Fraction Subtraction: Finding Remaining Pizza After 2/7 and 1/3 are Eaten

Question

Roberto, Diego, and Marcelo order a pizza.

Roberto eats 27 \frac{2}{7} of the pizza and Marcelo eats 13 \frac{1}{3} of the pizza.

How much is left for Diego to eat?

Video Solution

Solution Steps

00:00 What part did Daniel eat?
00:04 Subtract the given parts from the whole to find the remaining part
00:20 Multiply each fraction by the second denominator to find the common denominator
00:23 Make sure to multiply both numerator and denominator
00:36 Calculate the products
00:45 Add with the common denominator
00:50 Calculate the numerator
00:58 Convert from whole number to appropriate fraction
01:05 Subtract with the common denominator
01:12 Calculate the numerator
01:16 And this is the solution to the question

Step-by-Step Solution

To solve this problem, we'll follow these steps:

  • Step 1: Identify the total fraction consumed by Roberto and Marcelo.
  • Step 2: Find a common denominator to add these fractions.
  • Step 3: Subtract the total consumed from the whole pizza.

Let's work through each step:

Step 1: Roberto eats 27 \frac{2}{7} of the pizza, and Marcelo eats 13 \frac{1}{3} .

Step 2: To add these fractions, we need a common denominator. The least common denominator between 7 and 3 is 21.

Convert the fractions:
Roberto's fraction: 27=2×37×3=621 \frac{2}{7} = \frac{2 \times 3}{7 \times 3} = \frac{6}{21}
Marcelo's fraction: 13=1×73×7=721 \frac{1}{3} = \frac{1 \times 7}{3 \times 7} = \frac{7}{21}

Step 3: Add the converted fractions:
621+721=1321 \frac{6}{21} + \frac{7}{21} = \frac{13}{21}

This result represents the total fraction of the pizza eaten by Roberto and Marcelo.

Step 4: Subtract the eaten fraction from the whole pizza (1, or 2121 \frac{21}{21} ):
21211321=821 \frac{21}{21} - \frac{13}{21} = \frac{8}{21}

Therefore, the amount of pizza left for Diego to eat is 821 \frac{8}{21} .

Answer

821 \frac{8}{21}