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What statement about multiplying fractions and mixed numbers is not true?
A common misconception is that multiplying fractions always results in a smaller number. While it is true that multiplying two proper fractions (less than one) results in a smaller fraction, multiplying a fraction by a mixed number can yield a larger product if the mixed number is greater than one. Therefore, the statement "Multiplying fractions always results in a smaller number" is not true.
What is a general rule for multiplying fractions and whole numbers?
A general rule for multiplying fractions: You shall not multiply the denominator by the whole number,only the numerator.Another rule is you shall make the whole number as a fraction by putting the whole number as the numerator and 1 as the denominator before multiplying it.
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.
How is multiplying fractions different from multiplying whole numbers and fractions?
Multiplying fractions involves multiplying the numerators together and the denominators together, resulting in a new fraction. In contrast, when multiplying whole numbers by fractions, the whole number is treated as a fraction (with a denominator of 1) and then multiplied using the same method. This results in a fraction that may require simplification. Overall, the key difference lies in how the components are combined, but both processes follow the basic principle of multiplication.
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)
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.
What is a general rule for multiplying fractions and whole numbers?
A general rule for multiplying fractions: You shall not multiply the denominator by the whole number,only the numerator.Another rule is you shall make the whole number as a fraction by putting the whole number as the numerator and 1 as the denominator before multiplying it.
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 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 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.
What are two equivalent fractions for three ninths?
6/18 and 9/27......you can find out equivalent fractions by multiplying the numerator (top number) by the same number as the denominator (bottom number)
How is multiplying fractions different from multiplying whole numbers and fractions?
Multiplying fractions involves multiplying the numerators together and the denominators together, resulting in a new fraction. In contrast, when multiplying whole numbers by fractions, the whole number is treated as a fraction (with a denominator of 1) and then multiplied using the same method. This results in a fraction that may require simplification. Overall, the key difference lies in how the components are combined, but both processes follow the basic principle of multiplication.
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 do you add two fractions with a different denominator?
You add two fractions with a different denominator by multiplying the denominators by a number that will make them equal. Be sure to multiply the numerator by that number too.
What are three equivalent fractions for 20 over 30?
Three equivalent fractions for ( \frac{20}{30} ) can be found by multiplying the numerator and denominator by the same number. For example, multiplying by 2 gives ( \frac{40}{60} ), multiplying by 3 yields ( \frac{60}{90} ), and multiplying by 4 results in ( \frac{80}{120} ). All of these fractions simplify to ( \frac{2}{3} ).
How is the multiplying mixed numbers different from multiplying fractions?
Multiplying mixed numbers involves first converting the mixed numbers into improper fractions, while multiplying fractions directly uses the fractions in their given form. After conversion, the process for both is the same: multiply the numerators together and the denominators together. The final step when dealing with mixed numbers includes converting the improper fraction back to a mixed number if needed. This added step distinguishes the two processes.
