixed number into a?
improper fraction
When dividing fractions what is most helpful to change a mixed number?
an improper fraction
When dividing fractions it is most helpful to change a mixed number into an?
improper fraction
How is multiplying fractions by a whole number is different from adding adding and subtracting fractions with like denominators?
Adding and subtracting fractions can ONLY be done if the denominators are the same; then the calculation is done by adding or subtracting the numerators. Multiplying (and dividing) fractions does not require the denominators to be the same. To divide by a fraction the divisor is inverted (the original numerator becomes the new denominator and the original denominator becomes the new numerator) and then the fractions are multiplied. Multiplying fractions is achieved by multiplying the numerators together AND multiplying the denominators together. A whole number is the same as a fraction with the whole number as the numerator and a denominator of 1, so when multiplying by a whole number the denominator is multiplied by 1 (leaving it the same) and the is multiplication is effectively just multiplying the numerator by the whole number.
How is dividing fractions similar to multipying fractions?
Dividing anything by a fraction is equivalent to multiplying the same number by the reciprocal of the fraction. Thus, x / (p/q) = x * (q/p) where x is any number, and p and q are non-zero integers.
Why is multiplying or dividing the numerator and the denominator by the same number the same as multiplying or dividing the fraction by 1?
Because multiplying or dividing them by the same NON-ZERO number does not alter their ratio.
