6.4.5 - Quick Check: Subtracting Fractions with Unlike Denominators
Bill has start fraction 2 over 3 end fraction of his pizza left from lunch. If he eats start fraction 3 over 7 end fraction more of the pizza, how much pizza is left?
A. one-fourth
B. start fraction 1 over 3 end fraction
C. start fraction 1 over 21 end fraction
D. start fraction 5 over 21 end fraction
help im really bad with fractions
To find out how much pizza is left, we need to subtract the fraction Bill ate from the fraction he had left.
Step 1: Subtracting fractions with unlike denominators requires finding a common denominator. In this case, the denominators are 3 and 7. To find the least common multiple (LCM) of 3 and 7, we list their multiples:
Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...
Multiples of 7: 7, 14, 21, 28, 35, 42, ...
The first common multiple we see is 21. So, the common denominator is 21.
Step 2: Now we need to write the fractions with the common denominator.
Since the original fraction has a denominator of 3 and the other fraction has a denominator of 7, we'll multiply the numerator and denominator of the first fraction by 7, and the numerator and denominator of the second fraction by 3:
Original fraction: start fraction 2 over 3 end fraction * start fraction 7 over 7 end fraction = start fraction 14 over 21 end fraction
Other fraction: start fraction 3 over 7 end fraction * start fraction 3 over 3 end fraction = start fraction 9 over 21 end fraction
Step 3: Now we can subtract the fractions with the same denominator:
start fraction 14 over 21 end fraction - start fraction 9 over 21 end fraction = start fraction 5 over 21 end fraction
Therefore, D. start fraction 5 over 21 end fraction is the answer.
To subtract fractions with unlike denominators, you need to find a common denominator and then subtract the numerators.
In this case, the fractions have denominators of 3 and 7. To find a common denominator, you can multiply the two denominators together: 3 * 7 = 21.
Now, you need to rewrite the fractions with the new denominator. For the first fraction, 2/3, you can multiply both the numerator and denominator by 7 to get 14/21.
For the second fraction, 3/7, you can multiply both the numerator and denominator by 3 to get 9/21.
Now, you can subtract the numerators: 14/21 - 9/21 = 5/21.
Therefore, the answer is D. start fraction 5 over 21 end fraction.