![]() ★In multiplication: The original fractions are rewritten, and rearranged… In division: If we write out each step,the same simplification chance is available through Division:.★ Cross Cancelling is a short cut for longer Arithmetic processes… (In fraction multiplication, a numerator and denominator of opposite fractions divided by a common factor.) Ok! this is where it diverges, with and without cross cancel simplifying… Transform Mixed Numbers to Fractions: (denominator × whole number + numerator, keep denominator) One and three fourths × Seven and one fifths ★ Cross Cancellation simplifies before the fraction multiplication at a easier time, by the same GCF if used after multiplication. (since the individual fractions before and after are not equal) It's multiplying by a fraction that equals one, so after we simplify, we're back to 13/12 again. So mathematically the denominators are multiplied too, it's presumed 'known' to have occurred, we just don't bother writing it out because it always results in the denominator not equal to 1, the 'other' denominator.īecause it would be a miscalculation, and equivalent to: 9/9 × 13/12.ĩ/9 is a Multiplicative Identity Fraction: the same numerator and denominator is equal to 1. ![]() So the calculation is always the same, it's considered 'understood', so the following denominator math often isn't shown, except when learning it: Therefore the whole number 9 has a denominator of one! So it doesn't answer to 9 × 1 1/12, it results in a wrong value.įirst we transform the Mixed Number value into an Improper Fraction, (denominator × whole number + numerator, keep denominator), ex…Ī Whole Number's denominator always equals one, so that makes the multiplication always: We don't multiply the Whole Number to both the numerator and denominator, because it mimics a Multiplicative Identity Fraction 9/9 = 1, (so ×1, no longer ×9).So even without knowing why, by default we still get the correct denominator. So the calculation always equals the other denominator. (1 × other denominator), because all whole numbers have a denominator of one, When calculating a Whole Number × a Fraction it can appear like only the numerators are multiplied, (but the denominators are too).'When we have one mixed number and one whole number, why do we only multiply the numerators?'
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