How do you multiply mixed numbers in 6th grade?

To multiply mixed numbers in 6th grade, you need to convert them into improper fractions first, then multiply the numerators and denominators. Here's a detailed breakdown, leveraging the method shown in the provided reference:

Steps for Multiplying Mixed Numbers

1. Convert Mixed Numbers to Improper Fractions: This is the most crucial first step. To do this:

   • Multiply the whole number part of the mixed number by the denominator of the fractional part.
   • Add this result to the numerator of the fractional part.
   • Keep the same denominator.
     • Example: Let's convert the mixed number 1 2/3 to an improper fraction, as shown in the reference.
       • Multiply the whole number (1) by the denominator (3): 1 * 3 = 3
       • Add the numerator (2): 3 + 2 = 5
       • Keep the denominator (3). The improper fraction is 5/3.

2. Multiply the Improper Fractions: Once you've converted all mixed numbers into improper fractions, you can proceed to multiply:

   • Multiply the numerators (top numbers) together.
   • Multiply the denominators (bottom numbers) together.
   • Example: Using the 5/3 example from step 1 and multiplying it by the whole number 4:
     • We know that 4 can be expressed as the fraction 4/1
     • Multiply the numerators: 5 * 4 = 20.
     • Multiply the denominators: 3 * 1 = 3.
     • The result of 4 * 1 2/3 is 20/3.

3. Simplify the Result (If Necessary): After multiplying, simplify the resulting improper fraction if possible.

   • Convert improper fractions back to mixed numbers if requested. To convert 20/3 into a mixed number:
     • Divide the numerator (20) by the denominator (3). 20 divided by 3 is 6 with a remainder of 2.
     • The whole number part is the quotient (6).
     • The remainder (2) becomes the new numerator, and keep the same denominator (3).
     • So, 20/3 is equal to 6 2/3.

Example Summary

The reference shows, converting 1 2/3 to 5/3, and then multiplying this fraction by 4, or 4/1, resulting in 20/3, which can then be converted to a mixed number of 6 2/3.

Key Takeaway

The most important step when multiplying mixed numbers is to change them into improper fractions first. Then, you simply multiply the numerators and the denominators. Finally, you can simplify the result if needed and convert improper fractions back to mixed numbers for ease of comprehension.