Simplify the ratio 48:64.

Simplify the ratio 48:64.

• A. 3:4
• B. 4:3
• C. 6:8
• D. 2:3

Answer: (A)

Simplifying a ratio means dividing both numbers by the same nonzero number so there’s no common factor left. Here, 48 and 64 share the greatest common divisor, 16. Dividing both by 16 gives 48 ÷ 16 = 3 and 64 ÷ 16 = 4, so the simplified ratio is 3:4. Since 3 and 4 have no common factors besides 1, this is in simplest form. Other options aren’t correct for this ratio. Flipping the two numbers would give a different proportion (4:3), not 48:64. Writing 6:8 can be reduced by dividing both by 2 to 3:4, but as written it isn’t in simplest terms. A mismatch like 2:3 represents a different ratio (2/3) than 3/4, so it does not match 48:64.

Simplifying a ratio means dividing both numbers by the same nonzero number so there’s no common factor left. Here, 48 and 64 share the greatest common divisor, 16. Dividing both by 16 gives 48 ÷ 16 = 3 and 64 ÷ 16 = 4, so the simplified ratio is 3:4. Since 3 and 4 have no common factors besides 1, this is in simplest form.

Other options aren’t correct for this ratio. Flipping the two numbers would give a different proportion (4:3), not 48:64. Writing 6:8 can be reduced by dividing both by 2 to 3:4, but as written it isn’t in simplest terms. A mismatch like 2:3 represents a different ratio (2/3) than 3/4, so it does not match 48:64.