1 3/4 Times 2 2/3

3 min read Jun 17, 2024
1 3/4 Times 2 2/3

Multiplying Mixed Numbers: 1 3/4 x 2 2/3

This article will guide you through multiplying the mixed numbers 1 3/4 and 2 2/3.

Converting Mixed Numbers to Improper Fractions

Before multiplying mixed numbers, we need to convert them to improper fractions. Here's how:

1. Multiply the whole number by the denominator:

  • For 1 3/4: 1 x 4 = 4
  • For 2 2/3: 2 x 3 = 6

2. Add the numerator to the result:

  • For 1 3/4: 4 + 3 = 7
  • For 2 2/3: 6 + 2 = 8

3. Keep the same denominator:

  • 1 3/4 becomes 7/4
  • 2 2/3 becomes 8/3

Multiplying Improper Fractions

Now that we have improper fractions, we can multiply them:

(7/4) x (8/3)

To multiply fractions, we simply multiply the numerators and the denominators:

(7 x 8) / (4 x 3)

This simplifies to:

56/12

Simplifying the Answer

The improper fraction 56/12 can be simplified. We can find the greatest common factor (GCF) of 56 and 12, which is 4. Dividing both numerator and denominator by 4, we get:

14/3

Converting Back to Mixed Number

Finally, we can convert the improper fraction 14/3 back to a mixed number:

  • Divide the numerator (14) by the denominator (3): 14 ÷ 3 = 4 with a remainder of 2.
  • The quotient (4) becomes the whole number part: 4
  • The remainder (2) becomes the numerator of the fraction: 2
  • Keep the same denominator: 3

Therefore, 1 3/4 x 2 2/3 = 4 2/3.

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