Show that 2 1/3 x 3 3/4 = 8 3/4

Step-by-step explanation:

Conversion a mixed number 2 1/

3

to a improper fraction: 2 1/3 = 2 1/

3

= 2 · 3 + 1/

3

= 6 + 1/

3

= 7/

3

To find new numerator:

a) Multiply the whole number 2 by the denominator 3. Whole number 2 equally 2 * 3/

3

= 6/

3

b) Add the answer from previous step 6 to the numerator 1. New numerator is 6 + 1 = 7

c) Write a previous answer (new numerator 7) over the denominator 3.

Two and one third is seven thirds

Conversion a mixed number 3 3/

4

to a improper fraction: 3 3/4 = 3 3/

4

= 3 · 4 + 3/

4

= 12 + 3/

4

= 15/

4

To find new numerator:

a) Multiply the whole number 3 by the denominator 4. Whole number 3 equally 3 * 4/

4

= 12/

4

b) Add the answer from previous step 12 to the numerator 3. New numerator is 12 + 3 = 15

c) Write a previous answer (new numerator 15) over the denominator 4.

Three and three quarters is fifteen quarters

Multiple: 7/

3

* 15/

4

= 7 · 15/

3 · 4

= 105/

12

= 35 · 3/

4 · 3

= 35/

4

Multiply both numerators and denominators. Result fraction keep to lowest possible denominator GCD(105, 12) = 3. In the next intermediate step, , cancel by a common factor of 3 gives 35/

4

.

In words - seven thirds multiplied by fifteen quarters = thirty-five quarters.

Compare: the result of step No. 3 vs 35/

4

= 35/

4

vs 35/

4

= 35 vs 35 = Yes